Learn more about our help with Assignments: Math
Search & Filtering
17. You are designing a rectangular poster which will have a rectangular printed area surrounded by margins of width 10 cm at the top and the bottom, and margins of width 7.5 cm at both sides. If the total area of the poster is to be 1m^2, fi nd the maximum possible printed area.
1.Suppose that for all x >= 0, the average value of f(x) on [0; x] is equal to x. What is the
funtion f(x)?
2.The equation x^4+x^3-4 = 0 has a solution near x = 1. Use Newton's method to fi nd this
solution correct to 8 signfi cant fi gures.
3.At a certain moment, a triangle has base length 10 cm and perpendicular height 8 cm. The
length is increasing at a rate of 1 cm/s while the height is decreasing at 1 cm/s. How fast is the
area changing? Is the area increasing or decreasing?
funtion f(x)?
2.The equation x^4+x^3-4 = 0 has a solution near x = 1. Use Newton's method to fi nd this
solution correct to 8 signfi cant fi gures.
3.At a certain moment, a triangle has base length 10 cm and perpendicular height 8 cm. The
length is increasing at a rate of 1 cm/s while the height is decreasing at 1 cm/s. How fast is the
area changing? Is the area increasing or decreasing?
A piece of wire of length 52 m is cut into two parts. Each part is then bent to form a square. It is found that the combined area of two squares is 109 m^2. Find the measures of the sides of the two squares.
Find the value of:-
sin4A-cos4A=sin2A-cos2A
sin4A-cos4A=sin2A-cos2A
if tana=b/a, prove that acos2a+bsin2a=a
2. Car insurance companies assume that the longer a person has been driving, the less likely they will be in an accident, and therefore charge new drivers higher insurance premiums than experienced drivers. To determine whether driving experience is related to the number of car accidents, you survey a random sample of 12 Torontonians and ask them about the number of years they have been driving, and the number of car accidents they have been involved in during the past year. The data are presented below:
Driver # of years driving (X) # of car accidents (Y)
A 4.5 3
B 2.5 5
C 1.5 3
D 3 3
E 1.5 6
F 5 2
G 5 0
H 2 4
I 3 1
J 4 2
K 1 5
L 3 2
a. Determine whether the assumptions of car insurance companies are valid. Assuming α=0.05, include the hypotheses for a one-tailed test, critical test statistic, conclusion, and all formulas and calculations.
b. Is it appropriate to conclude that lack of driving experience causes accidents? Why or why not?
Driver # of years driving (X) # of car accidents (Y)
A 4.5 3
B 2.5 5
C 1.5 3
D 3 3
E 1.5 6
F 5 2
G 5 0
H 2 4
I 3 1
J 4 2
K 1 5
L 3 2
a. Determine whether the assumptions of car insurance companies are valid. Assuming α=0.05, include the hypotheses for a one-tailed test, critical test statistic, conclusion, and all formulas and calculations.
b. Is it appropriate to conclude that lack of driving experience causes accidents? Why or why not?
b) The height of 40 students were measured and recorded as follows;
38.7 40.2 55.4 60.9 70.1 72.5 50.4 63.7
39.4 54.6 59.3 60.2 45.1 66.5 37.9 74.2
44.5 59.6 55.2 60.7 68.0 70.0 71.2 48.3
49.4 54.4 60.9 64.7 69.3 57.4 46.2 68.9
55.3 70.2 71.7 63.2 55.4 39.0 40.3 44.5
Using classes of 35-39, 40-44,- - - calculate;
i. The arithmetic mean
ii. The standard deviation
38.7 40.2 55.4 60.9 70.1 72.5 50.4 63.7
39.4 54.6 59.3 60.2 45.1 66.5 37.9 74.2
44.5 59.6 55.2 60.7 68.0 70.0 71.2 48.3
49.4 54.4 60.9 64.7 69.3 57.4 46.2 68.9
55.3 70.2 71.7 63.2 55.4 39.0 40.3 44.5
Using classes of 35-39, 40-44,- - - calculate;
i. The arithmetic mean
ii. The standard deviation
A man is walking along a sidewalk at the rate of 5 feet/sec. A searchlight on the ground 30 feet from the walk is kept trained on him. At what rate is the searchlight revolving when the man is 20 feet away from the point on the sidewalk nearest the light?
A building 8 feet high is 27/8 feet from a building. Find the length of the shortest ladder which will clear the wall and rest with one end on the ground and the other end on the building. Also, find the angle which this ladder makes with the horizontal?
An airplane at an altitude at an altitude of 4400 feet is flying horizontally away from an observer. At the instant when the angle of elevation is 45 degrees, the angle is decreasing at the rate of 0.5 rad/sec. How fast is the airplane flying at that instant?
