Which statement is not true about the numbers represented by the points on the number

The height of a cone is twice the radius of its base. A cone has a height of 2 x and a radius of x. What expression represents t

notsponge [240]

Answer:

Let's Find it!

Step-by-step explanation:

So let's use the formula for the volume of a cone:

$V=\pi r^{2} \frac{h}{4} \\V=\pi *x^{2} *\frac{1}{2} x\\V=\frac{1}{2} \pi x^{3}$

So there you go!(you could also plug the things in google but thats okay)

Hope this Helps!

P.S. Stay Safe!

5 0

3 years ago

Read 2 more answers

A 500 gallon tank initially contains 200 gallons of water with 5 lbs of salt dissolved in it. Water enters the tank at a rate of

Lapatulllka [165]

Until the concerns I raised in the comments are resolved, you can still set up the differential equation that gives the amount of salt within the tank over time. Call it $A(t)$ .

Then the ODE representing the change in the amount of salt over time is

$\dfrac{\mathrm dA}{\mathrm dt}=\text{rate in}-\text{rate out}$
$\dfrac{\mathrm dA}{\mathrm dt}=\dfrac{2\text{ gal}}{1\text{ hr}}\times\dfrac{\frac15(1+\cos t)\text{ lbs}}{1\text{ gal}}-\dfrac{2\text{ gal}}{1\text{ hr}}\times\dfrac{A(t)\text{ lbs}}{500+(2-2)t}$
$\dfrac{\mathrm dA}{\mathrm dt}=\dfrac25(1+\cos t)-\dfrac1{250}A(t)$

and this with the initial condition $A(0)=5$

You have

$\dfrac{\mathrm dA}{\mathrm dt}+\dfrac1{250}A(t)=\dfrac25(1+\cos t)$
$e^{t/250}\dfrac{\mathrm dA}{\mathrm dt}+\dfrac1{250}e^{t/250}A(t)=\dfrac25e^{t/250}(1+\cos t)$
$\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/250}A(t)\right]=\dfrac25e^{t/250}(1+\cos t)$

Integrating both sides gives

$e^{t/250}A(t)=100e^{t/250}\left(1+\dfrac1{62501}\cos t+\dfrac{250}{62501}\sin t\right)+C$
$A(t)=100\left(1+\dfrac1{62501}\cos t+\dfrac{250}{62501}\sin t\right)+Ce^{-t/250}$

Since $A(0)=5$ , you get

$5=100\left(1+\dfrac1{62501}\right)+C\implies C=-\dfrac{5937695}{62501}$

so the amount of salt at any given time in the tank is

$A(t)=100\left(1+\dfrac1{62501}\cos t+\dfrac{250}{62501}\sin t\right)-\dfrac{5937695}{62501}e^{-t/250}$

The tank will never overflow, since the same amount of solution flows into the tank as it does out of the tank, so with the given conditions it's not possible to answer the question.

However, you can make some observations about end behavior. As $t\to\infty$ , the exponential term vanishes and the amount of salt in the tank will oscillate between a maximum of about 100.4 lbs and a minimum of 99.6 lbs.

5 0

4 years ago

A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arran

jeyben [28]

To solve this, simply multiply:

5 x 7 = 35

There are 35 different ways he can arrange his program :)

Hopefully this helps! If you have any more questions or don't understand, feel free to DM me, and I'll get back to you ASAP! :)

5 0

4 years ago

Read 2 more answers

What’s the missing length

mezya [45]

Answer:

a=9in

Step-by-step explanation:

Pythagoreans Theorem

a^2+5.6^2=10.6^2

a^2+31.36=112.36

a^2=81

(take square root of both sides)

a=9

7 0

3 years ago

A certain TV can be purchased from the manufacturer for $160.

levacccp [35]

I'd you buy it online, it will cost $208
At the Superstore, the TV will cost $224
The difference is $16
The more you Mark the TV up, the more it will cost

7 0

3 years ago