MATHEMATICS HIGH SCHOOL

Select one or more expressions that together represent all solutions to the equation. Your answer should be in radians. Assume n is any integer. 16 cos(15x)+8=2

Answers

Answer 1
Answer:

The value of x is for the given trigonometric function is found as: x = 0.1303 + 1/15 *2nπ.

Explain about the solutions of trigonometric functions?

  • The fact that too many trigonometric equations have infinitely multiple solutions rather than two makes a significant distinction.
  • We will learn how to interpret one solution of an equation in terms of all the other answers by using the inverse trigonometric functions.

The given expression is:

16 cos(15x) + 8 = 2

On simplification:

cos(15x) = (2-8)/16

cos(15x) = -3/8

15x = arcos ( -3/8 )

15x =  2π -  arcos ( -3/8 )

15x =  arcos ( -3/8 ) + 2nπ  ;or

15x =  2π - arcos ( -3/8 ) + 2nπ ; n ∈ Z

So,

15x = 1.955 + 2nπ

x = 1/15(1.955 + 2nπ)

x = 0.1303 + 1/15 *2nπ , n ∈ Z

Thus, the value of x is found as: x = 0.1303 + 1/15 *2nπ.

Know more about solutions of trigonometric functions, here

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If f(x) = 3x + 3, g(x) = 3x + 3, and h(x) = x + 3, what is [g o f o h](–5)?A: –30
B: –24
C: –15
D: –6

Answers

Answer:

The correct answer is D. -6    

Step-by-step explanation:

f(x) = 3x + 3

g(x) = 3x + 3

h(x) = x + 3

We need to find : [g o f o h](–5)

⇒ [g o f o h](–5)

⇒  [g o f]h(-5)

⇒ [g o f](-5 + 3)

⇒ [g o f](-2)

⇒ [g]f(-2)

⇒ [g](3 × -2 + 3)

⇒ [g](-6 + 3)

⇒ g(-3)

⇒ 3 × -3 + 3

⇒ -9 + 3

⇒ -6

Therefore, The correct answer is D. -6                
The answer would be -6.
Start by substituting -5 into the 'h' function.
h(-5) = -5 + 3 = -2
Now substitute this answer into the 'f' function.
f(-2) = 3(-2) + 3 = -3
now substitute this answer into the 'g' function
g(-3) = 3(-3) + 3 = -6
D is your answer

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