66,649 is 70% of what number

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

PLS ANSWER QUICK LOL

Setler [38]

(3j, 3k) and (3/j, 3k)

So if their x values have the same signs and their y values have the same signs, they are in the same quadrant.

If j is negative, both 3j and 3/j would be negative. If j is positive then both 3j and 3/j are positive.

And 3k is the same as 3k.

5 0

3 years ago

Read 2 more answers

What's the answer to -2(2x + 2)= 8

Yanka [14]

If you’re trying to find x, x = 3.

4 0

3 years ago

A square and a rectangle have the same perimeter. Find the side lengths of each figure.

aliina [53]

X + 1 + X + 1 + X +1+ X +1 = 2X -3+ 2X -3+ X -1+ X -1
4x + 4 = 4x-6+2x-2
4x+4=6x-8
12=2x
6=x

Side lengths:
6-1=5
6+1=7
2(6)-3=9

Hope that helps! Stay safe!

4 0

3 years ago

Read 2 more answers

HI! I HAVE A TEST ON MONDAY AND IM TRYING TO STUDY, IM KINDA STUCK ON HOW TO DO THIS PROBLEM..

sergij07 [2.7K]

Answer: See below

Step-by-step explanation:

number of yellow pieces/number of blue pieces

= 14/24

= 7/12 --> 7 to 12 --> 7:12

The ratio that represents the number of yellow pieces to the total number of pieces is part-to-whole

number of yellow pieces/total number of pieces

= 14/100

= 7/50 --> 7 to 50 --> 7:50

The ratio that represents the number of blue pieces to the total number of pieces is part-to-whole

= 24/100

= 6/25 --> 6 to 25 --> 6:25

8 0

2 years ago