Ask question

Ask question

All categories

2 years ago

7

(1 Convert the integral below to polar coordinates and evaluate the integral. ∫4/2√0∫16−y2√yxydxdy∫04/2∫y16−y2xydxdy Instruction

s: Please enter the integrand in the first answer box, typing theta for θθ. Depending on the order of integration you choose, enter dr and dtheta in either order into the second and third answer boxes with only one dr or dtheta in each box. Then, enter the limits of integration and evaluate the integral to find the volume. ∫BA∫DC∫AB∫CD =_____A = _______B = _______C = _______D =_______Volume =_______

1 answer:

Tanzania [10]2 years ago

4 0

Answer:

A = 0

B = π/4

C = 0

D = 4

Volume = 16

Step-by-step explanation:

∫BA∫DC∫AB∫CD is shown in the picture attached

You might be interested in

What values of c and d make the equation true? RootIndex 3 StartRoot 162 x Superscript c Baseline y Superscript 5 Baseline EndRo

Reil [10]

Answer:

<em>c=6, d=2</em>

Step-by-step explanation:

<em>Equations </em>

We must find the values of c and d that make the below equation be true

$\sqrt[3]{162x^cy^5}=3x^2y \sqrt[3]{6y^d}$

Let's cube both sides of the equation:

$\left (\sqrt[3]{162x^cy^5}\right )^3=\left (3x^2y \sqrt[3]{6y^d}\right)^3$

The left side just simplifies the cubic root with the cube:

$162x^cy^5=\left (3x^2y \sqrt[3]{6y^d}\right)^3$

On the right side, we'll simplify the cubic root where possible and power what's outside of the root:

$162x^cy^5=3^3x^6y^3 (6y^d)$

Simplifying

$x^cy^5=x^6y^{3+d}$

Equating the powers of x and y separately we find

c=6

5=3+d

d=2

The values are

$\boxed{c=6,d=2}$

3 0

2 years ago

Read 2 more answers

A three-digit number ends in number 7. If you put the number 7 in the first position, the number will increase by 324. Find the

liq [111]

Answer:

<u>The original three-digit number is 417</u>

Step-by-step explanation:

Let's find out the solution to this problem, this way:

x = the two digits that are not 7

Original number = 10x+7

The value of the shifted number = 700 + x

Difference between the shifted number and the original number = 324

Therefore, we have:

324 = (700 + x) - (10x + 7)

324 = 700 + x - 10x - 7

9x = 693 - 324 (Like terms)

9x = 369

x = 369/9

x = 41

<u>The original three-digit number is 417</u>

5 0

2 years ago

The sum of a number b and 3 is greater than 8 and less then 12

snow_lady [41]

The sum of a number b and 3 is greater than 8 and less than 12 <span>=> b + 3 < 8
=> b + 3 > 12

</span> <span>Now, let’s combine this into an expression:
=> 8 < b+3 < 12
=> (8 - 3) < b < (12 - 3)
=> 5 < b < 9
Thus, the answer in the given situation is 9 because 9 is greater than 8 but less than 12.

</span>

4 0

2 years ago

Eudora ran from her home to her secret laboratory at an average speed of 12\text{ km/h}12 km/h12, start text, space, k, m, slash

OleMash [197]

Answer:

Eudora spent 0.5 hours from home to library and 1.5 hours from library to school

Step-by-step explanation:

Given

Home to Library:

$S_1 = 12km/h$ -- Average Speed

Library to School

$S_2 = 76km/h$ -- Average Speed

Total

$Distance = 120km$

$Time = 2\ hr$

Required

Determine the time taken from home to library and from library to school

Let the time spent from home to library be x. So, from library to school will be: 2 - x

So, we have:

Home to Library:

$S_1 = 12km/h$ -- Average Speed

$T_1 =x$ -- Time

Library to School

$S_2 = 76km/h$ -- Average Speed

$T_2 =2 - x$ -- Time

Distance is calculated as:

$Distance = Speed * Time$

Home to Library:

$D_1 = S_1 * T_1$

$D_1 = 12 * x$

$D_1 = 12x$

Library to School:

$D_2 = S_2 * T_2$

$D_2 = 76 * (2- x)$

$D_2 = 152- 76x$

The total distance is 120km. So, we have:

$120km = D_1 + D_2$

$120 = 12x + 152 - 76x$

Collect Like Terms

$120 - 152 = 12x - 76x$

$-32 = -64x$

$-64x=-32$

Solve for x

$x = \frac{-32}{-64}$

$x = 0.5$

Recall that:

$T_1 =x$

$T_2 = 2 - x$

So, we have:

$T_1 = 0.5$

$T_2 = 2 -0.5 = 1.5$

4 0

1 year ago

What is square root of the product of the number z and itself<br>

dsp73

Answer:

$\large\boxed{z}$

Step-by-step explanation:

What is square root of the product of the number z and itself?

Break down into smaller parts

What is the product of the number z and itself?

Product = multiply

Write an equation multiplying z by itself

z * z

Bring back the full question: What is the square root of the product of the number z and itself?

Now we can just add a $\sqrt{}$ to the front of our equation to solve the problem.

$\sqrt{z * z}$

Simplify

z * z = $z^{2}$

$\sqrt{z^{2} }$

In this case, the square root cancels out the exponent ( $z^{2}$ ), so $\sqrt{z^{2} }$ can simplify to z.

Hope this helps :)

8 0

2 years ago