Answer:
1 time, though your answer would be ongoing. If you the actual answer, it's 1.2
Step-by-step explanation:
Round to the nearest tenth.
Answer:
1.2
Step-by-step explanation:
Five can go into six 1.2 times because (1.2)(5)=6. Of course, if you want to know how many times five can go into 6 as a WHOLE, then the answer would obviously be 1.
Hope this helps a bit :)
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 10 child bikes and 12 adult bikes in a week
Step-by-step explanation:
we only need to calculate directly the work hours needed for 10 child bikes and 12 adult bikes.
as a child bikes needs 4 hours to build and 4 hours to test, for 10 child bikes that means 10×4 = 40 hours to build and 40 hours to test
an adult bike needs 6 hours to build and 4 his to test.
so, for 12 bikes that are 12×6 = 72 hours to build and 12×4 = 48 hours to test.
together that means we need
40 + 72 = 112 hours to build
40 + 48 = 88 hours to test
the limits of the company are 120 build hours and 100 test hours per week.
as 112 < 120 and 88 < 100, yes, the company can build 10 child bikes and 12 adult bikes in one week.
in fact, with that they still have 8 work hours (120 - 112) and 12 test hours (100 - 88) left and could therefore build either 2 additional child bikes (8 build hours, 8 test hours) or one additional adult bike (6 build hours, 4 test hours).
Construct the class boundaries for the following frequency distribution table. also construct less than cumulative and greater than cumulative frequency tables.
ages:- 1 - 3, 4-6, 7-9, 10-12, 13-15
no of children:- 10,12,15,13,9
The class boundaries are 0.5 - 3.5, 3.5 - 6.5, 6.5 - 9.5, 9.5 - 12.5, 12.5 - 15.5.
To find the class boundaries, we need to add and subtract 0.5 from the upper and lower limits of each class interval, respectively.
Using this formula, we get the following class boundaries:
Class Boundaries:
0.5 - 3.5, 3.5 - 6.5, 6.5 - 9.5, 9.5 - 12.5, 12.5 - 15.5
To construct the less than cumulative frequency table, we need to add up the frequencies of all the classes up to each class. For example:
Less than Cumulative Frequency Table:
Ages No. of Children Cumulative Frequency
1-3 10 10
4-6 12 22
7-9 15 37
10-12 13 50
13-15 9 59
To construct the greater than cumulative frequency table, we need to subtract the frequency of each class from the total frequency and then add the resulting values up to obtain the cumulative frequency. For example:
Greater than Cumulative Frequency Table:
Ages No. of Children Cumulative Frequency
13-15 9 59
10-12 13 50
7-9 15 37
4-6 12 22
1-3 10 10
Note that the last value of the greater than cumulative frequency table is always equal to the total frequency, which in this case is 59.
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A rectangular pyramid fits exactly on top of a rectangular prism. The prism* 1 point has a length of 26 cm, a width of 5 cm, and a height of 14 cm. The pyramid has a height of 23 cm. Find the volume of the composite space figure. Round to the nearest hundredth .
The volume of the composite space figure is approximately 2818.33 cubic cm.
How to calculate the volume of the composite space figureTo find the volume of the composite space figure, we need to add the volumes of the rectangular prism and the rectangular pyramid.
The rectangular prism has a length of 26 cm, a width of 5 cm, and a height of 14 cm. So its volume is:
V_prism = length x width x height
V_prism = 26 cm x 5 cm x 14 cm
V_prism = 1820 cubic cm
The rectangular pyramid has a height of 23 cm and a rectangular base with a length of 26 cm and a width of 5 cm. To find its volume, we need to first find its base area:
A_base = length x width
A_base = 26 cm x 5 cm
A_base = 130 square cm
Then, we can use the formula for the volume of a pyramid:
V_pyramid = (1/3) x base area x height
V_pyramid = (1/3) x 130 square cm x 23 cm
V_pyramid = 998.33 cubic cm (rounded to the nearest hundredth)
To find the total volume of the composite space figure, we add the volumes of the prism and the pyramid:
V_total = V_prism + V_pyramid
V_total = 1820 cubic cm + 998.33 cubic cm
V_total = 2818.33 cubic cm (rounded to the nearest hundredth)
Therefore, the volume of the composite space figure is approximately 2818.33 cubic cm.
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Select the needed observations and steps before you can factor a difference of two squares.
binomial
trinomial
multiply factors
two negative
prime
two positive
look for a gcf
one positive
one negative
( its a multi choice question )
In factorization the needed observations and steps before you can factor a difference of two squares are binomial, two positive/negative, prime, multiply factors, and look for a GCF.
Finding the factors of a given number or statement is the process of factorization. Factorization is the process of taking a larger number or expression and turning it into a product of smaller numbers or expressions, or factors. The factors may be polynomials, integers, or other mathematical constructs.
Therefore, the needed observations and steps before you can factor a difference between two squares are:
Binomial: The expression must be written in the form of a binomial, which calls for two terms (for example, x² - 9).Two phrases that are positive or negative must be separated by a minus sign (-), and each term must be a perfect square. Because x² and 9 are both perfect squares and because 9 is the square of 3, for instance, x² - 9 is a difference of two squares.prime: The words must be prime, which means they can't be factored further.Factoring the difference between two squares involves multiplying and then removing the components of each perfect square.To learn more about Factorization, refer to:
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Substitution (SW Question 13, Use a change of variables or the table to evaluate the following indefinite integral. csc? dx cotx Click the icon to view the table of general integration formulas. csc?x dx= col X e the follo Integration Formulas cos ax dx sin ax+C sin ax dx = cos ax + C a Integration fo sec?ax dx = tan ax + CSC ax dx- cot ax+C sec axtan ax dx = sec ax + c a csc ax cotax dx- CSC ax + C [ Sescax 16*dx = 160* +0,620, 641 S -- sin.c.a> o 3dx +C Inb dx dx tan 2.C a +x dx مد و مداء 11 - Print Done Clear all
Answer: Note that we used the table of general integration formulas to recognize that the integral of csc(x) dx is - ln|csc(x) + cot(x)| + C.
Explanation:
To evaluate the indefinite integral of csc(x) cot(x) dx, we can use substitution.
Let u = cot(x), then du/dx = -csc^2(x) and dx = -du/csc^2(x).
Substituting these values in the integral, we get:
∫ csc(x) cot(x) dx = ∫ -du/u = -ln|u| + C
Now substituting back u = cot(x),
we get: ∫ csc(x) cot(x) dx = -ln|cot(x)| + C
This is the final answer.
Note that we used the table of general integration formulas to recognize that the integral of csc(x) dx is -ln|csc(x) + cot(x)| + C. We then used the substitution technique and the general integration formula for ln|u| to arrive at the final answer.
A. Plot point C so that its distance from the origin is 1. B. Plot point E 4/5 closer to the origin than C. What is its coordinate? c. Plot a point at the midpoint of C and E. Label it H
(A). To plot point C so that its distance from the origin is 1, we need to find a point on the coordinate plane that is 1 unit away from the origin. One such point is (1, 0), which is located on the positive x-axis.
(B). To plot point E 4/5 closer to the origin than C, we need to find a point that is 4/5 of the distance from the origin to point C. Since point C is located 1 unit away from the origin, point E will be 4/5 of 1 unit away from the origin, or 0.8 units away.
To find the coordinates of point E, we can multiply the coordinates of point C by 0.8. If point C is (1, 0), then point E is (0.8, 0).
(C). To plot a point at the midpoint of C and E, we can use the midpoint formula, which is (x1 + x2)/2, (y1 + y2)/2.
The coordinates of point C are (1, 0) and the coordinates of point E are (0.8, 0), so the coordinates of point H are ((1 + 0.8)/2, (0 + 0)/2), or (0.9, 0). We can label this point H.
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Please show me the working out
Given the function f (x) 02 +4,2 € (-2,0) + (a) Enter f' (2) 2*x (b) Enter the inverse function, f-1(x) sqrt(x-4) (c) Enter the compound function f' (s 1(x)) (d) Enter the derivative mets-() de 1-12
The inverse functions:
f'(2) = 4.
[tex]f^{-1}(x)[/tex] = sqrt(x - 4).
f'(s1(x)) = sqrt(x - 4).
(a) To find f'(2), we need to take the derivative of f(x) with respect to x and then substitute x = 2.
[tex]f(x) = x^2 + 4[/tex]
f'(x) = 2x
f'(2) = 2(2) = 4
Therefore, f'(2) = 4.
(b) To find the inverse function [tex]f^{-1}(x)[/tex], we need to first solve for x in terms of f(x) and then switch the roles of x and f(x).
[tex]f(x) = x^2 + 4[/tex]
[tex]x^2[/tex] = f(x) - 4
x = sqrt(f(x) - 4)
Switching x and f(x), we get:
[tex]f^{-1}(x)[/tex] = sqrt(x - 4)
Therefore, the inverse function is [tex]f^{-1}(x)[/tex] = sqrt(x - 4).
(c) To find the compound function f'(s1(x)),
we need to first find s1(x) and then take the derivative of f(x) with respect to s1(x) and then multiply by the derivative of s1(x) with respect to x.
s1(x) = sqrt(x - 4)
f(s1(x)) = (sqrt(x - 4)[tex])^2[/tex] + 4 = x
Taking the derivative of f(x) with respect to s1(x), we get:
f'(s1(x)) = 2s1(x)
Taking the derivative of s1(x) with respect to x, we get:
s1'(x) = 1/(2sqrt(x - 4))
Multiplying these two derivatives, we get:
f'(s1(x))s1'(x) = 2s1(x) * 1/(2sqrt(x - 4))
f'(s1(x))s1'(x) = sqrt(x - 4)
Therefore, the compound function is f'(s1(x)) = sqrt(x - 4).
(d) The given expression "derivative mets-() de 1-12" does not make sense and seems incomplete. Please provide more information or context so that I can help you with this part of the question.
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A computer generates 90 integers from 1 to 5 at random. The results are recorded in the table.
What is the experimental probability of the computer generating a 1?
Responses:
10%
20%
30%
40%
Outcome
1
2
3
4
5
Number of times outcome occurred
36
11
13
12
18
The experimental probability of the computer generating a 1 is D. 40 %.
How to find the experimental probability ?First, add up the outcomes to see the total number of times the integers were generated ;
= 36 + 11 + 13 + 12 + 18
= 90
The number of times 1 was generated was 36.
The experimental probability is therefore;
= number of times 1 was generated / total number of outcomes
= 36 / 90
= 0. 4
= 40 %
Therefore, the experimental probability of the computer generating a 1 is 40 %.
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h(x)=−(x+11) +1 What are the zeros of the function? What is the vertex of the parabola?
Answer:
x = -10 (zeros), vertex = infinity..?
Step-by-step explanation:
The graph is a straight line, not a parabola. I would assume the vertex would be infinity, and the zeros would be x = -10.
2. Hamilton claimed that there are only 4 circuits that begin with the letters LTSR Q. Find them. 3. Find all four possible Hamiltonian circuits that begin with JVTSR
To find the possible Hamiltonian circuits that begin with JVTSR, we can start by constructing a path that begins with JVTSR and visits each vertex exactly once. Such a path must be of the form JVTSRX, where X is the remaining vertex.
Case 1: JVTSRQX
To find the possible value of X, we note that the only edges incident to J are V and T, and the only edges incident to Q are S and R. Thus, we must have X = S or X = R, and the circuits are JVTSRQS and JVTSRQR.
Case 2: JVTSRXQ
To find the possible value of X, we note that the only edges incident to X are S and L. Thus, we must have X = L, and the circuit is JVTSRLQ.
Case 3: JVTSRLX
To find the possible value of X, we note that the only edges incident to J are V and T, and the only edges incident to L are T and R. Thus, we must have X = R, and the circuit is JVTSRLR.
Case 4: JVTSRXL
To find the possible value of X, we note that the only edges incident to Q are S and R, and the only edges incident to X are L and S. Thus, we must have X = L, and the circuit is JVTSRQL.
Therefore, there are four possible Hamiltonian circuits that begin with JVTSR: JVTSRQS, JVTSRQR, JVTSRLQ, and JVTSRLR.
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The percentage of the moon's surface that is visible to a person standing on the Earth varies with the time
since the moon was full.
The moon passes through a full eyele in 28 days, from full moon to full moon. The
maximum percentage of the moon's surface that is visible is 50%. Determine an equation, in the form
P=Acos(Bt)+C for the percentage of the surface that is visible, P, as a function of the number of days, t,
since the moon was full. Show the work that leads to the values of A, B, and C
The equation is P = [tex]25cos(0.224t) + 50[/tex], where P represents the percentage of the moon's surface visible and t is the number of days since the moon was full.
How to derive equation for moon visibility?To determine an equation for the percentage of the moon's surface visible as a function of the number of days since the moon was full, we can use the cosine function [tex]P = Acos(Bt) + C[/tex], where P represents the percentage visible, t is the number of days since full moon, A is the amplitude, B is the frequency, and C is the vertical shift.
Given that the maximum percentage visible is 50%, we know that C = 50. The period of the function is 28 days, so we can calculate B using the formula B = 2π/period = 0.224. The amplitude A can be calculated as half of the maximum percentage visible, or A = 25.
Therefore, the equation for the percentage of the moon's surface visible as a function of the number of days since full moon is P = 25cos(0.224t) + 50.
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SPEEDBOAT RACE Speedboats race around four buoys in the lake on a rectangular course. If the total length of the course is 2.4
kilometers and the ratio of the length to the width is 2:1, what are the length and width of the course?
length:
width:
Let's represent the width of the rectangular course as $w$. Then the length of the rectangular course can be represented as $2w$, since the ratio of the length to the width is given as 2:1.
We know that the total length of the course is 2.4 kilometers, so we can write an equation:
$\sf\implies\:2w + 2(2w) = 2.4$
Simplifying the equation:
$\sf\implies\:6w = 2.4$
$\sf\implies\:w = \frac{2.4}{6}$
$\bigstar\implies\sf{\textbf{\boxed{w = 0.4}}}$
Therefore, the width of the course is 0.4 kilometers.
The length of the course is $\sf\:2w = 2(0.4)=$
${\boxed{\sf{0.8 kilometers.}}}$
Hence, the length of the course is 0.8 kilometers and the width of the course is 0.4 kilometers.
[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]
please solve for each
Use a calculator or program to compute the first 10 iterations of Newton's method for the given function and initial approximation f(x)=2 sin x + 3x +3.x = 15 Complete the table (Do not found until th
The first 10 iterations of Newton's method for f(x) = 2 sin x + 3x + 3, with initial approximation x₀ = 15, are approximately 8.156, 6.099, 5.091, 4.941, 4.929, 4.929, 4.929, 4.929, 4.929, 4.929
The first 10 iterations of Newton's method for the given function and initial approximation
x₁ = x₀ - f(x₀)/f'(x₀) = 15 - (2sin(15) + 45) / (2cos(15) + 3) ≈ 8.156
x₂ = x₁ - f(x₁)/f'(x₁) ≈ 6.099
x₃ = x₂ - f(x₂)/f'(x₂) ≈ 5.091
x₄ = x₃ - f(x₃)/f'(x₃) ≈ 4.941
x₅ = x₄ - f(x₄)/f'(x₄) ≈ 4.929
x₆ = x₅ - f(x₅)/f'(x₅) ≈ 4.929
x₇ = x₆ - f(x₆)/f'(x₆) ≈ 4.929
x₈ = x₇ - f(x₇)/f'(x₇) ≈ 4.929
x₉ = x₈ - f(x₈)/f'(x₈) ≈ 4.929
x₁₀ = x₉ - f(x₉)/f'(x₉) ≈ 4.929
Therefore, the first 10 iterations are 8.156, 6.099, 5.091, 4.941, 4.929, 4.929, 4.929, 4.929, 4.929, 4.929
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Find the critical numbers of the function. (Enter your answers as a comma-separated list.) h(x) = sin^2 x + cos x, 0 < x < 2π x =
To find the critical numbers of h(x) = sin^2(x) + cos(x) in 0 < x < 2π steps are first to find the derivative h'(x), set h'(x) equal to zero and solve for x and check if solutions are within the given interval. The critical numbers are x = π, π/3, and 5π/3.
To find the critical numbers of the function h(x) = sin^2(x) + cos(x) in the interval 0 < x < 2π, we will follow these steps:
Find the derivative of the function, Set the derivative equal to zero and solve for x, Set h'(x) equal to zero and solve for x, Check if the solutions are within the given interval.
1: Differentiate h(x) with respect to x.
h'(x) = d(sin^2(x) + cos(x))/dx
Using chain rule, we get:
h'(x) = 2sin(x)cos(x) - sin(x)
2: Set h'(x) equal to zero and solve for x.
0 = 2sin(x)cos(x) - sin(x)
Factor out sin(x):
0 = sin(x)(2cos(x) - 1)
So, either sin(x) = 0 or 2cos(x) - 1 = 0.
3: Solve for x and check if the solutions are within the interval 0 < x < 2π.
For sin(x) = 0, x = π (since 0 < π < 2π).
For 2cos(x) - 1 = 0, cos(x) = 1/2.
x = π/3 and 5π/3 (since 0 < π/3 < 2π and 0 < 5π/3 < 2π).
Therefore, the critical numbers of the function h(x) = sin^2(x) + cos(x) in the interval 0 < x < 2π are x = π, π/3, and 5π/3.
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You bought a laptop computer for $525 on the "12 months is the same as cash" plan. The terms of the plan on the contract stated that if
not paid within 12 months, you would be assessed 15. 5 percent APR for the amount on the first day of the plan
If you pay the laptop in 11 months, how much will you have paid?
a. $525
b. $540. 50
c. $595. 50
d. $606. 38
Your answer: a. $525
The "12 months is the same as cash" plan means that if you pay off the laptop within 12 months, you won't be charged any interest.
Since you plan to pay off the laptop in 11 months, which is within the 12-month period, you will not be assessed the 15.5 percent APR.
Therefore, you only need to pay the original cost of the laptop, which is $525.
To summarize, as long as you pay the full amount within the specified 12-month period, you avoid the additional interest charges. In this case, you will pay the laptop off in 11 months, so your total payment will be $525.
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Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator. In(8x2 – 72x + 112) Enter the
The fully expanded expression using logarithm properties is:
[tex]In(8x^2 - 72x + 112) = 2.079 + In(x - 2) + In(x –-7)[/tex]
How to expand an expression?To expand the given expression[tex]In(8x^2 - 72x + 112)[/tex], we can use the following logarithmic properties:
Product Rule: [tex]logb (xy) = logb x + logb y[/tex]
Quotient Rule: [tex]logb (x/y) = logb x - logb y[/tex]
Power Rule:[tex]logb (x^a) = a logb x[/tex]
We can first factor out a common factor of 8 from the expression inside the logarithm:
[tex]In(8x^2 - 72x + 112) = In[8(x^2 - 9x + 14)][/tex]
Using the distributive property, we can expand the expression inside the logarithm:
[tex]In[8(x^2 - 9x + 14)] = In(8) + In(x^2 - 9x + 14)[/tex]
Now, we need to expand the second logarithm. We notice that the expression inside the logarithm can be factored as follows:
[tex]x^2 - 9x + 14 = (x - 2)(x - 7)[/tex]
Using the product rule, we can write:
[tex]In(x^2 - 9x + 14) = In[(x - 2)(x - 7)][/tex]
[tex]= In(x - 2) + In(x - 7)[/tex]
Putting all the pieces together, we get:
[tex]In(8x^2 - 72x + 112) = In(8) + In(x^2 - 9x + 14)[/tex]
[tex]= In(8) + In(x -2) + In(x - 7)[/tex]
Finally, we can simplify the numerical expression In(8) by using the fact that ln(e) = 1:
[tex]In(8) = ln(8)/ln(e) = 2.079/1 = 2.079[/tex]
So the fully expanded expression using logarithm properties is:
[tex]In(8x^2 - 72x + 112) = 2.079 + In(x - 2) + In(x -7)[/tex]
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to increase strength and/or muscle mass, weight trainers will try different approaches. one approach is to apply an electrical impulse through a
muscle as the person is lifting a weight. a researcher wants to determine if adding this electrical impulse increases the amount of weight a person
can lift. to conduct his research, he selects one hundred people, and randomly divides them into two groups. one group wears a device that
sends an electrical impulse through the muscle used to repeatedly lift a 5 pound weight. the other group lifts the same weight without the electrical
impulse. the researcher counts the number of repetitions until the subjects can no longer lift the weight. is this an example of an observational
study or an experiment?
This is an example of an experiment. In an experiment, researchers manipulate the independent variable (in this case, the presence or absence of an electrical impulse) to determine its effect on the dependent variable (the number of repetitions the subjects can lift a weight).
The researcher randomly assigned subjects to either receive the electrical impulse or not, which is a key feature of experimental design.
By doing so, the researcher can ensure that any differences observed between the two groups are due to the manipulation of the independent variable, rather than any pre-existing differences between the groups.
In contrast, an observational study merely observes existing characteristics or behaviors of a population, without any manipulation or control of variables.
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Ishaan tiene 2 veces la edad de Christopher.
Hace 35 años Ishaan tenía 7 veces la edad de
Christopher.
¿Cuántos años tiene Ishaan actualmente?
Ishaan's current age is 84.
How to solve for the current ageLet Ishaan's current age be I and Christopher's current age be C.
Given, I = 2C ...........(1) (Ishaan is twice the age of Christopher)
35 years ago, I - 35 = 7(C - 35) (Ishaan was 7 times the age of Christopher 35 years ago)
Simplifying the above equation, we get:
I - 35 = 7C - 245
I = 7C - 210 ...........(2)
Substituting equation (1) in equation (2), we get:
2C = 7C - 210
5C = 210
C = 42
Therefore, Christopher's current age is 42.
Substituting C = 42 in equation (1), we get:
I = 2C = 2(42) = 84
Therefore, Ishaan's current age is 84.
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The question is translated to English as
Ishaan is twice the age of Christopher. 35 years ago Ishaan was 7 times the age of Christopher. How old is Ishaan now?
Find the particular solution for:
f"(x) = 0.25x⁻³/², f'(4) = - 1/8 and f(0) = 2.
The particular solution for f(x) is:
f(x) = (2/3)x³/² - (17/8)x + 2
How to find the particular solution of f(x)?We will integrate the given differential equation twice and use the initial conditions to find the constants of integration.
Given: f"(x) = 0.25x⁻³/²
Integrating once, we get:
f'(x) = ∫(0.25x⁻³/²) dx = 0.5x¹/² + C₁
where C₁ is the constant of integration.
Using the initial condition f'(4) = -1/8, we can solve for C₁:
f'(4) = 0.5(4)¹/² + C₁ = 2 + C₁ = -1/8
C₁ = -1/8 - 2 = -17/8
So,
f'(x) = 0.5x¹/² - 17/8
Integrating again, we get:
f(x) = ∫(0.5x¹/² - 17/8) dx = (2/3)x³/² - (17/8)x + C₂
where C₂ is the second constant of integration.
Using the initial condition f(0) = 2, we can solve for C₂:
f(0) = (2/3)(0)³/² - (17/8)(0) + C₂ = 2
C₂ = 2
So, the particular solution for f(x) is:
f(x) = (2/3)x³/² - (17/8)x + 2
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For y = 72√x, find dy, given x = 4 and Δx = dx = 0.21
dy = (Simplify your answer.)
To find dy for the function y = 72√x, given x = 4 and Δx = dx = 0.21, we will first find the derivative of y with respect to x and then plug in the given values.
1. Differentiate y with respect to x: y = 72√x can be rewritten as y = 72x^(1/2)
Apply the power rule: dy/dx = 72 * (1/2)x^(-1/2)
Simplify: dy/dx = 36x^(-1/2)
2. Plug in the given values: x = 4 and dx = 0.21
dy/dx = 36(4)^(-1/2)
dy/dx = 36(1/√4)
dy/dx = 36(1/2)
dy/dx = 18
3. Calculate dy: dy = (dy/dx) * dx
dy = 18 * 0.21
dy = 3.78
So, for y = 72√x, dy is 3.78 when x = 4 and Δx = dx = 0.21.
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Find the finance charge for a 7000 two year loan with a 6.75 APR
The finance charge for a $7000 two year loan with a 6.75% APR is $945.
What is the finance charge for a 7000 two year loan with a 6.75 APR?To determine the finance charge for a $7000 two year loan with a 6.75% APR, we need to use the following formula:
Finance charge = (Amount borrowed × Annual percentage rate) × Time period
Given that, the amount borrowed is $7000, the annual percentage rate (APR) is 6.75%, and the time period is two years.
First, we need to convert the APR to a decimal by dividing it by 100:
APR = 6.75%
APR = 6.75/100
APR = 0.0675
Now we can plug in the values into the formula:
Finance charge = (Amount borrowed × Annual percentage rate) × Time period
Finance charge = ( $7000 × 0.0675) x 2
Finance charge = $945
Therefore, the finance charge is $945.
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Suppose that f(x) = g(h(x)). In each part, based on one of the functions provided, find a formula for the other formula such that their composition yields f(x) = g(h(x)).
Now let's check if f(x) = g(h(x)):
gh(x)) = g(x + 1) = (x + 1)² + 1 = x² + 2x + 1 + 1 - 1 = x² + 2x + 1
The formulas for g(x) and h(x), which are g(x) = x² + 1 and h(x) = x + 1, such that their composition yields:
f(x) = g(h(x)) = x² + 2x + 1.
In both cases, we use the composition of functions f(x) = g(h(x)) to relate the functions g(x), h(x), and their inverses. These formulas allow us to find the other function given one of the functions in the composition.
Suppose we have the function f(x) = g(h(x)). Here, we have three functions: f(x), g(x), and h(x). We're given one of these functions and asked to find the formulas for the other two functions so that their composition results in f(x).
To find a formula for one of the functions in the composition f(x) = g(h(x)), we can substitute the other function into it and simplify.
(1) If we want to find a formula for g(x) given f(x) = g(h(x)), we can substitute h(x) for x in g(x), which gives us g(h(x)). This means that g(x) = f(h^{-1}(x)), where h^{-1}(x) is the inverse function of h(x).
(2) If we want to find a formula for h(x) given f(x) = g(h(x)), we can substitute g(x) for f(x) and solve for h(x). This gives us h(x) = g^{-1}(f(x)), where g^{-1}(x) is the inverse function of g(x).
Given: f(x) = x² + 2x + 1
We need to find the formulas for g(x) and h(x) such that f(x) = g(h(x)).
One possible choice for g(x) could be g(x) = x² + 1. Now we need to find the function h(x) such that when we compose g(h(x)), it results in f(x) = x² + 2x + 1.
To do this, we can see that g(x) has x² + 1, and f(x) has x² + 2x + 1. We need to add a term '2x' in the composition. Therefore, we can choose h(x) = x + 1.
Now, let's check if f(x) = g(h(x)):
g(h(x)) = g(x + 1) = (x + 1)² + 1 = x² + 2x + 1 + 1 - 1 = x² + 2x + 1
Thus, we have successfully found the formulas for g(x) and h(x), which are g(x) = x² + 1 and h(x) = x + 1, such that their composition yields f(x) = g(h(x)) = x² + 2x + 1.
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Pls help! And actually answer please
The equation of the plotted absolute value function graph is
y = |x - 1| - 1
How to find the equation of the graphThe equation of the graph which is a graph of absolute value function is solved using transformation
The parents equation or original equation is
y = |x|
Then a shift 1 unit to the right direction is gotten by
y = |x - 1|
The second transformation is a downward shift of 1 unit, this results to the equation of the form
y = |x - 1| - 1
The graph is potted and attached
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16. [0/1 Points] DETAILS PREVIOUS ANSWERS TANAPCALCBR10 6.6.050. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Turbo-Charged Engine Versus Standard Engine In tests conducted by Auto Test Magazine on two identical models of the Phoenix Elite-one equipped with a standard engine and the other with a turbo-charger-it was found that the acceleration of the former is given by a = f(t) = 5 + 0.8t (Osts 12) ft/sec/sec, t sec after starting from rest at full throttle, whereas the acceleration of the latter is given by a = g(t) = 5 + 1.2t + 0.03t2 (0 sts 12) = ft/sec/sec. How much faster is the turbo-charged model moving than the model with the standard engine at the end of a 11-sec test run at full throttle? 41.25 X ft/sec Need Help? Read It Submit Answer
The turbocharged model is moving 41.25 ft/sec faster than the model with the standard engine at the end of the 11-second test run.
We need to find how much faster the turbo-charged model is moving than the model with the standard engine at the end of an 11-second test run at full throttle.
To find the final velocity of each model at the end of 11 seconds, we need to integrate their respective acceleration functions with respect to time from 0 to 11 seconds:
For the standard engine model:
v(t) = ∫(5 + 0.8t) dt = 5t + [tex]0.4t^2[/tex]
v(11) = 5(11) +[tex]0.4(11)^2[/tex] = 72.4 ft/sec
For the turbo-charged model:
v(t) = ∫(5 + 1.2t + 0.03[tex]t^2[/tex]) dt = 5t +[tex]0.6t^2 + 0.01t^3[/tex]
v(11) = 5(11) + [tex]0.6(11)^2 + 0.01(11)^3[/tex]= 113.65 ft/sec
The difference in final velocity between the two models is:
[tex]v_{turbo} - v_{standard[/tex] = 113.65 - 72.4 = 41.25 ft/sec
Therefore, the turbo-charged model is moving 41.25 ft/sec faster than the model with the standard engine at the end of the 11-second test run.
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A bead is formed by drilling a cylindrical hole, with a 2 mm diameter, through a sphere
with an 8 mm diameter. estimate the surface area of the bead. leave the answer in
terms of pi
The estimated surface area of the bead is 52π square millimeters.
To estimate the face area of the blob, we need to find the face area of the sphere and abate the face area of the spherical hole. The face area of a sphere is given by the formula A = 4πr2 where r is the compass of the sphere.
The radius of the sphere is: r = 8 mm / 2 = 4 mm.
The surface area of the sphere is: S_sphere = 4π[tex]r^{2}[/tex] = [tex]4π(4 mm)^{2}[/tex] =64 [tex]mm^{2}[/tex]
The radius of the cylinder is: r = 2 mm / 2 = 1 mm.
The height of the cylinder is: h = 8 mm - 2 mm = 6 mm.
The surface area of the cylinder is: S_cylinder = 2πrh = 2π(1 mm)(6 mm) = 12π [tex]mm^{2}[/tex]
The estimated surface area of the bead is: S_bead = S_sphere - S_cylinder = 64π [tex]mm^{2}[/tex] - 12π [tex]mm^{2}[/tex] = 52π [tex]mm^{2}[/tex]
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A set of 9 books has 5,481 pages.
How many pages would be in each
book, if each book has the same
number of pages.
Answer:
609 pages
Hope this helps!
Step-by-step explanation:
9 books = 5481 pages
1 book = ? pages
9 books ÷ 9 = 1 book so 5481 pages ÷ 9 = 609 pages
1 book has 609 pages.
It takes a boat hr to go 12 mi downstream, and 6 hr to return. Find the rate of the boat in still water and the rate of the current
The rate of the boat in still water is 5 miles per hour and rate of the boat in current is 3 miles per hour.
Let us represent the rate of boat in still water hence and rate of boat in current be y. Also, we know that speed = distance/time. Hence, keep the values in formula -
Converting mixed fraction to fraction, time = 3/2 hour
Time = 1.5 hour
1.5 (x + y) = 12 : equation 1
Divide the equation 1 by 3
0.5 (x + y) = 4 : equation 2
6 (x - y) = 12 : equation 3
Divide the equation 3 by 6
(x - y) = 2
x = 2 + y : equation 4
Keep the value of x from equation 4 in equation 2
0.5 (2 + y + y) = 4
1 + y = 4
y = 4 - 1
y = 3 miles/ hour
Keep the value y in equation 4 to get x
x = 2 + 3
x = 5 miles per hour
The rate in still water and current is 5 and 3 miles per hour.
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The complete question is-
It takes a boat 1 (1/2) hr to go 12 mi downstream, and 6 hr to return. Find the rate of the boat in still water and the rate of the current.
Consider the function f(x) = 1x - 3 a. Find the inverse function off. f-'(x) = Use STACK interval notation for the following. For example, enter [12,00) as co(12, inf). b. What is the domain off-l? c. What is the range off-l?
a. To find the inverse function of f(x), we need to interchange the roles of x and y and solve for y. So, we have:
y = 1x - 3
x = 1y - 3
x + 3 = y
Therefore, the inverse function of f(x) is f^-1(x) = x + 3.
The domain of f^-1(x) is the range of f(x). Since f(x) = 1x - 3 is a linear function, its domain is all real numbers. Therefore, the range of f(x) is also all real numbers. In interval notation, we can write this as (-inf, inf).
The range of f^-1(x) is the domain of f(x). As we determined in part b, the domain of f(x) is all real numbers. Therefore, the range of f^-1(x) is also all real numbers. In interval notation, we can write this as (-inf, inf).
Hi! I'd be happy to help you with your question.
a. To find the inverse function of f(x) = 1x - 3, you can follow these steps:
1. Replace f(x) with y: y = 1x - 3
2. Swap x and y: x = 1y - 3
3. Solve for y: y = x + 3
So, the inverse function f^(-1)(x) = x + 3.
The domain of f^(-1) refers to the set of all possible x-values. Since the inverse function is a linear function with no restrictions, the domain of f^(-1) is all real numbers. In interval notation, this is written as (-∞, ∞).
c. The range of f^(-1) refers to the set of all possible y-values (output). Again, since it's a linear function with no restrictions, the range of f^(-1) is also all real numbers. In interval notation, this is written as (-∞, ∞).
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The ratio of dolls thta jack had to peter was 5:2. After jack gave peter 15 dolls, they had the same amount of dolls. How many do they have together?
They have total of 70 dolls together.
Let the initial number of dolls Jack had be 5x and the number Peter had be 2x.
After Jack gave Peter 15 dolls, their amounts became equal. So, we can write the equation: 5x - 15 = 2x + 15
Now, solve the equation for x: 5x - 2x = 15 + 15, which simplifies to 3x = 30
Divide both sides by 3: x = 10
Now, find the initial number of dolls they had: Jack had 5x = 5(10) = 50 dolls, and Peter had 2x = 2(10) = 20 dolls.
After Jack gave Peter 15 dolls, both had 35 dolls (50 - 15 = 35, and 20 + 15 = 35).
So, together they have 35 + 35 = 70 dolls.
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How many zeros are in the product 50 x 6,000
The number of zeros are in the product of the number 50 and 6000 is 50 x 6000 = 300,000 are five.
Integers, natural numbers, fractions, real numbers, complex numbers, and quaternions are examples of typical special instances where it is possible to define the product of two numbers or the multiplication of two numbers.
A product is the outcome of multiplication in mathematics, or an expression that specifies the elements (numbers or variables) to be multiplied.
The commutative law of multiplication states that the result is independent of the order in which real or complex numbers are multiplied. The result of a multiplication of matrices or the elements of other associative algebras typically depends on the order of the components. For instance, matrix multiplication and multiplication in general in other algebras are non-commutative operations.
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