Answers
Answer:
a(5) = 1.080
a(10) = 0.393
a(20) = 0.122
Step-by-step explanation:
Take the derivative of velocity v(t) -> acceleration a(t)
v(t) -> a(t)
Quotient Rule: [tex]\frac{u*dv-du*v}{u^2}[/tex]
[tex]120*\frac{x}{5x+13}[/tex]
Make u= 5x+13 and v=x
[tex]120*\frac{x'*(5x+13)-x*(5x+13)'}{(5x+13)^2}\\\\120*\frac{1*(5x+13)-x*(5)}{(5x+13)^2}\\\\120*\frac{(5x+13)-5x}{(5x+13)^2}\\120*\frac{13}{(5x+13)^2} \\\\a(t)=\frac{1560}{(5x+13)^2}[/tex]
Now Subsitute your a(5) , a(10) , a(20). Also, round to 3 decimal place.
a(5) = 1.08033241 = 1.080
a(10) = 0.3930461073 = 0.393
a(20) = 0.122170826 = 0.122
Answer:
(a) 1.080 ft/s²
(b) 0.393 ft/s²
(c) 0.122 ft/s²
Step-by-step explanation:
Acceleration is the derivative of velocity. You are being asked to differentiate the given function and evalutate the derivative at three different times. The function is a rational function, so the formula for the derivative of a ratio is applicable.
(u/v)' = (vu' -uv')/v²
__
For the given velocity function, the accleration is ...
v(t) = (120t)/(5t +13)
a(t) = v'(t) = ((5t +13)(120) -(120t)(5))/(5t +13)² = 1560/(5t +13)²
(a)At t=5, the acceleration is ...
a(5) = 1560/(5·5 +13)² = 1560/1444 ≈ 1.080 . . . ft/s²
(b)At t=10, the acceleration is ...
a(10) = 1560/(5·10 +13)² = 1560/3969 ≈ 0.393 . . . ft/s²
(c)At t=20, the acceleration is ...
a(20) = 1560/(5·20 +13)² = 1560/12729 ≈ 0.122 . . . ft/s²
_____
Additional comment
Many graphing calculators are capable of finding the numerical value of the derivative of a function.
Related Questions
Write an expression that is equivalent to 3/4 (5z+16).
A.15/4 z + 16
B.15/4 z + 12
C.3/4 z + 16
D.3/4 z + 12
Answers
Answer:
B. 15/4 z + 12
Step-by-step explanation:
Apply the distributive property and multiply 3/4 by 5z and by 16.
3/4 (5z + 16) = 3/4 × 5z + 3/4 × 16 = 15/4 z + 12
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\large\text{Write an expression that is equivalent to }\rm{\dfrac{3}{4}(5z + 16).}[/tex]
[tex]\huge\textbf{In order to answer this question, you}\\\huge\textbf{have to distribute. If you're unsure what}\\\huge\textbf{the distributive property formula is, it is:}[/tex]
[tex]\large\textsf{a(b + c)}[/tex]
[tex]\rightarrow\large\textsf{a}\times\large\textsf{{b + a}}\times\large\textsf{c}[/tex]
[tex]\rightarrow\large\textsf{ab + ac}[/tex]
[tex]\huge\textbf{Now, that we have that much}\\\huge\textbf{information out of the way, we can}\\\huge\textbf{now begin to answer the given question.}[/tex]
[tex]\huge\textbf{Here's what your equation looks like:}[/tex]
[tex]\mathsf{\dfrac{3}{4}(5z + 16)}[/tex]
[tex]\huge\textbf{Solving it:}[/tex]
[tex]\mathsf{\dfrac{3}{4}(5z + 16)}[/tex]
[tex]\rightarrow\mathsf{\dfrac{3}{4} \times 5z + \dfrac{3}{4} \times 16}[/tex]
[tex]\rightarrow\mathsf{\dfrac{15}{4}z + 12}[/tex]
[tex]\huge\textbf{Therefore, your answer is most likely:\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] }[/tex][tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{Option\ B. \dfrac{15}{4}\mathsf{z} + 12}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The number of entertainment websites in 1995 was 54. By 2004, there were 793 entertainment websites.
Approximately what was the rate of change for the number of websites for this period of time?
Answers
Answer:
13.69%
Step-by-step explanation:
793-54=739
739/54=13.68518519
tan^(2)x-tanx=0
Pls Help
Answers
Answer:
[tex]x=\frac{3\pi }{4} ,\frac{7\pi }{4}[/tex]
If wrong then [tex]x=-\frac{\pi }{4}.[/tex]
Step-by-step explanation:
[tex]tan^2(x)-tan(x)=0[/tex]
Factor out the tan(x).
[tex]tan(x)*(tan(x)-1)=0[/tex]
Solve for x.
[tex]tan(x)\neq 0\\[/tex] thus only option is tan(x)-1=0
[tex]tan(x)-1=0\\tan(x)=1\\[/tex]
x=tan^-1(1)⇒
Either it is Quadrant 2 or 4.
[tex]x=\frac{3\pi }{4} ,\frac{7\pi }{4}[/tex]
If the teacher says its wrong. Then that could only mean that its range of tan(x) is between [tex]-\frac{\pi }{2} < x < \frac{\pi }{2}[/tex] thus it's only on quadrant 4. [tex]x=-\frac{\pi }{4}[/tex]
1. Evaluate each expression without using a calculator.
(a) [tex](-3)^{4}[/tex]
Answers
The result of the exponential expression is 81
Indices expressionsIndices are written in term of exponents
According to the expoenent law of indices
a^4 = a * a * a * a
Given the expression
(-3)^4
This means the product of -3 in four places. Mathematically
(-3)^4 = -3 * -3 * -3 * -3
(-3)^4 = 9 * 9
(-3)^4 = 81
Hence the result of the exponential expression is 81
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In which expression is the coefficient of the n term -1?
Answers
Answer: c ???????????????????
Step-by-step explanation:
1 2 3 4 5 6 7 8 9 10
Which expression is equivalent to (x Superscript one-half Baseline y Superscript negative one-fourth Baseline z) Superscript negative 2?
StartFraction x Superscript one-half baseline Over y z squared EndFraction
StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction
StartFraction y Superscript one-half Baseline Over x z squared EndFraction
StartFraction x z squared Over y Superscript one-half EndFraction
Answers
Using the conversion of exponent to power, the equivalent expression is given as follows:
[tex]\frac{\sqrt{x}}{\sqrt[4]{y}z^2}[/tex]
How to transform an exponent to a power?It happens according to the following rule, with the denominator as the root and the numerator as the exponent:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
In this problem, we are given the following expression:
[tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex]
Negative exponents go to the denominator, hence the equivalent expression is given by:
[tex]\frac{\sqrt{x}}{\sqrt[4]{y}z^2}[/tex]
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Four students were discussing how to find the unit rate for a proportional relationship. Which method is valid? “Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.” “Look at the graph of the relationship. Count the number of units up and the number of units to the right one must move to arrive at the next point on the graph. Write these two numbers as a fraction.” “Look at the graph of the relationship. Find the x-value of the point that corresponds to y = 2. That value is the unit rate.” “Look at the graph of the relationship. Find two points which have y-values that are one unit apart. The unit rate is the difference in the corresponding x-values.” PLS HURRY
Answers
Answer:
(A) " Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate. "
Step-by-step explanation:
help please I'm no good at this
Answers
Here are the completed tables
Gallons Quart
1 4
2 8
5 20
7 28
Quart Pint
1 2
3 6
6 12
8 16
Pint Cup
1 2
3 6
5 10
9 18
The capacity of the objects are:
Swimming pool - 5000 gallons
Watering can - 8 quarts
Juice box - 2 pints
Soup bowl - 2 cups
The measurement from least to greatest is: 6 pints, 2 galloons, 18 cups, 6 quart.
How would the tables be filled?In order to fill the tables, the unit of conversion has to be known:
1 gallon = 4 quart
2 gallon = 2 x 4 = 8 quarts5 gallons : 5 x 4 = 20 quarts7 gallons: 7 x 4 = 28 quarts1 quart = 2 pints
6 pint / 2 = 3 quarts
12 / 2 = 6 quarts
8 x 2 = 16 pints
How to order the measurment from least to largest?
In order to order the measurement, all the measurements have to be in the same units. All the units would be converted to cups
1 quart = 4 cups
4 x 6 = 24 cups
1 galloon = 16 cups
16 x 2 = 32 cups
1 pint = 2 cups
6 x 2 = 12 cups
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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer: correct
Step-by-step explanation theoretically it is indeed correct by acknowledging by surface+height which both angles are evenly congruent now
in terms of the 990 Degree angle i know for a fact that it corresponds with it no more to say.
2. Find m angle 1
73
88
60
80
Answers
Answer:
88
Step-by-step explanation:
angles on a straight line add up to 180
180-120=60
angles in a triangle add up to 180
60+32=92
180-92=88
angle 1=88
Find the perimeter of the stained-glass window if each small square is 6 in. on
a side.
Answers
Answer:
the answer is B . 72√2 look at the picture I added
Use the zero product property to find the solutions to the equation x? + 12 = 7x.
X= -4 orx= 3
4 or X = -3
X=-30rX=4
X=30rX=4
Answers
Answer:
(d) x = 3 or x = 4
Step-by-step explanation:
The zero product property can be used to find the solutions to a polynomial equation when it is written in factored form.
__
Your polynomial can be put in factored form like this:
x² +12 = 7x . . . . . given
x² -7x +12 = 0 . . . . . standard form
(x -3)(x -4) = 0 . . . . . factored form*
x = 3 or x = 4 . . . . . . values of x that make the factors zero
_____
* The constants in the binomial factors must have a sum of -7 and a product of +12. It is often convenient to find them by listing factor pairs of 12:
12 = (-1)(-12) = (-2)(-6) = (-3)(-4)
Negative factors are used because we know the sum must be negative. Both have the same sign so their product is positive. The sums of the pairs shown are -13, -8, -7. The last pair is what we're looking for.
Please help with this questions
Answers
Answer:
16 x ^ -1/5
Step-by-step explanation:
round 789 to the nearest 10
Answers
Rounding 789 nearest to tens will be 790.
Step-step Explanation:
Let's know how to round any number nearest to tens (Rules):-
We know tens place in any no. from left is at second place and number right to tens place need to be changed as:-
If last digit is 0, then we don't have to do any rounding, because it is already to the ten.We round the no. down to the nearest ten if the last digit in the no. is 1, 2, 3, or 4We round the no. up to the nearest ten if the last digit in the no. is 5, 6, 7, 8, or 9.Answer:
790
Step-by-step explanation:
Help quick please!
A coin is tossed 30 times, and it comes up heads 18 times.
What is the experimental probability of tossing tails?
Answers
Answer:
0.4 or 2/5
Step-by-step explanation:
If head is 18/30, then that means that tails must be 12/30, since they must add up to one whole.
Reduce it to simplest terms: 2/5 or 0.4
According to data from the U.S. Census Bureau, approximately 9/10 of the U.S population was less than 65 years old. What percent
of the population was less than 65?
Answers
Answer:
90%
Step-by-step explanation:
We know that 9 of 10 people were less than 65. It means, that if they would ask 100 people, the number would be 90.
The percent of population less than 65 is 90%
Ninety percent of the population was less than 65.
What is the percentage?The percentage is defined as the ratio expressed as a fraction of 100.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators .
According to data from the U.S. Census Bureau,
Approximately 9/10 of the U.S population was less than 65 years old.
Nine out of ten people, as far as we know, were under 65.
In other words, if they surveyed 100 persons, the answer would be 90.
Hence, Ninety percent of the population was less than 65.
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There are 20 girls and 30 boys in a class. What percentage of the pupils in the class are boys?
Answers
Answer:
60%
Step-by-step explanation:
There are 50 people in the class the total.
30/50 are boys. .6=60%
Give the Least Common Denominator for
7ths, 5ths, and halves.
Answers
Answer:
7x5x2 = 70
There are no other smaller factors that include all of the given numbers
(4.8 x 10^5 divided by (8 x 10^2)
Answers
Answer:
.6 x 10^3 = 6000
Step-by-step explanation:
4.8 E5 / 8 E2 = .6 E3
If f(x) = 1 / (3x – 5), what is the inverse of f?
Answers
Answer:f^-1(x) = 1/3x + 5/3
Step-by-step explanation:
لا
Subtract 43 from 21 raised to the 7th power, then multiply by 2.
Answers
The lens and mirror in Figure P23.51 are separated by 1.00 m and have focal lengths of +79.2 cm and -50.6 cm, respectively. If an object is placed 1.00 m to the left of the lens, locate the final image.
Answers
The location final image from the mirror, which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.
What is the focal length of the lens?The focal length of the lens is the length of the distance between the middle of the lens to the focal point.
It can be find out using the following formula as,
[tex]-\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}[/tex]
Here, (v)is the distance of the image, (u) is the distance of the object, and (f) is the focal length of the lens.
The lens and mirror in the Figure are separated by 1.00 m and have focal lengths of +79.2 cm and -50.6 cm, respectively. Change the units of focal length in meters,
[tex]f_l=79.2\text{ cm=0.792 m}\\f_m=-50.6\text{ cm=0.506 m}[/tex]
An object is placed 1.00 m to the left of the lens. Put the value in the lens formula as,
[tex]-\dfrac{1}{v_l}+\dfrac{1}{1}=\dfrac{1}{0.792}\\-\dfrac{1}{v_l}=\dfrac{1}{0.792}-1\\v_1=3.81[/tex]
The distance of the image made by lens is 3.81 meters. The distance of this image from the mirror is,
[tex]u_2=3.81-1\\u_2=2.81\rm \; m[/tex]
This distance is work as object distance for the mirror. The focal length of mirror is -0.506 m. Thus, the location of the final image is,
[tex]-\dfrac{1}{v_2}+\dfrac{1}{3.81}=\dfrac{1}{-0.506}\\\dfrac{1}{v_2}=-\dfrac{1}{3.81}-(-\dfrac{1}{0.506})\\v_2=-0.58[/tex]
Thus, the location final image from the mirror which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.
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a fence is being built around a small park how many feet of fence will be needed to surround the park
Answers
Start by deciding how long is your fence going to be and how much space you want between posts. Typically, the post space is somewhere between 6 and 8 feet; or 2 and 5 meters, depending on your preference.
Answer: the answer would be 6-8 feet
Step-by-step explanation: the guy below me explains it well
Find the arc length of the semicircle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answers
Answer:
arc = 9π units
Step-by-step explanation:
the arc is half the circumference of the circle, then
arc = [tex]\frac{1}{2}[/tex] × 2πr = πr , then
arc = π × 9 = 9π
Answer:
[tex]\boxed{\tt 9\pi }[/tex]
Step-by-step explanation:
What we want to find here is the arc length of 1/2 of a circle, we'll start by finding the of the circle.
Step 1:- find the circumference of the circle →
[tex]\boxed{\sf Circumference\; of\; the \:circle=2\pi r}[/tex]
[tex]\tt 2\pi \times 9[/tex]
[tex]\tt 9\times 2\pi[/tex]
[tex]=\tt 18\pi[/tex]
Step 2:- find the arc length of 1/2 of the circle →
The arc length is 1/2 of the circumference of the circle:-
[tex]\boxed{\sf Circumference \; of \;\cfrac{1}{2}\; of\; the \; circle=\cfrac{1}{2}\times 18\pi}[/tex]
[tex]\tt \cfrac{18}{2} \pi[/tex]
[tex]\boxed{\tt 9\pi}[/tex]
Therefore, the arc length of the semicircle is 9π.
you are buying wood to build a gate for your backyard. if your car trunk has the following dimensions (47 inches by 33 inches by 19.5 inches), what is the longest piece of wood that could fit in your trunk (hint: it would likely be diagonal)?
Answers
The longest piece of wood that could fit in your trunk to build a gate for the backyard is 60.65 inches.
How to measure diagonal of the cuboid?The length of the diagonal of the cuboid is found out using the following formula.
[tex]D=\sqrt{l^2+b^2+h^2}[/tex]
Here, (l) is the length of the cuboid, (w) is the width, and (h) is the height of the cuboid.
The wood has to buy to build a gate for backyard. The car trunk has the following dimensions (47 inches by 33 inches by 19.5 inches). Here, we have,
Length (l)=47 inWidth (w)=33 inHeight (h)=19.5 inThe longest piece of wood which fits is equal to the length of diagonal of cuboid. Put the values in the formula,
[tex]D=\sqrt{47^2+33^2+19.5^2}\\D=\sqrt{3678.25}\\D=60.65\rm\; in[/tex]
Thus, the longest piece of wood that could fit in your trunk to build a gate for the backyard is 60.65 inches.
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what's 40 x 40 x 40 please
Answers
Answer:
64000
Step-by-step explanation:
Step-by-step explanation:
[tex]40 \times 40 \times 40[/tex]
[tex]160 \times 40[/tex]
[tex]6400[/tex]
please helpppp
An air conditioner manufacturer recommends that its portable units provide between 4 and 6 BTUs of cooling per cubic foot to operate most efficiently. Which statement is true?
A 16,000-BTU air conditioner meets the manufacturer recommendation for a room measuring 20 feet by 20 feet with a standard 8-foot ceiling.
A 14,000-BTU air conditioner meets the manufacturer recommendation for a room measuring 10 feet by 20 feet with a standard 8-foot ceiling.
A 20,000-BTU air conditioner will be too large for a room measuring 20 feet by 40 feet with an 8-foot ceiling.
A 12,000-BTU air conditioner will be too small for a room that is 15 feet by 10 feet with a 10-foot ceiling.
Answers
The statement is true is: A 16,000-BTU air conditioner meets the manufacturer recommendation.
Recommended BTUOption A
BTUs=16,000/(20 feet×20 feet×8 foot)
BTUs=16,000/3200 feet
BTUs=5 BTUs
Option B
BTUs=14,000/(10 feet×20 feet×8 foot)
BTUs=14,000/1600 feet
BTUs=8.75 BTUs
Option C
BTUs=20,000/(20 feet×40 feet×8 foot)
BTUs=20,000/6400 feet
BTUs=3.125 BTUs
Option D
BTUs=12,000/(15 feet×10 feet×10 foot)
BTUs=12,000/1500 feet
BTUs=8 BTUs
Based on the calculation above only option A with 5 BTUs fall between 4 and 6 BTUs.
Therefore the statement is true is: Option A.
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PLEASE HELP ME with this question
Answers
Answer:
abc are correct
Step-by-step explanation:
i took the test
The cost of painting a wall that is 5 meters wide and 212 meters tall is $50. How many square meters can be painted for $1?
Answers
Answer:
21.2 square meters
Step-by-step explanation:
The area of a parallelogram is base • height.
So:
1. Calculate the area of what you can get for $50. 5 • 212 = 1060 square meters.
2. Now you divide the first price ($50) by the desired price ($1). This one is easy because 50 / 1 = 50, but I'm putting this here for future reference in case you need to solve a problem that has a desired price that's greater than $1.
3. Divide the answer to step one by the answer to step two to get the area you can have painted for $1. 1060 / 50 = 21.2 square meters.
Question 1,2, and 3 how do i factor those? Can you show the work and explain how?
Answers
1: [tex]3n^{2}+9n+6[/tex]
notice that each part is divisible by 3
[tex]3n^{2}[/tex] ÷ 3 = [tex]n^{2}[/tex]
9n ÷ 3 = 3n
6 ÷ 3 = 2
so it becomes [tex]3(n^{2} +3n+2)[/tex]
3n can be rewritten as 2n+n
-you want to rewrite it into two numbers that multiply to the number that's alone (in this case 2)
which would get you
[tex]3(n^{2} +2n+n+2)[/tex]
Now that it's rewritten, you can factor out n + 2 from the equation.
the answer is
3(n+2)(n+1)
And you can check that by multiplying (n+2)(n+1) which is [tex]n^{2} +2n+n+2[/tex] and then each of those by 3, which is [tex]3n^{2} +6n+3n+6[/tex] or [tex]3n^{2}+9n+6[/tex], our origional equation
2: [tex]28+x^{2} -11x[/tex]
So I rewrote this as [tex]x^{2} -11x+28[/tex] (it's the same thing, just reordered using the commutative property)
now -11x can be rewritten as -4x-7x
(remember, the two numbers should multiply to equal 28, which is our constant.)
[tex]x^{2} -4x-7x+28[/tex]
now we can factor out x from the first expression and -7 from the second
[tex]x(x-4)-7(x-4)[/tex]
and lastly you factor out x-4,
which would give you
(x-4)(x-7)
Make sure to check your work and make sure it multiplies to [tex]x^{2} -11x+28[/tex]
3: [tex]9x^{2} -12x+4[/tex]
The first thing I notice when looking at this problem is that both 9 and 4 are perfect squares. Not only that, but they are the squares of 2 and 3, which are products of -12
So if you rewrite 9 as [tex]3^{2}[/tex] and 4 as [tex]2^{2}[/tex], the equation becomes
[tex]3^{2} x^{2} -12x+2^{2}[/tex]
now that [tex]3^{2} x^{2}[/tex] is ugly so it can be turned into [tex](3x)^{2}[/tex]
and -12x can be rewritten as [tex]-2*3x*2[/tex]
so our equation now looks like [tex](3x)^2-2*3x*2+2^{2}[/tex]
There's a rule that says [tex]a^{2} -2ab+b^{2} = (a-b)^{2}[/tex]
In our case, a=3x and b=2
so the final answer is
[tex](3x-2)^2[/tex]