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VashaNatasha [74]

4 years ago

11

All angles and sides of a certain parallelogram are equal. Which of the following best describes the parallelogram?

1 answer:

lara31 [8.8K]4 years ago

8 0

we need picture to answer this...sorry but if you post them I can help you out

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Find the arc length of the given curve between the specified points. x = y^4/16 + 1/2y^2 from (9/16), 1) to (9/8, 2).

lutik1710 [3]

Answer:

The arc length is $\dfrac{21}{16}$

Step-by-step explanation:

Given that,

The given curve between the specified points is

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

The points from $(\dfrac{9}{16},1)$ to $(\dfrac{9}{8},2)$

We need to calculate the value of $\dfrac{dx}{dy}$

Using given equation

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

On differentiating w.r.to y

$\dfrac{dx}{dy}=\dfrac{d}{dy}(\dfrac{y^2}{16}+\dfrac{1}{2y^2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}\dfrac{d}{dy}(y^4)+\dfrac{1}{2}\dfrac{d}{dy}(y^{-2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}(4y^{3})+\dfrac{1}{2}(-2y^{-3})$

$\dfrac{dx}{dy}=\dfrac{y^3}{4}-y^{-3}$

We need to calculate the arc length

Using formula of arc length

$L=\int_{a}^{b}{\sqrt{1+(\dfrac{dx}{dy})^2}dy}$

Put the value into the formula

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4}-y^{-3})^2}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-2\times\dfrac{y^3}{4}\times y^{-3}}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4})^2+(y^{-3})^2+\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4}+y^{-3})^2}dy}$

$L= \int_{1}^{2}{(\dfrac{y^3}{4}+y^{-3})dy}$

$L=(\dfrac{y^{3+1}}{4\times4}+\dfrac{y^{-3+1}}{-3+1})_{1}^{2}$

$L=(\dfrac{y^4}{16}+\dfrac{y^{-2}}{-2})_{1}^{2}$

Put the limits

$L=(\dfrac{2^4}{16}+\dfrac{2^{-2}}{-2}-\dfrac{1^4}{16}-\dfrac{(1)^{-2}}{-2})$

$L=\dfrac{21}{16}$

Hence, The arc length is $\dfrac{21}{16}$

6 0

3 years ago

Find value the value of x in the image below please help

Marianna [84]

There is no image srry .-.

3 0

3 years ago

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Find the sum of the measures of Angle A, Angle B, Angle C and Angle D.

12345 [234]

Answer:

Q:

my problem is this. Solve the problem.The sum of the measures of the angles in any triangle is 180 degrees. In triangle ABC, angles A and B have the same measure, while angle C is 42 degrees larger t…

A:

In triangle ABC, angles A and B have the same measure, while angle C is 42 degrees larger than each of the other two angles. Find the measure of angle Step-by-step explanation:

Find the measures of angles A, B, and C in triangle ABC, if measure of angle B = 5 times the measure of angle A measure of angle C = measure of angle A + 110

✓ A + B + C = 180 A + 5A + A+110 = 180

4 0

3 years ago

Noah finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of the length x in inches of

11111nata11111 [884]

SOLUTION

Given the question on the question tab;

$From\text{ the graph; we will trace from x=1 upward to meet the curve, then trace to the y-axis.}$

The trace on the graph is given below;

$The\text{ value of y when x=1 is 15.}$

Final answer:

The volume of the box when x=1 is 15 cubic inches.

7 0

1 year ago

If a pair of shoes has an original price of 80 and they are on sale for 48, what is the percent of discount?

defon

60% is the correct answer.

8 0

4 years ago

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