Math Answers

Consider 𝑔(𝑥)=4sin3𝑥

a. Write down the period of 𝑔(𝑥)

b. Write down the number of solutions to the equation 𝑔(𝑥)=3, for 0≤𝑥≤2𝜋

c. Starting with the graph of 𝑦=sin𝑥, state the transformations which can be used to sketch 𝑔(𝑥).

Solve the equation √3sin𝜃−cos𝜃=0 for −180°≤𝑥≤180°

Solve the equation 8sin^2𝑥−7=2cos𝑥 for 0≤𝑥≤360°, giving your answers to 1 decimal place.

Prove:

a. (sin𝑥+cos𝑥)^2 ≡1+2sin𝑥cos𝑥

b. (1+sin𝑥+ cos𝑥)^2 ≡2 (1+sin𝑥) (1+cos𝑥)

c. (6−cos^2𝜃)/(sin^2𝜃+5) ≡1

Solve the following equations by Elimination method, Substitution method and Graphing method.

1. 2𝑥 + 3𝑦 = 8

5𝑥 − 3𝑦 = −1

2. 2𝑥 +5y = 19

x − 2y = −4

3. 𝑦 = 5 − 2𝑥

4𝑥 + 3𝑦 = 13

4. 𝑦 = 2𝑥 − 3

𝑦 = − 2/3𝑥 + 5

Suppose that A, B, and C are sets such that A ⊆ B and B ⊆ C. Show that A ⊆ C.

Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letter Y in the

set of all months of the year.

Heights of the students in a class are given in the distribution below:

5' - 5'2"      10

5'2" - 5'4" 40

5'4" - 5'6"   25 .

Find:

1. Skewness and Kurtosis

three cans of beans and five cans of soup weigh 700g.

four cans of beans weigh 300g.

what is thr weight of five cans of beans and three cans of soup?.

X=28 ; n=100