⚠️⚠️ DONT IGNOR ⚠️⚠️ <br><br> WHAT IS THE ANSWER AND WHICH IS PROPORTIONAL ¿

Consider an object moving along a line with the given velocity v. Assume t is time measured in seconds and velocities have units

Yakvenalex [24]

Answer:

a) positive direction: t < 2s & t>6s ; negative direction: 2s < t < 6s

b) 7 m

c) 71 m

Step-by-step explanation:

Given:

v(t) = 3t^2 -24t +36 [0 , 7]

Find:

a) The value of time when particle is moving in positive direction:

The change in direction of the particle can be determined by v(t) > 0

Hence,

0 < 3t^2 -24t +36

0 < t^2 - 8t + 12

0 < (t - 2)*(t - 6)

t < 2s , t > 6s

The particle travels in positive direction in the interval t < 2s and t > 6s , While it travels in negative direction when 2s < t < 6s.

b) The displacement ds over the given interval [ 0 , 7 ]

ds = integral (v(t)).dt

ds = t^3 -12t^2 +36t

ds = 7^3 -12*7^2 +36*7

ds = 7 m

c) Total distance traveled in the interval:

Total distance= ds(0-2) + ds(2-6) + ds(6-7)

D = 2*(2^3 -12*2^2 +36*2) - 2*(6^3 -12*6^2 +36*6) + 7

D = 2*32 - 2*0 + 7

D = 71 m

6 0

3 years ago

The accompanying frequency distribution represents the square footage of a random sample of 500 houses that are owner occupied y

ioda

Answer:

$\bar X = \frac{\sum x_i f_i}{n} = \frac{1220750}{500}=2441.5$

$s^2= \frac{3408029125 -\frac{(1220750)^2}{500}}{500-1} =856849.7$

$s= \sqrt{856849.7}=925.662$

Step-by-step explanation:

For this case we can create the following table

Interval Frequency (f) Midpoint(xi) xi *f xi^2* f

0-499 9 249.5 2245.5 560252.3

500-999 13 749.5 9743.5 7302753

1000-1499 33 1249.5 41233.5 51521258.25

1500-1999 115 1749.5 201193.5 361986278.8

2000-2499 125 2249.5 281187.5 632531281.3

2500-2999 81 2749.5 222709.5 612339770.3

3000-3499 47 3249.5 152726.5 496284761.8

3500-3999 45 3749.5 168727.5 632643761.3

4000-4499 22 4249.5 93489 397281505.5

4500-4999 10 4749.5 47495 225577502.5

Total 500 1220750 3408029125

$\sum f_i = 500 , \sum x_i f_i = 1220750, \sum x^2_i f_i = 3408029125$

For this case we can calculate the sample mean with this formula:

$\bar X = \frac{\sum x_i f_i}{n} = \frac{1220750}{500}=2441.5$

And for the sample variance we can use the following formula:

$s^2= \frac{\sum x^2_i f_i - \frac{(\sum x_i f_i)^2}{n}}{n-1}$

And if we replace we got:

$s^2= \frac{3408029125 -\frac{(1220750)^2}{500}}{500-1} =856849.7$

And the deviation is just the square root of the sample variance and for this case is:

$s= \sqrt{856849.7}=925.662$

4 0

3 years ago

Write 7.42 as a mixed num6in simplest form<br>

Ad libitum [116K]

Answer:

idkjdjdjsskjajsojdjdisiw8282i2i2i22 hsjsjsjwiw shsjs

3 0

3 years ago

Determine the slope and y-intercept of a line that passes through the points (-2, 6) and

Andrei [34K]

Answer:

Y = 3

Step-by-step explanation:

Y = -3/2x +3

Y = -3/2 × 0 + 3

Y = 3

3 0

3 years ago

Read 2 more answers

How to turn 19 / 11 in simplest form

Tasya [4]

It's technically in it's simplified form unless you want the decimal of 1.727 (1.73)

8 0

3 years ago

Read 2 more answers

⚠️⚠️ DONT IGNOR ⚠️⚠️ WHAT IS THE ANSWER AND WHICH IS PROPORTIONAL ¿