Find the rule. Solve for n

The base of a solid is the region in the first quadrant between the graph of y=x2 and the x -axis for 0≤x≤1 . For the solid, eac

nata0808 [166]

Answer:

The volume of the solid is π/40 cubic units.

Step-by-step explanation:

Please refer to the graph below.

Recall that the area of a semi-circle is given by:

$\displaystyle A=\frac{1}{2}\pi r^2$

The volume of the solid will be the integral from x = 0 to x = 1 of area A. Since the diameter is given by y, then the radius is y/2. Hence, the volume of the solid is:

$\displaystyle V=\int_0^1\frac{1}{2}\pi \left(\frac{y}{2}\right)^2\, dx$

Substitute:

$\displaystyle V=\frac{1}{2}\pi\int_0^1\left(\frac{x^2}{2}\right)^2\, dx$

Simplify:

$\displaystyle V=\frac{1}{2}\pi \int_0^1\frac{x^4}{4}\, dx$

Integrate:

$\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right]$

Evaluate:

$\displaystyle V=\frac{\pi}{40}\left((1)^5-\left(0\right)^5\right)=\frac{\pi}{40}\text{ units}^3$

The volume of the solid is π/40 cubic units.

4 0

3 years ago

Arliss has two pieces of carpet runner. One is2/13 yards long and the other3/13

Lunna [17]

Solution steps:

1. Add the two given fractions.

2. Subtract the sum from 10 to find your answer.

3 0

3 years ago

Read 2 more answers

The height of a triangle is 4 inches. Greater than twice it's base. The area of the triangle is no more than 168 in.². Which any

mestny [16]

Step-by-step explanation:

this problem seeks to test our knowledge on word problems and algebra

Solution

let the base be x, and

the height h = 2x+4

We know that area of a triangle is given as

$A= \frac{1}{2} b*h$

substituting our given values we have

$168= \frac{1}{2} x*(2x+4)\\\\168= \frac{2x^2+4x}{2} \\\\168= x^2+2x\\\\$

re-arranging we have

$x^2+2x-168=0\\\\$

we can now find two factors that will add up to give 2 and multiply to give -168

they are 14 and -12

$x^2-14x+12x-168=0\\\\x(x-14)+12(x- 14)=0\\\\x+12=0\\\\x=-12\\\\x-14=0\\\\x=14$

The possible base of the triangle is 14 in

and the height is

$h= 2x+4\\\\h=2(14)+4\\\\h= 28+4\\\\\h= 32 in$

7 0

3 years ago

A, B, and C are collinear, and B is between A and C. The ratio of AB to BC is 3 : 1.

S_A_V [24]

Coordinates of point C: (1,-1)

Step-by-step explanation:

In this problem, A, B and C are collinear, and B is between A and C.

The ratio AB : BC is 3 : 1.

This means that we can write the following two equations:

$x_B-x_A = 3(x_C-x_B)\\y_B-y_A=3(y_X-y_B)$

where:

$(x_A,y_A)=(-7,3)$ are the coordinates of point A

$(x_B,y_B)=(-1,0)$ are the coordinates of point B

$(x_C,y_C)$ are the coordinates of point C

Solving the equation for $x_C$ ,

$x_C = x_B + \frac{x_B-x_A}{3}=-1+\frac{-1-(-7)}{3}=1$

Solving the equation for $y_C$ ,

$y_C=y_B + \frac{y_B-y_A}{3}=0+\frac{0-3}{3}=-1$

So, the coordinates of point C are

$C(-1,1)$

Learn more about how to divide segments:

brainly.com/question/3269852

brainly.com/question/11280112

#LearnwithBrainly

4 0

3 years ago

A sofa is priced at $661.50. There is an 8% sales tax rate. What is the sales tax for the sofa in dollars and cents?

exis [7]

Answer:

$52.92

Step-by-step explanation:

The tax is 8% of $661.50.

8% of $661.50 = 8% × $661.50 = 0.08 × $661.50 = $52.92

Answer: $52.92

5 0

3 years ago