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2 years ago

Line I is shown in the coordinate plane. Is the point (16, 20) on line l ?

Mathematics

1 answer:

Dmitriy789 [7]2 years ago

8 0

Yes, this like has a slope of 4,5, so if you multiply both the x and y by 4 you get 16,20

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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

3 years ago

PLEASE HELP IM STUCK

stellarik [79]

Answer:

-2

Step-by-step explanation:

The slope of a line is rise/run

So, just see how much the line rises/how much the line runs

In this case, the line rises 2 units for every -1 unit it runs

So, the slope is -2

7 0

1 year ago

The heights of a maple tree and a cherry tree have a ratio of 5:2. If the maple tree grew 20 cm and 20 cm was cut off the top of

elena-14-01-66 [18.8K]

Let x be the <span>heights of a maple tree and y be the height of the cherry tree.
We know:
</span> $\frac{x}{y} = \frac{5}{2}$
<span>The new ratio is obtained like this:
</span> $\frac{x+20}{y-20} = \frac{3}{1}$ .
From the above equation we get $x= (y-20)\frac{3}{1} -20$ .
then $\frac{ (y-20)\frac{3}{1} -20}{y} = \frac{5}{2}$
Solving the above equation for y we get: $y=160$
So $x=400$
So the first tree is (400-160=240) more taller than cherry tree.

7 0

3 years ago

What is the answer to this question below guys.

Mashutka [201]

Answer:

Step-by-step explanation:

6+8=14

7 0

3 years ago

Which statement is NOT a step used when constructing an inscribed hexagon?

den301095 [7]

Answer:

Swing two arcs above and below the radius.

Step-by-step explanation:

We want to determine which statement is NOT a step used when constructing an inscribed hexagon?

1. Swing two arcs above and below the radius. False

2. Draw a radius of the circle using a straightedge. True

3. Place the compass on the point where the circle and radius intersect. True

4. Swing an arc the length of the radius from the point on the circle. True

The first choice is the correct answer.

3 0

3 years ago