The first derivative of the implicit function given by x^(2/3) + y^(2/3) = 14 can be found using implicit differentiation. We take the derivative of both sides with respect to x and use the chain rule to differentiate the terms involving y:(2/3)x^(-1/3) + (2/3)y^(-1/3) * dy/dx = 0Then, we solve for dy/dx:dy/dx = -(x/y)^(1/3)This is the first derivative of the implicit function. To evaluate it at a specific point, we need to substitute the coordinates of that point into the equation above.
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The continuous compound rate of decay of this isotope is approximately 1.41%.
In order to find the continuous compound rate of decay of the radioactive isotope, we can use the formula:
N(t) = N0 * e^(-λt)
Where N(t) is the amount of the isotope present at time t, N0 is the initial amount of the isotope, λ is the continuous decay constant, and t is the time elapsed (in this case, 6 years).
We are given that 91.9% of the isotope is still present after 6 years, so:
0.919 = e^(-λ * 6)
To solve for λ, we can take the natural logarithm of both sides:
ln(0.919) = -6λ
Now, we can solve for the decay constant:
λ = -ln(0.919) / 6 ≈ 0.0141
So, the continuous compound rate of decay of this isotope is approximately 1.41%.
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The three busiest airports in Europe are in London England ; Paris, France; and Frankfurt, Germany. The airport in London has 12.9 million more arrivals and departures than the Frankfurt airport. The Paris airport has 5.2 million more arrivals and departures than the Frankfurt airport. Write the sum of the arrivals and departures from these three cites as a simplified algebraic expression. Let x be the number of the arrivals and departures at the Frankfurt airport.(Source:Association of European Airline).
The sum of the arrivals and departures from these three cities is 3x + 18.1 million.
How to determine the sum of the arrivals and departures from these three citiesIf we let x be the number of arrivals and departures at Frankfurt airport, then the number of arrivals and departures at London airport is x + 12.9 million
The number of arrivals and departures at Paris airport is x + 5.2 million.
The sum of the arrivals and departures from these three cities is:
x + (x + 12.9 million) + (x + 5.2 million)
Simplifying this expression, we can combine like terms:
3x + 18.1 million
Therefore, the sum of the arrivals and departures from these three cities is 3x + 18.1 million.
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HELP PLEASE 45pts (WILL GIVE BRANLIEST!!!!)
How do you determine the scale factor of a dilation? Explain in general and with at least one example.
How do you determine if polygons are similar? Explain in general and give at least one example
If AB/DE = BC/EF = AC/DF, then triangle ABC is similar to triangle DEF.
To determine the scale factor of a dilation, you need to compare the corresponding lengths of the pre-image and image of a figure. The scale factor is the ratio of the lengths of any two corresponding sides.
For example, suppose you have a triangle ABC with sides AB = 3 cm, BC = 4 cm, and AC = 5 cm. If you dilate the triangle by a scale factor of 2, you get a new triangle A'B'C'.
To find the length of A'B', you multiply the length of AB by the scale factor: A'B' = 2 * AB = 2 * 3 = 6 cm. Similarly, B'C' = 2 * BC = 2 * 4 = 8 cm and A'C' = 2 * AC = 2 * 5 = 10 cm. Therefore, the scale factor of the dilation is 2.
To determine if polygons are similar, you need to check if their corresponding angles are congruent and their corresponding sides are proportional.
In other words, if you can transform one polygon into another by a combination of translations, rotations, reflections, and dilations, then they are similar.
For example, suppose you have two triangles ABC and DEF.
If angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F, and the ratios of the lengths of the corresponding sides are equal, then the triangles are similar. That is, if AB/DE = BC/EF = AC/DF, then triangle ABC is similar to triangle DEF.
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Suppose a life insurance policy costs $16 for the first unit
of coverage and then $4 for each additional unit of
coverage. Let C(x) be the cost for insurance of x units of
coverage. What will 10 units of coverage cost?
Therefore , the solution of the given problem of unitary method comes out to be $52 10 units of coverage will be purchased.
An unitary method is defined as what?To complete the work, the well-known straightforward strategy, actual variables, and any essential components from the very first and specialised inquiries can all be utilised. In response, customers might be given another opportunity to sample the product. Otherwise, important advancements in our comprehension of algorithms will be lost.
Here,
We are informed that the first unit of coverage will cost $16 and each additional unit will cost $4. We may calculate the price of x units of coverage using the following formula:
=> C(x) = 16 + 4(x-1)
The number of subsequent units of coverage following the initial unit is indicated by the (x-1) term in the calculation.
We may enter x=10 into the algorithm to get the price for 10 units of coverage:
=> C(10) = 16 + 4(10-1)
=> C(10) = 16 + 4(9)
=> C(10) = 16 + 36
=> C(10) = 52
For $52, 10 units of coverage will be purchased.
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The berry-picking boxes at bingo berry farm have square bottoms that are 8 centimeters on each side. mateo fills his box with raspberries to a height of 6 centimeters. what is the volume of raspberries in mateo's box?
The volume of raspberries in Mateo's box is 384 cubic centimeters.
To calculate the volume of raspberries in Mateo's box, we need to use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length and width are both 8 centimeters, as the box has a square bottom. The height is 6 centimeters, as Mateo fills the box to that height with raspberries.
So, the volume of raspberries in Mateo's box is:
Volume = length x width x height
Volume = 8 cm x 8 cm x 6 cm
Volume = 384 cubic centimeters
Therefore, the volume of raspberries in Mateo's box is 384 cubic centimeters. This calculation assumes that the raspberries are tightly packed in the box, without any gaps or air pockets. In reality, the actual volume of raspberries may be slightly less than this, depending on how they are arranged in the box. Nonetheless, this calculation provides a reasonable estimate of the amount of raspberries that Mateo is able to pick and fit in the box.
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By using integration by parts, find the integral 2∫⁷ in x dx b) Hence, find 2∫⁷ in √x dx
The integral is:
[tex](4/3)x^(3/2) ln(x) - (2/3)∫x^(1/2) dx = (4/3)x^(3/2) ln(x) - (4/5)x^(5/2) + C[/tex]
Solve the integrals using integration by parts.
a) To find [tex]2∫x⁷ln(x) dx[/tex], we'll use integration by parts with the formula: [tex]∫u dv = uv - ∫v du. Let's choose:u = ln(x) = > du = (1/x) dxdv = x⁷ dx = > v = (1/8)x⁸[/tex]
Now, apply the integration by parts formula:
[tex]2∫x⁷ln(x) dx = 2[uv - ∫v du] = 2[((1/8)x⁸ ln(x) - ∫(1/8)x⁸(1/x) dx)]= (1/4)x⁸ ln(x) - (1/4)∫x⁷ dx = (1/4)x⁸ ln(x) - (1/32)x⁸ + C[/tex]
b) To find 2∫√x ln(x) dx, we'll use a similar approach. Let's choose:
[tex]u = ln(x) = > du = (1/x) dxdv = √x dx = > v = (2/3)x^(3/2)[/tex]
Now, apply the integration by parts formula:
[tex]2∫√x ln(x) dx = 2[uv - ∫v du] = 2[((2/3)x^(3/2) ln(x) - ∫(2/3)x^(3/2)(1/x) dx)]= (4/3)x^(3/2) ln(x) - (2/3)∫x^(1/2) dx = (4/3)x^(3/2) ln(x) - (4/5)x^(5/2) + C[/tex]
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Express the number as a ratio of integers.
5.490 = 5.490490490
5.490490490 can be expressed as the ratio of integers 5485/999. Hi! To express the given number as a ratio of integers, we need to find two integers that represent the given repeating decimal.
The number 5.490490490 can be written as 5.490(490 repeating). To convert the repeating part into a ratio, we can use the following method:
Let x = 0.490490...
Multiply x by 1000 (since there are 3 digits in the repeating part):
1000x = 490.490490...
Subtract the original x from the 1000x equation:
1000x - x = 490.490490... - 0.490490...
999x = 490
Now, divide both sides by 999:
x = 490/999
So, the repeating decimal 0.490490... can be represented as the ratio 490/999. To express the entire number as a ratio of integers, add the non-repeating part (5) to the ratio:
5 + (490/999) = (5 * 999 + 490) / 999 = (4995 + 490) / 999 = 5485/999.
Your answer: 5.490490490 can be expressed as the ratio of integers 5485/999.
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A company that maintains swimming pools eams $60 for each pool the workers clean and treat with chemicals.
. The revenue, in dollars, the company earns to clean and treat z pools can be described using the function r(z) = 60z.
• The cost, in dollars, the company pays for chemicals and for the workers to clean and treat z pools can be described using the function c (z) = 3z² + 42r.
. The profit the company earns, in dollars, can be described using the function p (z)=r(z) - c(z).
Determine a simplified expression to describe p (z), the profit the company earns, in dollars. Use the on-screen keyboard to type the answer in the box.
WHAT IS P(x) =
The simplified expression for p(z), the profit the company earns, in dollars is: p(z) = -3z² + 18z
What is function?The set X is known as the domain of the function, and the set Y is known as the codomain of the function. A function from a set X to a set Y assigns each element of X to exactly one element of Y. Originally, functions were an idealization of how one variable depends on another.
According to question:First, let's substitute the expressions for r(z) and c(z) in the expression for p(z):
p(z) = r(z) - c(z)
p(z) = 60z - (3z² + 42z)
p(z) = 60z - 3z² - 42z
p(z) = -3z² + 18z
Therefore, the simplified expression for p(z), the profit the company earns, in dollars is:
p(z) = -3z² + 18z
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Find the volume of the solid generated when the rectangle below is rotated about side
LO. Round your answer to the nearest tenth if necessary.
The volume of the obtained solid is 36 units³.
Given that a rectangle of dimension 9 units x 2 units, has been rotated to form a solid we need to find its volume,
So we know that a rectangle rotated to form a rectangular prism.
Volume of a rectangular prism = product of the dimensions.
The dimensions of the obtained solid will be 9 units x 2 units x 2 units,
So the volume = 9 x 2 x 2 = 36 units³
Hence the volume of the obtained solid is 36 units³.
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The curve y = ax2 + bx + c passes through the point (2, 12) and is tangent to the line yat at the origin. Find a, b, and c. a = 4,6 - 0,C-1 Oa - 2. b = 0,C=0 O a = 1,"
The equation of the curve is y = x2 + 4.
To solve this problem, we need to use the fact that the curve y = ax2 + bx + c passes through the point (2, 12) and is tangent to the line yat at the origin.
First, we know that the tangent to the curve at the origin is the line y = 0x + c = c. Since the curve is tangent to this line at the origin, we know that the derivative of the curve at x = 0 is equal to 0.
Taking the derivative of y = ax2 + bx + c, we get y' = 2ax + b. Setting x = 0, we get y' = b. Since y' = 0 at x = 0, we know that b = 0.
So now we have y = ax2 + c. We can use the fact that the curve passes through the point (2, 12) to solve for a and c.
Substituting x = 2 and y = 12 into the equation y = ax2 + c, we get 12 = 4a + c.
Since we know that a = 4, 6, or 1, we can substitute each of these values into the equation and solve for c.
When a = 4, we get 12 = 4(4)(2) + c, which simplifies to 12 = 32 + c. Solving for c, we get c = -20.
When a = 6, we get 12 = 4(6)(2) + c, which simplifies to 12 = 48 + c. Solving for c, we get c = -36.
When a = 1, we get 12 = 4(1)(2) + c, which simplifies to 12 = 8 + c. Solving for c, we get c = 4.
So the values of a, b, and c are:
a = 1
b = 0
c = 4
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In the last 215 days, builders have completed 700 m2 of the alligator habitat that will eventually be 1,200 m2. How much longer will it take to complete the alligator habitat?
In the last 215 days, builders have completed 700 m2 of the alligator habitat that will eventually be 1,200 m2.
It will take approximately 153 days to complete the remaining part of the alligator habitat.
Determine how much longer it will take to complete the alligator habitat, first, we need to find the rate at which the builders are working.
Calculate the work rate
The builders have completed 700 m2 of the 1,200 m2 alligator habitat in 215 days.
Work rate = (completed work) / (number of days)
Work rate = 700 m2 / 215 days = 3.26 m2/day (approximately)
Calculate the remaining work
The total area of the alligator habitat is 1,200 m2, and 700 m2 has been completed.
Remaining work = Total area - Completed work
Remaining work = 1,200 m2 - 700 m2 = 500 m2
Calculate the time to complete the remaining work
Time to complete = (remaining work) / (work rate)
Time to complete = 500 m2 / 3.26 m2/day ≈ 153.37 days
It will take approximately 153 days to complete the remaining part of the alligator habitat.
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It will take approximately 394 more days to complete the alligator habitat.
We can start by finding the proportion of the habitat that has already been completed:
proportion completed = 700 m^2 / 1200 m^2 = 0.5833
This means that there is still 1 - 0.5833 = 0.4167 (or 41.67%) of the habitat left to complete.
Next, we can use a proportion to find out how long it will take to complete the remaining 41.67% of the habitat:
215 days / 0.5833 = x days / 0.4167
Solving for x, we get:
x = 215 days * 0.4167 / 0.5833 ≈ 153 days
Therefore, the total time it will take to complete the alligator habitat is approximately 215 + 153 = 368 days, or about 394 more days from the start.
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Frank solved the equation using the following steps. Is he correct? Explain.
1/5 t + 2 = 17 1/5 t + 2 - 2 = 17 1/5 y = 17. t = 85
Answer:
see below
Step-by-step explanation:
Here are the steps that Frank took:
1/5t+2=17
1/5t+2-2=17
1/5t=17
t=85
Frank is incorrect. He is incorrect because in step 2, he forgot to subtract both sides by 2, and only did this to the left side of the equal sign. He has to subtract 2 from both sides of the equal side to have the equation remain balanced. Frank should've gotten t=75.
Hope this helps! :)
Give the Laplace transform of f(x)= (-2x-3)/4
The Laplace transform of f(x)= (-2x-3)/4 is (-2L{x}-3L{1})/4, where L{x} is the Laplace transform of x and L{1} is the Laplace transform of 1.
Hi! The Laplace transform of a given function f(t) is denoted by L{f(t)} and is defined as the integral of f(t) multiplied by e^(-st), where s is a complex variable. For the function f(x) = (-2x - 3)/4, the Laplace transform can be calculated as follows:
L{f(t)} = L{(-2t - 3)/4}
To find the Laplace transform, we will treat the function as two separate parts:
L{(-2t - 3)/4} = (-2/4) * L{t} + (-3/4) * L{1}
The Laplace transforms of t and 1 are well-known:
L{t} = 1/s^2
L{1} = 1/s
Now, substitute these transforms back into our expression:
L{f(t)} = (-1/2) * (1/s^2) + (-3/4) * (1/s)
L{f(t)} = -1/(2s^2) - 3/(4s)
And that's the Laplace transform of f(x) = (-2x - 3)/4.
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24*
24) You must order a new rope for the
flagpole. To find out what length of rope
is needed, you observe the pole casts a
shadow 11.6 m long on the ground. The
angle between the suns rays and the
ground is 36.8°. How tall is the pole?
A) 17.5
C) 8.7
B) 9.3
D) 6.9
The correct answer is (C) as the height of the pole is 8.7 meters.
What are Trigonometric functions?
Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle.
Tangent (tan): the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.
We can use the tangent function to solve this problem.
Let's call the height of the pole "h" and the length of the rope "r".
We know that the length of the shadow cast by the pole is 11.6 meters, and the angle between the sun's rays and the ground is 36.8°. This means that:
tan(36.8°) = h / 11.6
To solve for "h", we can rearrange this equation to get:
h = 11.6 * tan(36.8°)
Using a calculator, we find that h ≈ 8.7 meters.
So the height of the pole is approximately 8.7 meters. Therefore, the correct answer is (C) 8.7.
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how does 12 - 4.6 make 7.6
Learning Task 4: Fin in the boxes for the correct information needed.
Quadrilaterals
Remember that we can relate triangle to quadrilateral through the
illustration that each triangle has a total of 180 degrees and a
quadrilateral has 360 degrees, therefore, there are two triangles in a
quadrilateral to have both equal to 360 degrees.
The relationship of triangles and quadrilaterals is in their area. The
formula in getting the area of a quadrilateral is A=BxH while in a triangle
it is A=(BxH)/2. This shows that in every quadrilateral there are two
triangles.
There are many different types of quadrilaterals and they all share the
similarity of having four sides, two diagonals, and the sum of their interior
angles is 360 degrees. They all have relationships to one another, but
they are not all exactly alike and have different properties.
answer right if not I will report or banned you
Quadrilaterals have four sides, two diagonals, and the sum of their interior angles is 360 degrees. They can be related to triangles through the fact that each triangle has a total of 180 degrees and a quadrilateral has 360 degrees, so there are two triangles in a quadrilateral with their angles adding up to 360 degrees.
However, triangles and quadrilaterals differ in terms of their area formulas, where the area of a quadrilateral is calculated as the product of its base and height (A = BxH), while the area of a triangle is half the product of its base and height (A = (BxH)/2). Quadrilaterals have different types and properties, although they share the common characteristics mentioned above.
- Quadrilaterals have four sides and two diagonals. The sum of the interior angles in a quadrilateral is always 360 degrees.
- Triangles have three sides and the sum of their interior angles is always 180 degrees.
- The relationship between triangles and quadrilaterals is based on the fact that a quadrilateral can be divided into two triangles. Each triangle within the quadrilateral contributes 180 degrees to the total sum of 360 degrees.
- The formula for calculating the area of a quadrilateral is A = BxH, where A represents the area, B represents the base, and H represents the height.
- In contrast, the formula for calculating the area of a triangle is A = (BxH)/2, where A represents the area, B represents the base, and H represents the height. This formula demonstrates that the area of a triangle is half the area of a quadrilateral with the same base and height.
- While all quadrilaterals share the characteristics of having four sides, two diagonals, and interior angles summing up to 360 degrees, they have different types and properties.
Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. Each type has its own unique properties and relationships to other quadrilaterals.
In conclusion, quadrilaterals and triangles are related through the concept of dividing a quadrilateral into two triangles. They differ in their area formulas, and although all quadrilaterals have four sides, two diagonals, and interior angles summing up to 360 degrees, they have different types and properties.
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7. the interest on a particular savings account is compounded continuously. the account initially had $3500 deposited in it. the worth of the account after t-years can be calculated using the formula: a(t)- 3500041 (a) by what percent will the worth of the account increase per year? round to the nearest hundredth of a percent. (b) to the nearest tenth of a year, how long will it take for the worth of the account to triple?
With the given formula [tex]a(t) = 3500e^{(0.041t)[/tex], the percent increase per year for savings account is 4.1% and it will take about 16.9 years for the worth of the account to triple.
a) The formula given is: [tex]a(t) = 3500e^{({0.041t)[/tex]
To find the percent increase per year, we need to find the annual growth rate. We can do this by taking the derivative of a(t) with respect to t:
[tex]a'(t) = 0.041 * 3500 * e^{(0.041t)[/tex]
The annual growth rate is equal to a'(t)/a(t). Plugging in the formula for a(t) and simplifying, we get:
a'(t)/a(t) = 0.041
So the percent increase per year is 4.1%.
b) We want to find the time it takes for the account to triple in value, so we need to solve for t in the equation:
[tex]3a(0) = 3500e^{(0.041t)[/tex]
Dividing both sides by 3500 and taking the natural logarithm of both sides, we get:
ln(3) = 0.041t
t = ln(3)/0.041
Using a calculator, we get:
t ≈ 16.92 years
So it will take about 16.9 years for the worth of the account to triple.
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PLEASE HELP FAST!!!!!
To the nearest hundredth, what is the length of line segment AB? Drag your answer into the box. The length of line segment AB is approximately units. Two points, A and B, plotted in a coordinate plane. Point A is at (2, 2), and point B is at (-6, 4)
The length of the line segment AB is 8.25 units, under the condition that the length of line segment AB is approximately units. Two points, A and B, plotted in a coordinate plane. Point A is at (2, 2), and point B is at (-6, 4)
In order to evaluate the length of line segment AB, we can apply the distance formula which is derived from the Pythagorean theorem.
The distance formula is given by d = √[(x₂ - x₁)² + (y₂ - y₁)²].
Here,
x₁ = 2,
y₁ = 2,
x₂ = -6
y₂ = 4.
Staging these values in the formula,
d = √[(-6 - 2)² + (4 - 2)²]
= √[(-8)² + 2²]
= √(64 + 4)
= √68
≈ 8.25 units
Then, the length of line segment AB is approximately 8.25 units.
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Use the following scenario to answer questions 1 and 2.
Tom and Jerry are sometimes late for school. The events Tand J are defined as follows:
T= the event that Tom is late for school.
J = the event that Jerry is late for school.
P (T) = 0. 25
P (TNJ) = 0. 15
P (Tºn JC) = 0. 7
On a randomly selected day, find the probability that at least one of Tom or Jerry are late for school.
The probability that at least one of Tom or Jerry are late for school is 0.4.
To find the probability that at least one of Tom or Jerry are late for school, we can use the formula:
P(T or J) = P(T) + P(J) - P(T and J)
Since we don't know the probability of Jerry being late (P(J)), we can use the complement rule:
P(J) = 1 - P(JC)
where JC represents the event that Jerry is not late for school.
Substituting the given probabilities:
P(T or J) = P(T) + [1 - P(JC)] - P(T and J)
P(T or J) = 0.25 + 0.3 - 0.15
P(T or J) = 0.4
Therefore, the probability that at least one of Tom or Jerry are late for school is 0.4.
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The Maclaurin series for a function f is given by f(x)=x−x^3/3!+x^5/5!−x^7/7!+⋯+(−1)^n*x^2n+1/(2n+1)!+⋯ and converges to f(x) for all x. Let g be the function defined by g(x)=f(x2)
The Maclaurin series for g(x) is given by g(x) =[tex]x^2 - x^6/3! + x^10/5! -[/tex] [tex]x^14/7![/tex] [tex]+ ⋯ + (-1)^n*x^(4n)/(2n+1)! + ⋯[/tex]
How to the Maclaurin series of g(x)?The function g(x) is defined as g(x) = [tex]f(x^2)[/tex], where f(x) is a function with a Maclaurin series expansion.
To find the Maclaurin series for g(x), we substitute [tex]x^2[/tex] into the Maclaurin series of f(x). The resulting series for g(x) is obtained by replacing each occurrence of x in the series for f(x) with x^2:
g(x) = [tex]f(x^2) = (x^2) - (x^2)^3/3! + (x^2)^5/5! - (x^2)^7/7! + ⋯ + (-1)^n*(x^2)^(2n+1)/(2n+1)! + ⋯[/tex]
Simplifying the terms, we have:
g(x) =[tex]x^2 - x^6/3! + x^10/5! - x^14/7! + ⋯ + (-1)^n*x^(4n+2)/(2n+1)! + ⋯[/tex]
This represents the Maclaurin series expansion for the function g(x) in terms of the original function f(x) with the argument squared.
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Please help factor this expression completely, then place the factors in the proper location on the grid.
1/8 x^3-1/27 y^3
will mark brainly
Using cubes formula the factored expression is given as:
1/8x^3 - 1/27y^3 = (1/2x - 1/3y)(1/4x^2 + 1/6xy + 1/9y^2)
To factor the expression [tex]1/8x^3 - 1/27y^3[/tex], we can utilize the difference of cubes formula, which states that the difference of two cubes can be factored as the product of their binomial factors.
In our given expression, we have[tex](1/8x^3 - 1/27y^3).[/tex] We can identify[tex]a^3 as (1/2x)^3 and b^3 as (1/3y)^3.[/tex]
Applying the difference of cubes formula, we get:
[tex](1/8x^3 - 1/27y^3) = (1/2x - 1/3y)((1/2x)^2 + (1/2x)(1/3y) + (1/3y)^2)[/tex]
Simplifying the expression within the second set of parentheses, we have:
[tex](1/8x^3 - 1/27y^3) = (1/2x - 1/3y)(1/4x^2 + 1/6xy + 1/9y^2)[/tex]
Therefore, the factored form of the expression 1/8x^3 - 1/27y^3 is given by (1/2x - 1/3y)(1/4x^2 + 1/6xy + 1/9y^2). This represents the product of the binomial factors resulting from the application of the difference of cubes formula.
To factor the expression 1/8x^3 - 1/27y^3, we can use the difference of cubes formula, which states that:
[tex]a^3 - b^3 = (a - b)(a^2 + ab + b^2)[/tex]
Applying this formula, we get:
1/8x^3 - 1/27y^3 = (1/2x - 1/3y)(1/4x^2 + 1/6xy + 1/9y^2)
Therefore, the expression is completely factored as:
[tex]1/8x^3 - 1/27y^3 = (1/2x - 1/3y)(1/4x^2 + 1/6xy + 1/9y^2)[/tex]
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What is a sine wave in Trigonometry
Answer:
Read Below
Step-by-step explanation:
A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the sine trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in mathematics, as well as in physics, engineering, signal processing and many other fields
Answer:
It is a type of wave. There are also cosine waves and tangent waves.
Step-by-step explanation:
what is 2X (2² + sin 3) = ?
2X (2² + sin 3) can be simplified as 8X + 2X sin 3
How to simplify the functionTo solve the expression, we will first have to compute the values inside the parentheses and then apply the given operations. so we Calculate the values inside the parentheses by multiplying across the bracket:
2² is equal to 4, and sin 3 is a trigonometric function that returns the sine of the angle 3
Therefore, the expression 2X (2² + sin 3) simplifies to:
2X (4 + sin 3)
or
8X + 2X sin 3
where X is an unknown variable and sin 3 is a trigonometric function
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Answer:
Solution
verified
Verified by Toppr
I=∫e
2x
sin3xdx
I=sin3x∫e
2x
dx−∫(
dx
d
sin3x∫e
2x
dx)dx
I=sin3x
2
e
2x
−∫
2
3
cos3xe
2x
dx
I=sin3x
2
e
2x
−
2
3
∫cos3x∫e
2x
dx−∫(
dx
d
cos3x∫e
2x
dx)dx
I=sin3x
2
e
2x
−
2
3
[
2
cos3xe
2x
−∫(−sin3x
2
e
2x
)dx]
I=
2
sin3xe
2x
−
4
3
cos3xe
2x
−
4
3
∫sin3xe
2x
dx
I=
2
sin3xe
2x
−
4
3
cos3xe
2x
−
4
3
I
I+
4
3
I=
2
sin3xe
2x
−
4
3
cos3xe
2x
4
7I
=
4
2e
2x
sin3x−3cos3xe
2x
I=
7
e
2x
(2sin3x−3cos3x)
∴∫e
2x
sin3dx=
7
e
2x
(2sin3x−3cos3x)
Solve any question of Integrals with:-
Patterns of problems
Patterns of problems
>
Solve :∫e xe e xe e e x
dx
Medium
View solution>Solve:-∫ a 2b 2(a 2 −b 2) 2
Step-by-step explanation:
pls brain
A group of neighbors is holding an end of summer block party. They buy p packs of hot dogs, with 8 hot dogs in each pack. All together, they have 56 hot dogs for the party. Write an equation to describe this situation. How many packs of hot dogs did the neighbors buy
Step-by-step explanation:
8p= 56
p= 7
therefore, the neighbours bought 7 packets of hotdogs.
please help ASAP (can give brainliest)
Answer:
x = 6
Step-by-step explanation:
In order for it to be a parallelogram, the 2 lines must be equal.
2x=3x-6
2x - 3x = 3x - 3x -6
-1x = -6
x = 6/1
x = 6
Find the value of each variable
Answer:
Step-by-step explanation:
Some parallelograms are squares true or false
Answer:
True
Step-by-step explanation:
Parallelogram: A parallelogram is 4-sided shape that has parallel opposite sides
Square: A square is 4-sided shape where all sides are congruent and has 4 right angles. A square also has 2 pairs of opposite parallel sides.
Based on these definitions, we can see that not ALL parallelograms can be squares because a parallelogram can have no right angles, or can have all 4 angles be right angles.
All squares have to be parallelograms though because a square and a parallelogram both have 2 pairs of opposite parallel sides.
Hope this helps :)
652 10(3) trying to determine platelet count from a test result.
The platelet count is 652 x 10^3.
How to determine platelet count?Based on the information provided, it seems that the platelet count from a test result is 652, and the normal range for platelet count is 150,000 to 450,000 platelets per microliter of blood. The value "10(3)" likely refers to the measurement being in thousands.
To convert the measurement to the standard unit of platelet count, we need to multiply the given value by 1,000. Thus, 652 * 1,000 = 652,000 platelets per microliter.
It's important to note that platelet counts can vary depending on various factors, and medical professionals typically interpret the results in conjunction with other clinical information. If the obtained value of 652,000 platelets per microliter is accurate, it would be significantly higher than the upper limit of the normal range.
It's crucial to consult a healthcare professional or a qualified medical practitioner for an accurate interpretation of test results and any necessary medical advice or treatment.
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#SPJ11The area of a rectangle is 72x^13y^9z^16 square yards. The length of the rectangle is 3x9y4z^5 yards. Find the simplified expression of the width of the rectangle in yards.
The expression of the width of the rectangle is 2x¹²y⁸z¹¹/3.
Given that the area of a rectangle is 72x¹³y⁹z¹⁶ sq. yds and the length of the rectangle is 3x9y4z⁵, we need to find the width,
Using these expressions, we have,
Area = length × width
72x¹³y⁹z¹⁶ / 3x9y4z⁵ = width
Width = 72x¹³/3x × y⁹/9y × z¹⁶/4z⁵
Width = 24x¹²y⁸z¹¹/36 = 2x¹²y⁸z¹¹/3
Hence the expression of the width of the rectangle is 2x¹²y⁸z¹¹/3.
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A rectangular prism has a square
base with edge length (x + 1). Its
volume is (x + 1)2(x – 3). What
does the expression (x + 1)(x – 3)
represent?
area of the base
area of one side
height of the prism
surface area of the prism
The expression (x + 1)(x - 3) represents the Area of base of the prism.
What is Prism?a crystal is a polyhedron containing a n-sided polygon base, a respectable halfway point which is a deciphered duplicate of the first, and n different countenances, fundamentally all parallelograms, joining relating sides of the two bases. Translations of the bases exist in every cross-section that runs parallel to the bases.
According to question:
The volume of a rectangular prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a square with edge length (x + 1), so its area is (x + 1)^2. The volume of the prism is given as (x + 1)^2(x - 3).
We can find the height of the prism by dividing the volume by the area of the base:
B = V/h = (x + 1)^2(x - 3)/(x + 1) = (x + 1)(x - 3)
Therefore, the expression (x + 1)(x - 3) represents the Area of base of the prism.
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Each side y of a square is increased by 5 units. Which expression represents the number of square units in the area of the new square?
O 2y + 10
O y^2 + 10y + 25
O y^2 + 25
O y^2 + 10y + 10
The expression for the area of the new square is y² + 10y + 25.
How to find area?To find the expression that represents the area of the new square, we need to consider that when each side of a square is increased by 5 units, the new side length becomes y + 5. The area of the new square is then given by:
(New side length)² = (y + 5)²
Expanding the square, we get:
(y + 5)² = y² + 10y + 25
Therefore, the expression that represents the area of the new square is y² + 10y + 25.
So, the correct option is:
O y² + 10y + 25
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