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Julli [10]
2 years ago
7

The graph of a sinusoidal function intersects its midline at (0,−3)and then has a maximum point at (2,-1.5). Write the formula o

f the function, where x is entered in radians. f(x)= Please answer fast
Mathematics
1 answer:
amm18122 years ago
7 0

The <em>sinusoidal</em> function that represents the graph is equal to y = 1.5 · cos (2π · t/8) - 3.

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

In this question we must derive a <em>sinusoidal</em> function based on two given points. <em>Sinusoidal</em> functions are <em>periodic</em> functions that uses <em>trigonometric</em> functions and have the following form:

y = A · cos (2π · x/T) + B      (1)

Where:

  • A - Amplitude
  • T - Period
  • B - Vertical midpoint

The <em>horizontal</em> distance between the midline and the <em>maximum</em> point is equal to a quarter of the period. Hence,

T = 4 · (2 - 0)

T = 8

The <em>vertical</em> midpoint and amplitude of the <em>sinusoidal</em> function are now calculated:

Vertical midpoint

B = - 3

Amplitude

A = - 1.5 - (- 3)

A = 1.5

Then, the <em>sinusoidal</em> function that represents the graph is equal to y = 1.5 · cos (2π · t/8) - 3.

To learn more on sinusoidal functions: brainly.com/question/12060967

#SPJ1

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Apply the laws of exponents, calculate the result and express the result in scientific notation, and as a decimal: (8.1*10^-4)^2
AfilCa [17]
<h3>Answer:</h3>
  • the result in scientific notation is 6.561×10⁻⁷
  • the result as a decimal is 0.000 000 656 1
<h3>Explanation:</h3>

The rules of exponents say the exponent outside parentheses applies to each factor inside parentheses.

... (8.1*10^-4)^2 = 8.1^2 × (10^-4)^2

... = 65.61 × 10^-8

... = 6.561 × 10^-7 . . . . adjust to scientific notation with one digit left of the decimal point

The exponent of -7 means the decimal point in the decimal number is 7 places to the left of where it is in scientific notation. That is ...

... 6.561 × 10^-7 = 0.0000006561

4 0
3 years ago
Austin is 69 years younger than Jamie. 3 years ago, Jamie's age was 4 times Austin's age. How old is Austin now?
matrenka [14]

Answer: 26 years old

Step-by-step explanation:

  1. Create an equation with Austin as x and Jamie as x+69 (I just like workin with addition signs more)= 4(x-3)= x+69-3
  2. Simplify the equations --> 4x-12=x+66
  3. Solve the equation: 3x-12=66 --> 3x=78 --> x=26

This is the same as other age problems, just with the extra step of distributing the multiplication.

4 0
3 years ago
A polynomial has zeros x=0, x= -3, X = 4. What are some possible factored equations for this fourth degree polynomial.
kati45 [8]

Answer:

x^{2} (x + 3)(x - 4)

Step-by-step explanation:

You can multiply this out to get the full equations.

It's to the 4th degree so the x on the outside has to be squared to add the fourth degree.

To get other zeros:

x + 3 = 0

x = -3

x - 4 = 0

x = 4

Hope this helped. :0)

5 0
3 years ago
Find
shepuryov [24]

Answer:

The two odd numbers are 15 and 17

Step-by-step explanation:

Given

<em>Let the odd numbers be represented with x and y</em>

<em>Let x be the greater number</em>

<em></em>x + 5y = 92<em></em>

<em></em>

<em>Required</em>

Find x and y

Since x and y are consecutive odd numbers and x is greater, then

x = y + 2

Substitute y + 2 for x in x + 5y = 92<em></em>

<em></em>y + 2 + 5y = 92<em></em>

<em></em>

Collect Like Terms

<em></em>y + 5y = 92 - 2<em></em>

<em></em>6y = 90<em></em>

Divide both sides by 6

\frac{6y}{6} = \frac{90}{6}

y = \frac{90}{6}

y = 15

Substitute 15 for y in x = y + 2

x = 15 + 2

x = 17

<em>Hence; the two odd numbers are 15 and 17</em>

4 0
3 years ago
Charlie runs a screen printing company and is resetting a machine he uses to print triangular banners. He knows the amount of ma
aliina [53]

Answer: b= 2a/h

Step-by-step explanation:

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