What does the tape measure say Measurement # 3 is? *

Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graph

diamong [38]

Answer:

a) 8π

b) 8/3 π

c) 32/5 π

d) 176/15 π

Step-by-step explanation:

Given lines : y = √x, y = 2, x = 0.

using the shell method

y = √x = , x = y^2

h = y^2 , p = y

vol = ( 2π ) $\int\limits^2_0 {ph} \, dy$

= $( 2\pi ) \int\limits^2_0 {y.y^2} \, dy$

∴ Vol = 8π

<u>b) The line y = 2 ( using the shell method )</u>

p = 2 - y

h = y^2

vol = ( 2π ) $\int\limits^2_0 {ph} \, dy$

= $( 2\pi ) \int\limits^2_0 {(2-y).y^2} \, dy$

= ( 2π ) * [ 2/3 * y^3 - y^4 / 4 ] ²₀

∴ Vol = 8/3 π

<u>c) The y-axis ( using shell method )</u>

h = 2-y = h = 2 - √x

p = x

vol = $(2\pi ) \int\limits^4_0 {ph} \, dx$

= $(2\pi ) \int\limits^4_0 {x(2-\sqrt{x} ) } \, dx$

= ( 2π ) [x^2 - 2/5*x^5/2 ]⁴₀

vol = ( 2π ) ( 16/5 ) = 32/5 π

<u>d) The line x = -1 (using shell method )</u>

p = 1 + x

h = 2√x

vol = $(2\pi ) \int\limits^4_0 {ph} \, dx$

Hence vol = 176/15 π

attached below is the graphical representation of P and h

3 0

3 years ago

Which of the following statements is false?

kramer

Option D

The sum of two irrational numbers is always rational is false statement

<em><u>Solution:</u></em>

<h3><u>The sum of two rational numbers is always rational</u></h3>

"The sum of two rational numbers is rational."

So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number.

For example:

$\frac{1}{4} + \frac{1}{5} = \frac{9}{20}$

rational number + rational number = rational number

Hence this statement is true

<h3><u>The product of a non zero rational number and an irrational number is always irrational</u></h3>

If you multiply any irrational number by the rational number zero, the result will be zero, which is rational.

Any other situation, however, of a rational times an irrational will be irrational.

A better statement would be: "The product of a non-zero rational number and an irrational number is irrational."

So this statement is correct

<h3><u>The product of two rational numbers is always rational</u></h3>

The product of two rational numbers is always rational.

A number is said to be a rational number if it is of the form p/q,where p and q are integers and q ≠ 0

Any integer is a rational number because it can be written in p/q form.

Hence it is clear that product of two rational numbers is always rational.

So this statement is correct

<h3><u>The sum of two irrational numbers is always rational</u></h3>

"The sum of two irrational numbers is SOMETIMES irrational."

The sum of two irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational.

Thus this statement is false

5 0

3 years ago

It's a math question please help!

Phoenix [80]

Answer:

Ok

Step-by-step explanation:

I will help you or maybe

4 0

3 years ago

Harry solved a quadratic equation. His work is shown below.

Pie

Answer:

x = 11 or x = -1

Step-by-step explanation:

(x-5)^2 = 36

(x-5) = 6 or (x-5)= -6

then x = 11 or x = -1

4 0

2 years ago

Read 2 more answers

Find the circumference and area of a circle with radius 3 yd. use the value 3.14 for pie

just olya [345]

Answer: circumference = 2Πr²

Where r= 3

Π=3.14

Therefore Circumference = 2×3.14× 3²

= 2×28.26

Circumference=56.52

Formula:

Subtitute in 3 for r.

Solve and the answer is 28.26

4 0

3 years ago

Read 2 more answers