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3 years ago

Find the volume of the solid by rotating the region bounded by y=x^3, y=8, and x=0 about the y axis.

Mathematics

1 answer:

dimulka [17.4K]3 years ago

7 0

Answer:

Solution : Volume = 96/5π

Step-by-step explanation:

If we slice at an arbitrary height y, we get a circular disk with radius x, where x = y^(1/3). So the area of a cross section through y should be:

A(y) = πx^2 = π(y^(1/3))^2 = πy^(2/3)

And now since the solid lies between y = 0, and y = 8, it's volume should be:

V = ∫⁸₀ A(y)dy (in other words ∫ A(y)dy on the interval [0 to 8])

=> π ∫⁸₀ y^(2/3)dy

=> π[3/5 * y^(5/3)]⁸₀

=> 3/5π(³√8)⁵

=> 3/5π2^5

=> 96/5π ✓

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Point A is located at (-3, 9) and point B is located at (12,-10). Find the distance from point A to point B rounded to the neare

Nezavi [6.7K]

Answer:

Step-by-step explanation:

$\sqrt{(( - 10) - 9)^{2} + (12 - ( - 3)) ^{2} }$

$\sqrt{( - 19)^{2} + (15)^{2} }$

$\sqrt{361 + 225}$

$\sqrt{586}$

$24.2074$

7 0

2 years ago

Write a number in each blank to complete each equation so that it has the requested number of solutions. a. Equation with no sol

Setler79 [48]

Answer:

The answer is 8 $x$ - 3 $x$ + 2 - $x$ = 4  $x$ + 2  .

Step-by-step explanation:

Given:

8x - 3x + 2 -x = __ x + __

Now, to write a number in each blank to complete each equation so that it has the requested number of solutions.

So, to solve the equation:

$8x-3x+2-x$

So, we add the variables:

$5x+2-x$

And, then subtract it:

$4x-2.$

Thus, it remains:

$4x-2$ .

So the complete equation is:

8 $x$ - 3 $x$ + 2 - $x$ = 4 $x$ + 2

Therefore, the answer is 8 $x$ - 3 $x$ + 2 - $x$ = 4  $x$ + 2  .

4 0

2 years ago

If v = 6i + 3j, what is ||-10v||

tia_tia [17]

The values of ||-10v|| is 51.96 units

Complex numbers are square roots of negative numbers. They are expressions that consist of both the real and imaginary axis.

The general form of a complex number is expressed as z = x + iy

Given the complex number v = 6i + 3j,

10v is expressed as 10(6i + 3j)

10(6i + 3j) = 60i + 30j

Take the modulus of the complex number:

$|10v|=\sqrt{60^2+30^2}\\|10v|= \sqrt{1800+900}\\|10v|= \sqrt{2700} \\|10v|=51.96units$

Hence the values of ||-10v|| is 51.96 units

Learn more on the complex numbers here: brainly.com/question/10662770

6 0

2 years ago

Find the distance between (3,-3) and (2,7)

yarga [219]

Answer:

$\sqrt{101} = D$

Step-by-step explanation:

Method #1

We can draw a right triangle on the graph upon where the points are located and use the Pythagorean Theorem:

${a}^{2} + {b}^{2} = {c}^{2}$

${1}^{2} + {10}^{2} = {c}^{2}$

$1 + 100 = {c}^{2}$

$101 = {c}^{2}$

$\sqrt{101} = c$

* Whenever we talk about distance, we ONLY want the NON-NEGATIVE root.

_______________________________________________

Method #2

Or, we can use the Distance Formula:

$\sqrt{[-x_1 + x_2]^{2} + [-y_1 + y_2]^{2}} = D$

[2, 7] [3, −3]

$\sqrt{[-3 + 2]^{2} + [3 + 7]^{2}} = D$

$\sqrt{[-1]^{2} + 10^{2}} = D$

$\sqrt{1 + 100} = D$

$\sqrt{101} = D$

** You see? It does not matter which method you choose, as long as you are doing the work correctly.

I am delighted to assist you anytime.

5 0

2 years ago

The quotient of the oppositeof 30 and 6,plus the opposite of 8

siniylev [52]

30 = 6 x 5
6 = 3 x 2
8 = 4 x 2

4 x 2 + 3 x 2 + 6 x 5 = 44

5 0

2 years ago