Please help! refer to picture ! edit: nvm

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.

a) The x-axis

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

b) The line y = 2 ( using the shell method )

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

c) The y-axis ( using shell method )

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

d) The line x = -1 (using shell method )

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

In triangle abc, cos A= -0.6. Find A and Tan A

Tresset [83]

Answer:

Part 1) $A=126.87^o$

Part 2) $tan(A)=-\frac{4}{3}$

Step-by-step explanation:

we have

$cos(A)=-0.6$

The cos(A) is negative, that means that the angle A in the triangle ABC is an obtuse angle and the value of the sin(A) is positive

The angle A lie on the II Quadrant

step 1

Find the measure of angle A

$cos(A)=-0.6$

using a calculator

$A=cos^{-1}(-0.6)=126.87^o$

step 2

Find the sin(A)

we know that

$sin^2(A)+cos^2(A)=1$

substitute the value of cos(A)

$sin^2(A)+(-0.6)^2=1$

$sin^2(A)=1-0.36$

$sin^2(A)=0.64$

$sin(A)=0.8$

step 3

Find tan(A)

we know that

$tan(A)=\frac{sin(A)}{cos(A)}$

substitute the values

$tan(A)=\frac{0.8}{-0.6}$

Simplify

$tan(A)=-\frac{4}{3}$

5 0

2 years ago

A)Three out of my four brothers play soccer. What percent of my brothers do not play soccer?

exis [7]

A. 1)25%
B. 2)7
C. 3)48

7 0

3 years ago

Read 2 more answers

Please help me due today

Sati [7]

Answer:

1) C. (3, 5)

2) B. Counterclockwise turn 90 degrees about the origin

3) A. C' (0, -2)

Step-by-step explanation:

i got u bro

5 0

3 years ago

In a class 3/4 of the boys like math, 1/2 like science, 1/4 of those who like science do not like math. How many boys like neith

wariber [46]

Brainiest Answer:
D.1/8

5 0

2 years ago

Please help! refer to picture !edit: nvm