Use the graph of the function to find its domain and range. Write the domain and range in interval notation

alisha [4.7K]

10√2 is the answer for square root of 200

4 0

3 years ago

At a rate of 36 miles per hour, it takes Henry 15 minutes to drive from the library to his house. Show how to find the distance

EastWind [94]

This is applying the formula
$distance=rate*time$

We have a slight problem, though, because we are measuring rate in miles per hour, and we are measuring time in minutes. To make this problem solvable, we need to convert to either miles per minute or convert the time to hours. I'm going to convert the 15 minutes into hours:
$15min*\frac{1 hour}{60 min}=\frac{1}{4}hour$

Now that all of the units match, we have:
$distance=36\frac{mi}{hr}*\frac{1}{4}hr$

You can finish from there I'm sure.

4 0

3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.? y = 2 + se

sertanlavr [38]

Answer:

The volume of the solid is: $\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}$

Step-by-step explanation:

GIven that :

$y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2$

This implies that the distance between the x-axis and the axis of the rotation = 2 units

The distance between the x-axis and the inner ring is r = (2+sec x) -2

Let R be the outer radius and r be the inner radius

By integration; the volume of the of the solid can be calculated as follows:

$V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx$

$V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ]$

$\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}$

7 0

3 years ago

ETHANHUNT HELP PLS NOBODY ELSE DONT ANSWER I DONT TRUST U PEOPLE

notsponge [240]

A regular polygon<span> is a </span>polygon <span>that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

Here, Figure C is an equilateral Triangle which fits the most.

In short, Your Answer would be Option C

Hope this helps!</span>

6 0

3 years ago

Read 2 more answers

Twelve flags are evenly spaced around a running track. Ryan started running at the first flag and took 30 seconds to reach the s

aniked [119]

Answer:

Ryan takes 6n+36m -42 seconds to reach the nth flag for the mth time.

Step-by-step explanation:

It takes Ryan to run from 1st to 6th flag in 30 seconds, so it takes him

30 * 6/3 = 36 seconds to make one complete round.

or it takes 6 seconds to run from one flat to the next.

To reach the nth flag (n=1,2,3,4,5, or 6)

Ryan takes 6(n-1) seconds.

To reach it the mth times, he needs to add 36(m-1) seconds.

So time it takes Ryan to reach the nth flag for the mth time takes

6(n-1) + 36(m-1)

= 6n - 6 + 36m - 36

= 6n+36m -42 seconds

3 0

3 years ago