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Date: May 30th
Algebra 2 and Trigonometry
3rd Quarter – Weekly Review #17
This assignment is due on June 6th at the start of the class period. No late papers will be accepted. Do NOT copy – if a
question/paper is found to be copied, all students involved will receive a zero for the assignment. Please show all formulas
and formula substitutions, when needed. Please show all appropriate work – following the guidelines we discuss in class –
in order to earn full credit. ALL FRACTIONS SHOULD BE IN REDUCED FORM and NO RADICALS can be left in
the denominator. For any item worth more than 1 point, you must show work to explain how you arrived at your answer.
1. The angle of elevation to the top of a tree from the base of a boulder, a distance of 54 meters
away, is 23o32’. To the nearest hundredth of a meter, how tall is the tree?
(3 points)
2. Solve for x. Only an algebraic solution will be accepted for full credit. To earn full credit, you
must show each step in the process. (part a is 4 points, and parts b and c are each 5 points)
a.
4
 2048
8x
b. 5 3 x 9  25 2 x 3 
1
625
27 x 1
c.
 243
812 x 3
3. The quantities a and b vary inversely. Find all values of y, in simplest radical form, that satisfy the
given statement. If a = 12 when b = 14, and a = y - 2 when b = 3y – 4.
(5 points)
4. From an observation tower, a forest ranger whose eye level is 35 feet above ground level sights a
fire at ground level. The angle of depression from the observer to the fire is 2o47’. To the nearest
tenth of a foot, how far is the fire from the base of the tower?
(4 points)
5. Evaluate. (Part a is 5 points and part b is 9 points)
a. 7 sin
3
 4 
 4 cos 2 

2
 3 
6. Solve for all values of x for the given equation.
b.  2 csc
5
7
2
 9 cot 2
 8 sec
6
6
3
27x4 – 429x2 = 48
(6 points)
7. A manufacturing company earns a weekly profit of P dollars according to the function
P(x) = -0.2x2 + 46x – 225, where x is the number of units sold. When P(x) = 0, the roots of the
equation represent the level of sales needed for which the manufacturer will break even. Interpret the
meaning of the discriminant value, in the context of the question. Use the discriminant to determine
if there is a level of sales for which the weekly profit would be $4000. Explain your answer.(4 points)