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denis-greek [22]
2 years ago
13

A sinusoidal function whose period is 4π, maximum value is 6, and minimum value is -2 has a y intercept of 6. What is the equati

on of the function described?
Mathematics
1 answer:
IRINA_888 [86]2 years ago
4 0

Equation of the function: f(x) = 4 sin (x/2) + 6.

<h3>What is sinusoidal function ?</h3>

The term sinusoidal is used to describe a curve, referred to as a sine wave or a sinusoid, that exhibits smooth, periodic oscillation. It is named based on the function y=sin(x).

Given: max value= 6, min value= -2, y-intercept= 6.

As, standard form f(x) = A sin (ωx +φ) + k,

where A is the amplitude, ω is the angular velocity with ω=2πf.

Now,

A = |6- (-2)/2|

A = |6 +2/2| = 8/2

A = 4

Also, ω:

The period of a sinusoidal is T = 1/f

so, f = 1 / T

ω = 2πf

ω = 2π ( 1/T) with T = 4π

ω = 2π (1/(4π) = 2π (2)

ω = 1/2

The y-intercept k = 6

So, equation with values A =4, ω = 1/2, k = 6, φ = 0.

f(x) = A f(x)

f(x) = A sin (ωx +φ) + k

f(x) = 4 sin (x/2) + 6.

Hence, equation of the function f(x) = 4 sin (x/2) + 6.

Learn more about this concept here:

brainly.com/question/26315885

#SPJ1

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In Grafton, a rural area in Vermont, the distance (in meters) between telephone poles has a uniform distribution between 40 and
coldgirl [10]

Answer:

a) 60% probability that the distance is environment friendly.

b) The mean of the distances between the telephone poles is 52.5 meters.

c) The standard deviation of the distance between the telephone poles is 7.22 meters.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

P(X \leq x) = \frac{x - a}{b-a}

Uniform distribution between 40 and 65 meters.

This means that a = 40, b = 65

a) Any distance between poles greater than 50 meters is considered to be environment friendly. What is the probability that the distance is environment friendly?

This is P(X > 50)

We have that

P(X \leq 50) + P(X > 50) = 1

So

P(X > 50) =  1 - P(X \leq 50)

P(X \leq 50) = \frac{50 - 40}{65 - 40} = 0.4

P(X > 50) =  1 - P(X \leq 50) = 1 - 0.4 = 0.6

60% probability that the distance is environment friendly.

b) Find the mean of the distances between the telephone poles

The mean of the uniform distribution is

M = \frac{a + b}{2}

So

M = \frac{a + b}{2} = \frac{40 + 65}{2} = 52.5

c) Find the standard deviation of the distance between the telephone poles.

The standard deviation of the uniform distribution is:

S = \sqrt{\frac{(b-a)^{2}}{12}}

So

S = \sqrt{\frac{(65-40)^{2}}{12}} = 7.22

5 0
3 years ago
Plz help me well mark brainliest if correct!!......
Elenna [48]

Answer:

Option C

Step-by-step explanation:

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8 0
2 years ago
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5x+9=3x+9+2x<br><br> Solve for x
horrorfan [7]

Answer:

5x=5x Infinitely Many Solutions

Step-by-step explanation:

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3 years ago
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A certain recipe asks for 3/5 cup of granola. How much is needed to make 3/4 of a recipe?​
Alex73 [517]

Answer:

9/20

Step-by-step explanation:

1 recipe=3/5 cups

3/4 recipe=? cups

By cross multiplying both eqs

Cups of granola=3/5*3/4

Cups=3*3/5*4

Cups=9/20

6 0
3 years ago
I will give you brainiest if you can answer the questions below.
Anon25 [30]

Answer:

a. i. 3000 cm² ii. 220 cm  b.  6 feet

Step-by-step explanation:

A. i. The area of the sector AOB is A = ¹/₂r²θ where r = radius of circle = 50 cm and θ = angle subtended at the center of the circle by the sector in radians = 2.4 radians.

So, A = ¹/₂r²θ

= ¹/₂(50 cm)² × 2.4 rad

= ¹/₂ × 2500 cm² × 2.4 rad

= 1250 cm² × 2.4 rad

= 3000 cm²

ii. The perimeter of the sector is P = 2r + rθ = (2 + θ)r

substituting r and θ, we have

P = (2 + θ)r

= (2 + 2.4) × 50 cm

= 4.4 × 50 cm

= 220 cm

B. Since length of an arc L = rθ where r = radius = length of pendulum and θ = angle swept by pendulum =  ½ radian and length of the arc swept = 3 feet, the radius is

r = L/θ

= 3 feet ÷ ½ rad

= 3 × 2

= 6 feet

8 0
3 years ago
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