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jok3333 [9.3K]
2 years ago
11

Ff is a trigonometric function of the form f(x)=a\sin(bx+c)+df(x)=asin(bx+c)+df, left parenthesis, x, right parenthesis, equals,

a, sine, left parenthesis, b, x, plus, c, right parenthesis, plus, d.
Below is the graph f(x)f(x)f, left parenthesis, x, right parenthesis. The function intersects its midline at (3,-6.5)(3,−6.5)left parenthesis, 3, comma, minus, 6, point, 5, right parenthesis and has a maximum point at (4,-2)(4,−2)left parenthesis, 4, comma, minus, 2, right parenthesis.
Find a formula for f(x)f(x)f, left parenthesis, x, right parenthesis. Give an exact expression.
\qquad f(x)=f(x)=f, left parenthesis, x, right parenthesis, equals
\qquad

Mathematics
1 answer:
andriy [413]2 years ago
3 0

The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

<h3>How to derive a sinusoidal expression</h3>

In this problem we need to find a <em>sinusoidal</em> expression that models the curve seen in the picture. The most typical <em>sinusoidal</em> model is described below:

f(x) = a · sin (b · x + c) + d    (1)

Where:

  • a - Amplitude
  • b - Angular frequency
  • c - Angular phase
  • d - Vertical midpoint

Now we proceed to find the value of each variable:

Amplitude

a = - 2 - (-6.5)

a = 4.5

Angular frequency

b = 2π / T, where T is the period.

0.25 · T = 4 - 3

T = 4

b = 2π / 4

b = π / 2

Midpoint

d = - 6.5

Angular phase

- 2 = 4.5 · sin (π · 4/2 + c) - 6.5

4.5 = 4.5 · sin (π · 4/2 + c)

1 = sin (2π + c)

π = 2π + c

c = - π

The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

To learn more on trigonometric functions: brainly.com/question/15706158

#SPJ1

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Pls help me with this​
Free_Kalibri [48]

Answer:

\boxed{\sf \frac{15}{22} }

Step-by-step explanation:

The radius of the circle is 7 cm.

The two legs of the triangles are 7cm as well.

Area of a trinagle is ( base × height )/2.

\frac{7 \times 7}{2} =24.5

Multiply the value by 2 since there are two triangles.

24.5 \times 2 = 49

Calculate the area of the circle.

\pi r^2

The radius is given.

\pi (7)^2

Take \pi as \frac{22}{7}

49(\frac{22}{7} )

=154

Subtract the area of the two triangles from the area of the whole circle.

154-49=105

The area of the shaded part is 105 cm². The total area of the shape is 154cm².

\frac{105}{154} =\frac{15}{22}

5 0
3 years ago
Help me on this math question please
Sunny_sXe [5.5K]

Answer:

its simplest form is 4/5

3 0
3 years ago
Can somebody help me with this question, please? I have no idea how to do this or find the answer. :/ How many ways are there to
san4es73 [151]

Answer:

28 different ways

Step-by-step explanation:

This is a combination question. Combination has to do with selection.

Total number of element in the set = 8

Number divisible by 6 or 8 are {-98, -48, -42, -36, -18, -6}

Total number divisible by 6 or 8 is 6

The number of ways we can choose 6 items from 8 is expressed as;

8C6 = 8!/(8-6)!6!

8C6 = 8!/(2)!6!

8C6 = 8*7*6!/2!6!

8C6 = 8*7/2

8C6 = 56/2

8C6 = 28 ways

Hence there are 28 different ways

5 0
3 years ago
The wheel on a car completes
mars1129 [50]

Answer:

Step-by-step explanation:

Let d be the diameter of the wheel.

Circumference = πd

(35.325 m)/(25 revolutions) = (1.413 m)/revolution

πd = 1.413

d = 1.413/π = 0.45 m

4 0
3 years ago
Paul has $30,000 to invest. His intent is to earn 15% interest on his investment. He can invest part of his money at 8% interest
jeka94

Answer:

Amount invested at 8% is $9000 and amount invested at 18% is $21000.

Step-by-step explanation:

Let amount invested at 8% be x.

Let amount invested at 18% be y.

We get the 1st equation as:

x+y=30000       ........(1)

We get the second equation as:

0.08x+0.18(y)=0.15\times30000

=> 0.08x+0.18y=4500

or getting rid of the decimal by multiplying by 100 on both sides.

8x+18y=450000          ........(2)

Multiplying (1) by 8 and subtracting from (2) we get

10y=210000  

So, y = 21000

And x+21000=30000

x = 30000-21000

So, x = 9000

Therefore, amount invested at 8% is $9000 and amount invested at 18% is $21000.

6 0
3 years ago
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