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3 years ago

Cynthia can wallpaper a room in 4 hours and her brother can do it in 6 hours. How long would it take them if they work together

Mathematics

1 answer:

Debora [2.8K]3 years ago

3 0

Answer:

2 hours and 24 minutes

Step-by-step explanation:

cynthia can wallpaper a room 4 hours with means in 1 hour she can wallpaper 1/4th of the room, her brother can wallpaper the same room in 6 hours so I'm 1 hour he can wallpaper 1/6 of the room.

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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:

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.

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3 years ago

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Please help me out!!!

Tasya [4]

Answer:

you hgave a 2 and you use 5 and you have to add it and it will be 12 and your answer is 15

Step-by-step explanation:

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Aleksandr-060686 [28]

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3 years ago

Please help! ! ! ! !

Vladimir [108]

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3 years ago

Use the vertical line test to determine if the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} is a function. Explain your response

omeli [17]

When you are trying to figure this out put them into a list vertically. Remember, ONE X CAN'T HAVE TO Y's BUT ONE Y CAN HAVE MULTIPLE X's, But dont worry about the y's right now. Lets focus on the x's.

Ask yourself, Are there 2 or more x's that are the same value?
Yes) Continue to next step
No) It's a function :)

If there are 2 or more of the same x value, ask your self now if those x's have different y Values.
Yes) It is not a function, one x can not have more that 1 y value
No) Its a function :)

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3 years ago