Part III
1.
2.
3.
4.
5.
#36
Solve the following equation and express the roots in simplest a + bi form.
x 2  4 x  12  0
Solve the following equation and express the roots in simplest a + bi form.
x2  4x  5  0
Solve the following equation and express the roots in simplest a + bi form.
4 x 2  6x  9  0
Solve the following equation and express the roots in simplest a + bi form.
9 x 2  8x  16  0
Solve the following equation and express the roots in simplest a + bi form.
2 x 2  4  5x
#37 Answer a or b but not both
1. a) One force of 30 pounds and one force of 20 pounds act on a body at the same
point so that the resultant force is 25 pounds. Find, to the nearest degree, the angle
between the original two forces.
b) In acute triangle RST, m <R = 420 , m <T = 860 , and ST = 16. Find RT to the
nearest whole number.
2. a) One force of 30 pounds and one force of 20 pounds act on a body at the same
point so that the resultant force is 45 pounds. Find, to the nearest degree, the angle
between the original two forces.
b) In acute triangle RST, m <R = 310 , m <T = 760 , and ST = 16. Find RT to the
nearest whole number.
3. a) One force of 50 pounds and one force of 85 pounds act on a body at the same
point so that the resultant force is 66 pounds. Find, to the nearest degree, the angle
between the original two forces.
b) In acute triangle RST, m <R = 420 , m <T = 1060 , and ST = 55. Find RT to the
nearest whole number.
4. a) One force of 17.4 pounds and one force of 55.2 pounds act on a body at the
same point so that the resultant force is 71.9 pounds. Find, to the nearest degree,
the angle between the original two forces.
b) In acute triangle RST, m <R = 120 , m <T = 750 , and ST = 41. Find RT to the
nearest whole number.
5. a) One force of 300 pounds and one force of 200 pounds act on a body at the same
point so that the resultant force is 250 pounds. Find, to the nearest degree, the
angle between the original two forces.
b) In acute triangle RST, m <R = 670 , m <T = 420 , and ST = 28.6. Find RT to the
nearest whole number.
#38
1. a) On the same set of axes, sketch and label the graph of y  sin 2 x and
y  3cos x in the interval 0  x  2 . b) Based on the graphs drawn in part a find
all values of x in the interval graphed where the two functions are equal.
2. a) On the same set of axes, sketch and label the graph of y  sin 3x and
y  2 cos x in the interval 0  x  2 . b) Based on the graphs drawn in part a find
all values of x in the interval graphed where the two functions are equal.
1
3. a) On the same set of axes, sketch and label the graph of y  sin x and
2
y  2 cos 2 x in the interval 0  x  2 . b) Based on the graphs drawn in part a
find all values of x in the interval graphed where the two functions are equal.
4. a) On the same set of axes, sketch and label the graph of y  tan x and
y  2 cos x in the interval 0  x  2 . b) Based on the graphs drawn in part a find
all values of x in the interval graphed where the two functions are equal.
1
5. a) On the same set of axes, sketch and label the graph of y  sin x and
2
y  2 cos 2 x in the interval 0  x  2 . b) Based on the graphs drawn in part a
find all values of x in the interval graphed where the two functions are equal.
#39
39. The table below represents data gathered by a research company.
a) Graph the scatter plot of the given information.
b) Find the linear equation of best fit for the given data. Round decimals to two
places.
c) Find the correlation coefficient “r” correct to four decimal places.
d) Use the equation found in part b, with the rounded values, to estimate the
value of y when x = 15.
x
3
5
7
9
11
y
4
6
32
55
83
39. The table below represents data gathered by a research company.
a) Graph the scatter plot of the given information.
b) Find the linear equation of best fit for the given data. Round decimals to two
places.
c) Find the correlation coefficient “r” correct to four decimal places.
d) Use the equation found in part b, with the rounded values, to estimate the
value of y when x = 22.
x
7
9
11
13
15
y
-2
1
7
16
27
39. The table below represents data gathered by a research company.
a) Graph the scatter plot of the given information.
b) Find the linear equation of best fit for the given data. Round decimals to two
places.
c) Find the correlation coefficient “r” correct to four decimal places.
d) Use the equation found in part b, with the rounded values, to estimate the
value of y when x = 23.
x
0
5
10
15
20
y
-5
1
8
14
21
39. The table below represents data gathered by a research company.
a) Graph the scatter plot of the given information.
b) Find the exponential equation of best fit for the given data. Round decimals to
two places.
c) Find the correlation coefficient “r” correct to four decimal places.
d) Use the equation found in part b, with the rounded values, to estimate the
value of y when x = 8.
x
1
2
3
4
5
6
y
2
6
10
25
60
120
39. The table below represents data gathered by a research company.
e) Graph the scatter plot of the given information.
f) Find the quadratic equation of best fit for the given data. Round decimals to
two places.
g) Find the correlation coefficient “r2” correct to four decimal places.
h) Use the equation found in part b, with the rounded values, to estimate the
value of y when x = 11.
x
0
1
2
3
4
5
6
7
8
9
y
8
12
13
8
3
2
6
10
14
9
39. The table below represents data gathered by a research company.
i) Graph the scatter plot of the given information.
j) Find the quadratic equation of best fit for the given data. Round decimals to
two places.
k) Find the correlation coefficient “r2” correct to four decimal places.
l) Use the equation found in part b, with the rounded values, to estimate the
value of y when x = 15.
x
3
5
7
9
11
y
4
6
32
55
83
39. The table below represents data gathered by a research company.
e) Graph the scatter plot of the given information.
f) Find the quadratic equation of best fit for the given data. Round decimals to
two places.
g) Find the correlation coefficient “r2” correct to four decimal places.
h) Use the equation found in part b, with the rounded values, to estimate the
value of y when x = 22.
x
7
9
11
13
15
y
-2
1
7
16
27
39. The table below represents data gathered by a research company.
e) Graph the scatter plot of the given information.
f) Find the quadratic equation of best fit for the given data. Round decimals to
two places.
g) Find the correlation coefficient “r2” correct to four decimal places.
h) Use the equation found in part b, with the rounded values, to estimate the
value of y when x = 23.
x
0
5
10
15
20
y
-5
1
8
14
21
39. The table below represents data gathered by a research company.
e) Graph the scatter plot of the given information.
f) Find the quadratic equation of best fit for the given data. Round decimals to
two places.
g) Find the correlation coefficient “r2” correct to four decimal places.
h) Use the equation found in part b, with the rounded values, to estimate the
value of y when x = 8.
x
1
2
3
4
5
6
y
2
6
10
25
60
120
39. The table below represents data gathered by a research company.
i) Graph the scatter plot of the given information.
j) Find the linear equation of best fit for the given data. Round decimals to two
places.
k) Find the correlation coefficient “r” correct to four decimal places.
l) Use the equation found in part b, with the rounded values, to estimate the
value of y when x = 18.
x
3
7
9
11
13
15
Y
2
6
10
25
60
120