The dot on the number line represents which fraction?

3 regions are defined in the figure find the volume generated by rotating the given region about the specific line

anastassius [24]

The volume generated by rotating the given region $R_{3}$ about OC is $\frac{4}{g} \pi$

<h3>Washer method</h3>

Because the given region ( $R_{3}$ ) has a look like a washer, we will apply the washer method to find the volume generated by rotating the given region about the specific line.

solution

We first find the value of x and y

$y=2(x)^{\frac{1}{4} }$

$x=(\frac{y}{2} )^{4}$

$y=2x$

$x=\frac{y}{2}$

$\int\limits^a_b {\pi } \, (R_{o^{2} } - R_{i^{2} } ) dy$

$R_{o} = x = \frac{y}{2}$

$R_{i} = x= (\frac{y}{2}) ^{4}$

$a=0, b=2$

$v= \int\limits^2_o {\pi } \, [(\frac{y}{2})^{2} - ((\frac{y}{2}) ^{4} )^{2} ) dy$

$v= \pi \int\limits^2_o= [\frac{y^{2} }{4} - \frac{y^{8} }{2^{8} }} ] dy$

$v= \pi [\int\limits^2_o {\frac{y^{2} }{4} } \, dy - \int\limits^2_o {\frac{y}{2^{8} } ^{8} } \, dy ]$

$v=\pi [\frac{1}{4} \frac{y^{3} }{3} \int\limits^2_0 - \frac{1}{2^{8} } \frac{y^{g} }{g} \int\limits^2_o\\v= \pi [\frac{1}{12} (2^{3} -0)-\frac{1}{2^{8}*9 } (2^{g} -0)]\\v= \pi [\frac{2}{3} -\frac{2}{g} ]\\v= \frac{4}{g} \pi$

A similar question about finding the volume generated by a given region is answered here: brainly.com/question/3455095

6 0

1 year ago

Simplify (11 + 5i)(11 - 51)

Ede4ka [16]

Answer:

(146 + 0i)

Step-by-step explanation:

(11+5i)(11-5i)

The formula is :

(a+bi) • (x+yi) = ax+by•i^2+(ay+bx)i

and since i^2 = -1 it can be written as :

ax - by + (ay + bx) i

( 11 + 5i) • ( 11 - 5i) =

(146 + 0i)

hope this helped brainlest owo???

7 0

2 years ago

Read 2 more answers

What are the coordinates of the vertex of the parabola with the equation y = x + 2x - 3?

loris [4]

Answer:

<em>The coordinates of the vertex are (-1,-4).</em>

Step-by-step explanation:

<u>Equation of the Quadratic Function </u>

The vertex form of the quadratic function has the following equation:

$y-k=a(x-h)^2$

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.

We are given the function:

$y=x^2+2x-3$

We must transform the equation above by completing squares:

The first two terms can be completed to be the square of a binomial. Recall the identity:

$x^2+2xy+y^2=(x+y)^2$

Thus if we add and subtract 1:

$y=(x^2+2x+1)-3-1$

Operating:

$y=(x^2+2x+1)-4$

The trinomial in parentheses is a perfect square:

$y=(x+1)^2-4$

Adding 4:

$y+4=(x+1)^2$

Comparing with the vertex form of the quadratic function, we have the vertex (-1,-4).

The coordinates of the vertex are (-1,-4).

4 0

2 years ago

Set up a System of Equations and Solve

Bumek [7]

Answer:

The cost of each ice cream cone is $4.50

The cost of each ice cream basket is $3.75

The cost of each donut is $1.50

Step-by-step explanation:

Let

x-----> the cost of the ice cream cone

y----> the cost of the ice cream basket

z---> the cost of the donut

we know that

2x+y=12.75 ------> y=12.75-2x ------> equation A

x+2z=7.50 ------> z=(7.50-x)/2 -----> equation B

x+y+z=9.75 ----> equation C

substitute equation A and equation B in equation C and solve for x

x+(12.75-2x)+((7.50-x)/2)=9.75

Multiply by 2 both sides

2x+25.50-4x+7.50-x=19.50

3x=25.50+7.5-19.50

3x=13.5

x=$4.50

Find the value of y

y=12.75-2(4.50)=$3.75

Find the value of z

z=(7.50-4.50)/2=$1.50

therefore

The cost of each ice cream cone is $4.50

The cost of each ice cream basket is $3.75

The cost of each donut is $1.50

6 0

2 years ago

Erica babysits for 4 hours and is paid $33

Aleksandr-060686 [28]

Answer: a: 8.25 b: 49.5

Step-by-step explanation:

7 0

2 years ago