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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>

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Surveys indicate that two-thirds of all voters in Ward 5 plan on choosing Spike Jones for commissioner. If there are 500 voters
olya-2409 [2.1K]

<u>Answer:</u>

333 people of ward 5 are going to be voting for Spike Jones.

<u>Solution:</u>

We have been given that two-thirds of all voters in Ward 5 plan on choosing Spike Jones for commissioner.  

There are 500 voters in Ward 5.

Since 2/3 of all voters in Ward 5 are voting for Spike Jones the remaining 1/3 will not be voting for him.

To find out how many people in ward 5 are exactly voting for Spike Jones. We need to calculate how much is two thirds of 500 is.

This is done as follows:

\begin{array}{l}{\frac{2}{3} \times 500} \\\\ {=\frac{1000}{3}} \\\\ {=333.334}\end{array}

Since people cannot be denoted in decimal points we have to round it off to a whole number. That’s is 333.

Therefore 333 people of ward 5 are going to be voting for Spike Jones.

4 0
3 years ago
A car drives 195miles in 3hours and 15minutes. What is the average speed of the car? ​
lisabon 2012 [21]

Answer: It is 60 miles per hour

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Now you know the answer as well as the formula. Hope this helps, have a BLESSED AND WONDERFUL DAY!

- Cutiepatutie ☺❀❤

7 0
3 years ago
Find integrate (1/(xsqrt(1+(lnx)^2)),1,e,x) ...?
prohojiy [21]
Note that x² + 2x + 3 = x² + x + 3 + x. So your integrand can be written as 

<span>(x² + x + 3 + x)/(x² + x + 3) = 1 + x/(x² + x + 3). </span>

<span>Next, complete the square. </span>

<span>x² + x + 3 = x² + x + 1/4 + 11/4 = (x + 1/2)² + (√(11)/2)² </span>

<span>Also, for the x in the numerator </span>

<span>x = x + 1/2 - 1/2. </span>

<span>So </span>

<span>(x² + 2x + 3)/(x² + x + 3) = 1 + (x + 1/2)/[(x + 1/2)² + (√(11)/2)²] - 1/2/[(x + 1/2)² + (√(11)/2)²]. </span>

<span>Integrate term by term to get </span>

<span>∫ (x² + 2x + 3)/(x² + x + 3) dx = x + (1/2) ln(x² + x + 3) - (1/√(11)) arctan(2(x + 1/2)/√(11)) + C </span>

<span>b) Use the fact that ln(x) = 2 ln√(x). Then put u = √(x), du = 1/[2√(x)] dx. </span>

<span>∫ ln(x)/√(x) dx = 4 ∫ ln u du = 4 u ln(u) - u + C = 4√(x) ln√(x) - √(x) + C </span>

<span>= 2 √(x) ln(x) - √(x) + C. </span>

<span>c) There are different approaches to this. One is to multiply and divide by e^x, then use u = e^x. </span>

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4 0
3 years ago
Evaluate -6-9÷(-3) ?​
sdas [7]
Answer- 21

-6+-9
—
-3
-6+27=21
5 0
2 years ago
Plz help asap will markbrainliest
kicyunya [14]

This is called a Supplementary Angle, meaning the angles <em><u>MUST</u></em> add up to 180 Degree.

Angle 1 will be 94 (94-18 = 76).

Angle 2 will be 13 (8x13 = 104).

(Please mark this as the brainliest if this helps!)

7 0
3 years ago
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