Evaluate the expression : 3m + 2n3m+2n for : m = 12m=12 and : n = 5

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

3 years ago

The angle measurement in the diagram are represented by the following expressions.

8_murik_8 [283]

Answer:

x = 9 and ∠ B = 40°

Step-by-step explanation:

See the diagram given with the question first.

Here we have ∠ A = ∠ B {They are corresponding angles}

Now, it is given that ∠ A = 5x - 5 and ∠ B = 3x + 13

Hence, 5x - 5 = 3x + 13

⇒ 2x = 18

⇒ x = 9

Therefore, ∠ B = 3x + 13 = 3(9) + 13 = 40° (Answer)

5 0

4 years ago

Matt, the coordinator at the local emergency food hamper program, noticed the following trends: typically 200 hampers were distr

photoshop1234 [79]

Answer:

<em>793 food hampers were distributed</em>

Step-by-step explanation:

We need to find how many food hampers were distributed in a typical week, knowing that

200 hampers were distributed on Mondays

40 fewer hampers were distributed on Tuesdays than on Mondays, thus:

160 hampers were distributed on Tuesdays

on Wednesdays, the volume is 1.3 times Tuesday’s volume, thus 160*1.3=

208 hampers were distributed on Wednesdays

on Thursdays the number of hampers distributed was 3/4 of Monday’s volume, thus 3/4*200=

150 hampers were distributed on Thursdays

on Fridays, 50% of Thursday’s volume was distributed, therefore 50%*150=

75 hampers were distributed on Fridays

The total number of food hampers distributed in the week is

200+160+208+150+75=793

793 food hampers were distributed

4 0

3 years ago

Which graph shows this system of equations?

SashulF [63]

Answer:

I believe it is B tell me if I am wrong please

8 0

3 years ago

One way to recognize a ___ is to look for a line that divides the original image into two congruent parts.

Sphinxa [80]

A because the line of symmetry is where the two parts of the image will meet

5 0

3 years ago

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