MATH 17 FINAL EXAM 10-14-2013 MATH 17 FINAL EXAM 10-14-2013
I. Perform as indicated. Show all solutions. I. Perform as indicated. Show all solutions.
1. If sin( π2 −x) = − 45 and cos( π2 −x) = 87 , find the exact 1. If sin( π2 −x) = − 45 and cos( π2 −x) = 78 , find the exact
value of tan x. [4 pts] value of tan x. [4 pts]
2. Find the value of k so that k + 3, k − 2 and 2k + 1 2. Find the value of k so that k + 3, k − 2 and 2k + 1
form an arithmetic progression. [4 pts] form an arithmetic progression. [4 pts]
3. Solve for the third side of the triangle ABC if a = 15, 3. Solve for the third side of the triangle ABC if a = 15,
b = 8 and γ = 49o . [3 pts] b = 8 and γ = 49o . [3 pts]
4. Given that x = (log3 25)(log5 27), find the value of x 4. Given that x = (log3 25)(log5 27), find the value of x
without log. [3 pts] without log. [3 pts]
5. Given that sin x = 35 where x is in Quadrant I, find 5. Given that sin x = 35 where x is in Quadrant I, find
the value of sin( x2 ). [3 pts] the value of sin( x2 ). [3 pts]
6. Find z 10 if z = −1 − i. [3 pts] 6. Find z 10 if z = −1 − i. [3 pts]
4 cis 98o 28 cis 137o 4 cis 98o 28 cis 137o
7. Evaluate z = . [3 pts] 7. Evaluate z = . [3 pts]
7 cis 78o 16 cis 67o 7 cis 78o 16 cis 67o
II. Solve as indicated. Show all solutions. II. Solve as indicated. Show all solutions.
1. Find the solution set of the following equations. 1. Find the solution set of the following equations.
[5 pts each] [5 pts each]
a. e2x+1 − ex+1 = 0 a. e2x+1 − ex+1 = 0
b. [logx (2x + 3)]2 + logx 1 = 3 logx (2x + 3) − log2 4 b. [logx (2x + 3)]2 + logx 1 = 3 logx (2x + 3) − log2 4
c. sin−1 (cos θ) = 2θ where 0 ≤ θ ≤ π
2
c. sin−1 (cos θ) = 2θ where 0 ≤ θ ≤ π
2
2. A sequence has 9 terms. The first five terms form 2. A sequence has 9 terms. The first five terms form
an AP and the last five terms form a GP . If the 1st an AP and the last five terms form a GP . If the 1st
term is 2 and the 5th term is 18, find [3 pts each] term is 2 and the 5th term is 18, find [3 pts each]
a. the sum of the first five terms a. the sum of the first five terms
b. the 9th term if the 7th term is 2 for r > 0. b. the 9th term if the 7th term is 2 for r > 0.
3. A variable E varies directly as the cube of T and 3. A variable E varies directly as the cube of T and
inversely as the square of L. How is E affected when inversely as the square of L. How is E affected when
both T and L are tripled? [5 pts] both T and L are tripled? [5 pts]
4. Find the positive two-digit number for which the 4. Find the positive two-digit number for which the
units digit is 3 more than the tens digit and the sum units digit is 3 more than the tens digit and the sum
of their squares is 29. [5 pts] of their squares is 29. [5 pts]
5. The sketch below shows the cross section of a roof 5. The sketch below shows the cross section of a roof
of a fairly large house. One side must have an angle of a fairly large house. One side must have an angle
of 20o above the horizontal in order to facilitate the of 20o above the horizontal in order to facilitate the
installation of solar electricity batteries. However, installation of solar electricity batteries. However,
the peak of the roof may be only 3.50 m above the the peak of the roof may be only 3.50 m above the
base level. Determine the lengths x, y, and z and base level. Determine the lengths x, y, and z and
the angle θ. [6 pts] the angle θ. [6 pts]
....... .......
.. ..
... ..
y z ..
...
y z ..
...
.. ..
3.50 m 3.50 m
..
20o θ .
...
.. 20o θ ..
...
... .......
. . ...
.
.. . .
................................................................................................ 14.50 m ............................................................................................ ................................................................................................ 14.50 m ............................................................................................
.
......................................................................... x ............................................................ .
......................................................................... x ............................................................
6. A boat has to travel to a port in Istanbul 900 6. A boat has to travel to a port in Istanbul 900
I. Perform as indicated. Show all solutions. I. Perform as indicated. Show all solutions.
1. If sin( π2 −x) = − 45 and cos( π2 −x) = 87 , find the exact 1. If sin( π2 −x) = − 45 and cos( π2 −x) = 78 , find the exact
value of tan x. [4 pts] value of tan x. [4 pts]
2. Find the value of k so that k + 3, k − 2 and 2k + 1 2. Find the value of k so that k + 3, k − 2 and 2k + 1
form an arithmetic progression. [4 pts] form an arithmetic progression. [4 pts]
3. Solve for the third side of the triangle ABC if a = 15, 3. Solve for the third side of the triangle ABC if a = 15,
b = 8 and γ = 49o . [3 pts] b = 8 and γ = 49o . [3 pts]
4. Given that x = (log3 25)(log5 27), find the value of x 4. Given that x = (log3 25)(log5 27), find the value of x
without log. [3 pts] without log. [3 pts]
5. Given that sin x = 35 where x is in Quadrant I, find 5. Given that sin x = 35 where x is in Quadrant I, find
the value of sin( x2 ). [3 pts] the value of sin( x2 ). [3 pts]
6. Find z 10 if z = −1 − i. [3 pts] 6. Find z 10 if z = −1 − i. [3 pts]
4 cis 98o 28 cis 137o 4 cis 98o 28 cis 137o
7. Evaluate z = . [3 pts] 7. Evaluate z = . [3 pts]
7 cis 78o 16 cis 67o 7 cis 78o 16 cis 67o
II. Solve as indicated. Show all solutions. II. Solve as indicated. Show all solutions.
1. Find the solution set of the following equations. 1. Find the solution set of the following equations.
[5 pts each] [5 pts each]
a. e2x+1 − ex+1 = 0 a. e2x+1 − ex+1 = 0
b. [logx (2x + 3)]2 + logx 1 = 3 logx (2x + 3) − log2 4 b. [logx (2x + 3)]2 + logx 1 = 3 logx (2x + 3) − log2 4
c. sin−1 (cos θ) = 2θ where 0 ≤ θ ≤ π
2
c. sin−1 (cos θ) = 2θ where 0 ≤ θ ≤ π
2
2. A sequence has 9 terms. The first five terms form 2. A sequence has 9 terms. The first five terms form
an AP and the last five terms form a GP . If the 1st an AP and the last five terms form a GP . If the 1st
term is 2 and the 5th term is 18, find [3 pts each] term is 2 and the 5th term is 18, find [3 pts each]
a. the sum of the first five terms a. the sum of the first five terms
b. the 9th term if the 7th term is 2 for r > 0. b. the 9th term if the 7th term is 2 for r > 0.
3. A variable E varies directly as the cube of T and 3. A variable E varies directly as the cube of T and
inversely as the square of L. How is E affected when inversely as the square of L. How is E affected when
both T and L are tripled? [5 pts] both T and L are tripled? [5 pts]
4. Find the positive two-digit number for which the 4. Find the positive two-digit number for which the
units digit is 3 more than the tens digit and the sum units digit is 3 more than the tens digit and the sum
of their squares is 29. [5 pts] of their squares is 29. [5 pts]
5. The sketch below shows the cross section of a roof 5. The sketch below shows the cross section of a roof
of a fairly large house. One side must have an angle of a fairly large house. One side must have an angle
of 20o above the horizontal in order to facilitate the of 20o above the horizontal in order to facilitate the
installation of solar electricity batteries. However, installation of solar electricity batteries. However,
the peak of the roof may be only 3.50 m above the the peak of the roof may be only 3.50 m above the
base level. Determine the lengths x, y, and z and base level. Determine the lengths x, y, and z and
the angle θ. [6 pts] the angle θ. [6 pts]
....... .......
.. ..
... ..
y z ..
...
y z ..
...
.. ..
3.50 m 3.50 m
..
20o θ .
...
.. 20o θ ..
...
... .......
. . ...
.
.. . .
................................................................................................ 14.50 m ............................................................................................ ................................................................................................ 14.50 m ............................................................................................
.
......................................................................... x ............................................................ .
......................................................................... x ............................................................
6. A boat has to travel to a port in Istanbul 900 6. A boat has to travel to a port in Istanbul 900
