3 and 3/5 divided by 1 and 1/3

The base of a solid is the region enclosed by the graphs of y=e^x, y=0, x=0, and x = 1. If each cross-section perpendicular to t

yanalaym [24]

Answer:

A

Step-by-step explanation:

The base of a solid in the region enclosed by the graphs of y = eˣ, y = 0, x = 0, and x = 1. Each cross-section perpendicular to the x-axis is an equilateral triangle. We want to find the volume of the solid.

Please refer to the graph below. We are concerned with the red region.

In order to find the volume, we essentially sum up the area of the figure at each x value. So, we integrate from x = 0 to x = 1.

The area for an equilateral triangle is given by:

$\displaystyle A=\frac{\sqrt{3}}{4}s^2$

Where s is the side length of the triangle.

Since the triangle lies perpendicular on the region, the side length of the triangle at x is simply y, which is eˣ.

Therefore, our volume is:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(y)^2\, dx$

Substitute:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(e^x)^2\, dx$

Evaluate the integral. Simplify:

$\displaystyle V=\frac{\sqrt3}{4}\int_0^1e^{2x}\, dx$

Integrate using u-substitution:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2x}\Big|_0^1\right)$

Evaluate:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2(1)}-e^{2(0)} \right)$

Therefore, the volume of the solid is:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^2-1\right)$

Our answer is A.

3 0

3 years ago

Read 2 more answers

I'm stuck. how tall is Becky

Korvikt [17]

6ft because 4 to 7 was adding 3 so that means 3 +3 to get 6

Becky is 6ft

3 0

3 years ago

Read 2 more answers

For the following questions, use the system of equations. 3x + 2y = 14, 2x - 4y = 4. A. Solve the system of equations using eith

Irina18 [472]

Answer:

not the matrix equation but this works

x=4, y=1

Step-by-step explanation:

2x-4y=4 (original equation)

2(3x+2y=14) (do this so that you can subtract or add- it's still equal)

2x-4y=4 (original equation)

6x+4y=28 (after multiplying)

8x=32 (add 2 equations together to cancel out 4y, can also subtract)

x=4 (division)

2(4)-4y=4 (substitution)

8-4y=4 (multiplication)

4y=4 (addition/subtraction)

y=1 (division)

8 0

4 years ago

Find the sum and classify the polynomial based on degree and number of terms.

Andru [333]

$3n^2(5m^2 -2n + 1) + 4m^2 - 11n^4 - 9 = 15m^2n^2 - 6n^3 + 3n^2 + 4m^2 - 11n^4 - 9 =\\15m^2n^2 -11n^4 -6n^3 + 3n^2 + 4m^2 - 9.\\$The degree with respect to the variables m, y is 2.\\With respect to m is 2, with respect to n is 4$

8 0

3 years ago

P and Q are points on the line 3y - 4x = 12

Lorico [155]

Answer:

Step-by-step explanation:

Since the coordinates of P are (0, 1), this makes P the y-intercept of that line. The y-intercept exists where x = 0. And in the coordinate (0, 1), x does in fact equal 0.

Since the one coordinate given in Q is (?, 0), this means that Q is the x-intercept of the line. The x-intercept exists where y = 0. And in the coordinate (?, 0), y does in fact equal 0. So in order to solve for the x coordinate of Q, we plug in a 0 for y and solve for x:

3(0) - 4x = 12 and

-4x = 12 so

x = -3

6 0

3 years ago