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3 years ago

Find the area of this quadrilateral.

Mathematics

1 answer:

3241004551 [841]3 years ago

3 0

I think the area is 24

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Find the volume of the solid generated when R (shaded region) is revolved about the given line. x=6−3sec y, x=6, y= π 3, and

Dmitrij [34]

Answer:

$V=9\pi\sqrt{3}$

Step-by-step explanation:

In order to solve this problem we must start by graphing the given function and finding the differential area we will use to set our integral up. (See attached picture).

The formula we will use for this problem is the following:

$V=\int\limits^b_a {\pi r^{2}} \, dy$

where:

$r=6-(6-3 sec(y))$

$r=3 sec(y)$

a=0

$b=\frac{\pi}{3}$

so the volume becomes:

$V=\int\limits^\frac{\pi}{3}_0 {\pi (3 sec(y))^{2}} \, dy$

This can be simplified to:

$V=\int\limits^\frac{\pi}{3}_0 {9\pi sec^{2}(y)} \, dy$

and the integral can be rewritten like this:

$V=9\pi\int\limits^\frac{\pi}{3}_0 {sec^{2}(y)} \, dy$

which is a standard integral so we solve it to:

$V=9\pi[tan y]\limits^\frac{\pi}{3}_0$

so we get:

$V=9\pi[tan \frac{\pi}{3} - tan 0]$

which yields:

$V=9\pi\sqrt{3}$ ]

6 0

4 years ago

Andrew believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request.

nadya68 [22]

Answer:

Honor students have a probability of 43% to non-honor students 25%.

Step-by-step explanation:

Prob of honor student getting math class choice = 215/500 = 43%

Prob of non-honor student getting math class choice = 125/500 = 25%

5 0

3 years ago

If m^2 = 3 then what is the value of 5m^6 a. 15 b. 30 c. 45 d. 135

Virty [35]

Answer:

135

Step-by-step explanation:

m^2 = 3

Cube m^2

(m^2)^3 = 3^3

m^(2*3) = 27

m^6 = 27

Now multiply by 5

5 * m^6 = 5*27

5 m^6 =135

4 0

3 years ago

You have $4.55 made up of an equal number of pennies, nickles, dimes, quarters and half dollars. How many of each coin do you ha

Papessa [141]

So...

You have 16 quarters. 5 dimes. And 1 nickel. (Half dollars are 2 quarters put together)

I hope this helps!

4 0

3 years ago

The graph of g(x) is the graph of f(x) = x^2 shifted 4 units left, vertically streched by a factor of 3, then shifted 5 units up

Papessa [141]

I think it would be (x)=2x2

5 0

3 years ago

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