How do you get the square root of 100000

allochka39001 [22]

Jdjdndndjdjdmdjdjdjndmdjd

4 0

3 years ago

The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in s

Norma-Jean [14]

The positions when the particle reverses direction are:

$s(t_1)=55ft\\\\s(t_2)=28ft$

The acceleraton of the paticle when reverses direction is:

$a(t_1)=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=18\frac{ft}{s^{2}}$

Why?

To solve the problem, we need to remember that if we derivate the position function, we will get the velocity function, and if we derivate the velocity function, we will get the acceleration function. So, we will need to derivate two times.

Also, when the particle reverses its direction, the velocity is equal to 0.

We are given the following function:

$s(t)=2t^{3}-21t^{2}+60t+3$

So,

- Derivating to get the velocity function, we have:

$v(t)=\frac{ds}{dt}=(2t^{3}-21t^{2}+60t+3)\\\\v(t)=3*2t^{2}-2*21t+60*1+0\\\\v(t)=6t^{2}-42t+60$

Now, making the function equal to 0, to find the times when the particle reversed its direction, we have:

$v(t)=6t^{2}-42t+60\\\\0=6t^{2}-42t+60\\\\0=t^{2}-7t+10\\(t-5)*(t-2)=0\\\\t_{1}=5s\\t_{2}=2s$

We know that the particle reversed its direction two times.

- Derivating the velocity function to find the acceleration function, we have:

$a(t)=\frac{dv}{dt}=6t^{2}-42t+60\\\\a(t)=12t-42$

Now, substituting the times to calculate the accelerations, we have:

$a(t_1)=a(2s)=12*2-42=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=12*5-42=18\frac{ft}{s^{2}}$

Now, substitutitng the times to calculate the positions, we have:

$s(t_1)=2*(2)^{3}-21*(2)^{2}+60*2+3=16-84+120+3=55ft\\\\s(t_2)=2*(5)^{3}-21*(5)^{2}+60*5+3=250-525+300+3=28ft$

Have a nice day!

3 0

3 years ago

an air conditioning system can circulate 360, cubic feet of air per minute. how many cubic yards of air can it circulate per min

ahrayia [7]

Alright, lets get started.

3 feet = 1 yard

If we cube both sides of the equation, we will get the conversion into cubic yards

So,

$3*3*3 cubic feet = 1 * 1*1 cubic yards$

27 cubic feet = 1 cubic yards

So, 1 cubic feet = $\frac{1}{27}$ cubic yards

So, 360 cubic feet = $360 *\frac{1}{27}$ cubic yards

So, 360 cubic feet = 13.33 cubic yards

13.33 cubic yards of air can it circulate per minute. : Answer

Hope it will help :)

3 0

3 years ago

Read 2 more answers

Which relation is a function? Help please

WARRIOR [948]

Answer:

The bottom right (v shaped one) is a function

Step-by-step explanation:

Hope this helps:)

4 0

2 years ago

Read 2 more answers

Dave has a 32-ounce energy drink. He drinks 10 ounces. Enter the percentage of ounces Dave had left from his energy drink. Round

balandron [24]

68.75 percent hope this helps

3 0

4 years ago

Read 2 more answers