xavier

1. If a ball is thrown into the air with an initial velocity of 48 ft/s, its height in feet after t seconds is given by 

y = 48t − 16t^2.

(a)

Find the average velocity of the ball (in ft/s) for the time interval beginning at t = 2 and lasting for each of the following.

(i)

0.5 seconds

 ft/s

(ii)

0.1 seconds

 ft/s

(iii)

0.05 seconds

 ft/s

(iv)

0.01 seconds

 ft/s

(b)

Use your answers from part (a) to estimate the instantaneous velocity (in ft/s) when 

t = 2.

 ft/s

2.The table shows the position of a motorcyclist after accelerating from rest.

t (seconds) 0    1      2     3      4       5       6

s (feet)        0  4.9 10.6 23.1 50.2 109.4 238.1

(a)

Find the average velocity (in ft/s) for each time period.

(i)

[2, 4]

 ft/s

(ii)

[3, 4]

 ft/s

(iii)

[4, 5]

 ft/s

(iv)

[4, 6]

 ft/s

(b)

Plot the points in the table to create a graph of s as a function of t to estimate the instantaneous velocity (in ft/s) when t = 3. (Round your answer to one decimal place.)

 ft/s

A tank holds 6,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.

t (min) 5          10        15      20      25    30

V (gal) 4,164  2,592  1,470  702    174    0                                          

(a)

If P is the point (15, 1,470) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with 

t = 5,

 10, 20, 25, and 30.

(b)

Estimate the slope of the tangent line at P by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to P.

What statistical calculation, which results in the same units as the measured data, represents the average variance of data points from the calculated average of the data set? Proper spelling is required.

Suppose a 15.9722 g sample of a 

N

a

C

l

 and 

K

C

l

 mixture contains 3.5831 g of 

N

a

C

l

.

What is the percent of 

K

C

l

 in the mixture?

Suppose a student starts with 2.4018 g of a sand mixture and separates the components into 1.3012 g of 

NaCl

, 0.5613 g of 

SiO2

, and 0.4503 g of 

CaCO3

Based on the amount of recovered, what is the percent of 

SiO2

 in the sand mixture?