Overview
Dear writer, you are to provide solutions for the following problems:
1.In the triangle
ABC , AB 6
cm and
BC 9
cm. Given that the area of the triangle is
18
cm2
, find the possible values of the angle
B .
2.Find the exact value of
tan 30 (6sin135 4cos 210 )
, giving your answer in the form
a b 6 .
3.Show that for a small angle
, measured in radians,
3
sin 3 (1 cos 2 ) 6 .
4.Prove that
2 2 sin (3sin 4cos ) 3
3cos cos
tan
.
5.Simplify (36 + 4 . 27 ÷ 4 – 18) ÷ 5.
6.Proper aerobic exercise involves exercising at a person’s correct training heart rate. To
find the correct training heart rate the following formulas are used.
a. Training heart rate = (maximum heart rate – resting heart rate) × 0.65 +
resting heart rate
b. maximum heart rate = 220 – person’s age
Find the training heart rate for a 50-year-old with a resting heart rate of 65 beats per
minute
7. Translate the following into an algebraic expression:
the sum of five times a number and three
8. Solve 4(x + 1) = –15.
9.Evaluate | y + 7 | if y = –2.