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MAXImum [283]
3 years ago
13

Write one sine and one cosine equation for each graph below.

Mathematics
1 answer:
pychu [463]3 years ago
6 0

Answer:

Q13. y = sin(2x – π/2); y = - 2cos2x  

Q14. y = 2sin2x -1; y = -2cos(2x – π/2) -1

Step-by-step explanation:

Question 13

(A) Sine function

y = a sin[b(x - h)] + k

y = a sin(bx - bh) + k; bh = phase shift

(1) Amp = 1; a = 1

(2) The graph is symmetrical about the x-axis. k = 0.

(3) Per = π. b = 2

(4) Phase shift = π/2.  

2h =π/2

h = π/4

The equation is

y = sin[2(x – π/4)} or

y = sin(2x – π/2)

B. Cosine function

y = a cos[b(x - h)] + k

y = a cos(bx - bh) + k; bh = phase shift

(1) Amp = 1; a = 1

(2) The graph is symmetrical about the x-axis. k = 0.

(3) Per = π. b = 2

(4) Reflected across x-axis, y ⟶ -y

The equation is y = - 2cos2x  

Question 14

(A) Sine function

(1) Amp = 2; a = 2

(2) Shifted down 1; k = -1

(3) Per = π; b = 2

(4) Phase shift = 0; h = 0

The equation is y = 2sin2x -1

(B) Cosine function

a = 2, b = -1; b = 2

Phase shift = π/2; h = π/4

The equation is

y = -2cos[2(x – π/4)] – 1 or

y = -2cos(2x – π/2) - 1

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Answer:

<em>C(19)=12 responses</em>

Step-by-step explanation:

<u>Exponential Decay Function</u>

The exponential function is frequently used to model natural growing or decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function can be expressed as follows:

C(t)=C_o\cdot(1-r)^t

Where:

C(t) is the actual value of the function at time t

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The company puts out an advertisement for a job opening. Initially, the company got 90 responses to the advertisement. Each day, the responses declined by 10%.

This is an example where the decay model can be used to calculate the responses to the advertisement at the day t.

The initial value is Co=90, the decaying rate is r=10% = 0.10. The model is written as:

C(t)=90\cdot(1-0.1)^t

Calculating:

C(t)=90\cdot(0.9)^t

We are required to calculate the number of responses at day t=19, thus:

C(19)=90\cdot(0.9)^{19}

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8 0
3 years ago
How do you Simplify 16/12
vlada-n [284]
You need to find a common factor that both the numerator and denominator have. 16 and 12 have common divisible factors of 2 and 4(excluding 1, because 1 is self-defined but doesn't simplify values at all). 

We use the highest factor, in this case, 4. 

Divide 16 by 4 and 12 by 4.

16/4 = 4
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We put 4 in place of the numerator and 3 in place of the denominator.

\frac{4}{3}
4 0
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Answer:

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Step-by-step explanation:

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