Use the number line.what fraction of 1 foot is 3 inches? what fraction of 1 yard is 3 inches

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

Can someone help me with this real quick?

valentina_108 [34]

Answer:

11. A) 6x = 13

Step-by-step explanation:

11. Subtract 10 from both sides to make it equal 6x=13

12. For #12... None of the answers seem right? If you distribute and subtract, it should be

-4x + 44 = 66 then

-4x = 22...

Sorry if this didn’t help much, I know that 11 is right though ;)

6 0

3 years ago

The temperature in your town is 31 degrees Fahrenheit. The radio announcer says that the temperature will drop 15 degrees.What w

laiz [17]

Hi,

New temperature will be 31 F - 15 F = 16 F.

Green eyes.

4 0

3 years ago

Read 2 more answers

Whaaaaaaaaaaaaat????

IrinaK [193]

9514 1404 393

Answer:

7 pizzas

Step-by-step explanation:

For a difference in price of $58 -25 = $33, a customer gets a difference in number of 5 -2 = 3 pizzas. Then a pizza costs $33/3 = $11.

The cost of 2 pizzas is $22, so the delivery charge is $25 -22 = $3.

For $80, after subtracting the $3 delivery charge, $77 goes to the cost of pizzas. For that amount, $77/$11 = 7 pizzas will be delivered.

3 0

3 years ago

rancher wants to fence in an area of 2000000 square feet in a rectangular field and then divide it in half with a fence down the

zheka24 [161]

Answer:

7000ft

Step-by-step explanation:

let's break down 2,000,000 into its multiples,

Multiples of 2,000,000= 2⁷ × 5⁶

Using above values to find different combinations of length(l) and breadth (b) of rectangle and corresponding parameter of rectangle

l=5, b=400,000 ,parameter= 2(5) + 2(400,000)= 800,010, total length of fence required= parameter+ side with shortest length= 800,015

l=2 b=1,000,000 parameter= 2,000,004, shortest fence required= 2,000,008

l=4, b= 500,000 parameter= 1,000,008, shortest fence required= 1,000,012
From above, we can see a trend that the parameter of rectangle decreases if length and breadth are increased provided that area is constant. So, a rectangle will have shortest parameter if all of its sides are equal.
length of side of rectangle with shortest possible parameter= 2^3 ×5^3= 1000 and breadth of side of rectangle with shortest possible parameter= 2^4× 5^3=2000
Shortest possible length of fence= 2(2000)+2(1000)+1000=7000ft

4 0

3 years ago

Read 2 more answers

Use the number line.what fraction of 1 foot is 3 inches? what fraction of 1 yard is 3 inches​

Use the number line.what fraction of 1 foot is 3 inches? what fraction of 1 yard is 3 inches