Mark as true any statement that is always true. Mark as false any statement that is never true or that is not necessarily true. Be able to justify your answers.
1. The sentence “a:b = c:d” is a ratio.
2. 
3. The mean proportional of m and n is
4. If three angles of one triangle are congruent to three angles of a second triangle, then the
triangles are similar.
5. If two triangles are similar, then they are congruent.
1. F—It is a proportion.
2. T
3. F—The mean proportional is ?mn
4. T
5. F: There are many counterexamples.
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Solve the initial value problem.
= 5t + sec2 t, r(-?) = 4
A. r = 5t2 + tan t + 4 - 5?2
B. r = 
t2 + tan t + 4 - 
?2
C. r = 
t2 + cot t + 4 - 
?2
D. r = 5 + tan t - 1
Find the slope of the line tangent to the graph of the function at the given value of x.y = -4 - x2; x = 7
A. -2 B. -14 C. 7 D. 14
Solve the problem.The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 36 feet and the height of the arch over the center of the roadway is 14 feet. Two trucks plan to use this road. They are both 12 feet wide. Truck 1 has an overall height of 
and Truck 2 has an overall height of 
. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.
A. Neither Truck 1 nor Truck 2 can pass under the bridge. B. Truck 2 can pass under the bridge, but Truck 1 cannot. C. Truck 1 can pass under the bridge, but Truck 2 cannot. D. Both Truck 1 and Truck 2 can pass under the bridge.
Use the given information to find the exact value of the trigonometric expression.tan ? = 
; ? < ? < 
Find sin(2?).
A. 
B. 
C. - 
D. - 