1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
docker41 [41]
3 years ago
12

A sinusoidal function whose period is π2 , maximum value is 10, and minimum value is −4 has a y-intercept of 10. what is the equ

ation of the function described?

Mathematics
2 answers:
valentina_108 [34]3 years ago
8 0

Answer:

The equation of the function is f(x)=7\sin(4x+\frac{\pi}{2})+3.

Step-by-step explanation:

The general form of sinusoidal function is

f(x)=a\sin(bx+c)+d .... (1)

where, a is amplitude, b is frequency, c is phase shift and d is vertical shift.

a=\frac{maximum-minimum}{2}=\frac{10-(-4)}{2}=7

b=\frac{2\pi}{period}=\frac{2\pi}{\frac{\pi}{2}}=4

d=\frac{maximum+minimum}{2}=\frac{10+(-4)}{2}=3

Substitute these values in equation (1).

f(x)=7\sin(4x+c)+3 ....(2)

It is given that the y-intercept of the function is 10. It means f(x)=10 at x=0.

10=7\sin(4(0)+c)+3

7=7\sin(c)

1=\sin(c)

\sin^{-1}(1)=c

c=\frac{\pi}{2}

Put this value in equation (2).

f(x)=7\sin(4x+\frac{\pi}{2})+3

Therefore the equation of the function is f(x)=7\sin(4x+\frac{\pi}{2})+3.

lions [1.4K]3 years ago
7 0
<span>the general equation of the sine curve is ⇒ y = a sin ( nx + α ) + b
</span><span>
</span><span>where : a is the amplitude
</span><span>
</span><span>             n = 2π/period
</span><span>
</span>             b = shift in the direction of y
             α°= shift in the direction of x

<span>Given period = π/2 ,
</span><span>
</span><span>maximum value is 10,
</span><span>
</span><span>minimum value is −4
</span><span>
</span><span>a y-intercept of 10.
</span>
 a = (maximum - minimum)/2 = (10 - -4)/2 = 7
 n = 2π/period = 2π/(π/2) = 4
 b = maximum - a = 10 - 7 = 3
to find α <span>⇒ y-intercept = 10
</span><span>
</span><span>y = 10 at x = 0
</span>
<span>substitute in the general function
</span><span>
</span>∴   y <span>= a sin ( nx + α ) + b
</span><span>
</span><span>∴ 10 = 7 sin ( 4*0 + α ) + 3
</span><span>
</span><span>∴ sin α = 1 ⇒⇒⇒ α = π/2</span>

So, <span>the equation of the function described is as attached in the figure
</span><span>
</span><span> y = 7 sin ( 4x + π/2 ) + 3
</span>

You might be interested in
Shannon's family is going to install a custom swing set in the backyard. There are 5 kinds of swings and 3 kinds of slides, and
asambeis [7]

Answer:

15 different swing sets

Step-by-step explanation:

The swing set is composed by one swing and one slide.

There is 5 different types of swing, so there are 5 possibilities to fill the one swing we need.

There are 3 different types of slides, so there are 3 possibilities to fill the one slide we need.

So, to find the total number of swing sets, we just need to multiply the swing possibilities and the slide possibilities:

Number of sets = 5 * 3 = 15 different sets

8 0
3 years ago
What are the zeros of f(x)=x^2-10+25
BartSMP [9]
Answer:
-5

Explanation:
Because it’s right
7 0
3 years ago
A bicycle shop advertised all mountain bikes priced at 1/3 discount.
Talja [164]

Answer:

a. 109$

b. 327/3= 109

you're welcome

4 0
3 years ago
Read 2 more answers
Verizon has a special and is selling the new iPhone 7 for $299 to new customers. If the Apple Store is charging twice as much as
-Dominant- [34]

Answer:

$598

Step-by-step explanation:

2 x 299 = 598 so Apple is charging $598 for the new phone.

6 0
2 years ago
PLEASE HELP! I DON'T UNDERSTAND!
Mademuasel [1]
Yes, her estimate is reasonable. She has 430 flowers and each bouquet needs 17. If we divide 430 by 17 we get roughly 25.29. So she can make 25 complete bouquets, which is between 20 and 30
3 0
3 years ago
Other questions:
  • What is LCM of two numbers if one number is a multiple of the other?Give on Example.
    12·2 answers
  • What are 2 phrases for the expression 85-y
    10·2 answers
  • Which graph correctly solves the system of equations below? y = − x2 + 1 y = x2 − 4
    5·2 answers
  • Solve for r -4(r+6)= -49
    6·1 answer
  • Determine the equation of the inverse of y=2^3x-1
    7·2 answers
  • Plot a point C that divides the segment into the<br> ratio AC:AB= 3/4
    7·1 answer
  • What is the simplified expression for 5 to the power of negative 3 multiplied by 2 to the power of 2 multiplied by 5 to the powe
    7·1 answer
  • This chart shows a bamboo plants growth over 10hours. The plant grew at a constant speed what is the rate of speed for this bamb
    14·1 answer
  • If Ali is x years old, write Omar’s age in terms of x if omar is 6 years younger
    13·1 answer
  • 8 times 1/2 Pretty basic
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!