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Irina18 [472]
3 years ago
6

The graph of a sinusoidal function has a maximum point at (0,10) and then intersects its midline at (pi/4,4). Write the formula

of the function, where x is entered in radians. f(x)=
Mathematics
1 answer:
docker41 [41]3 years ago
5 0

Answer: y = 6 cos (2x) + 4

<u>Step-by-step explanation:</u>

A cosine function is expressed as: y = A cos (Bx - C) + D   where

  • amplitude (A) is the distance from the midline to the max/min.
  • B = 2π/P  where P is the period
  • C/B is the phase shift
  • D is the center line (aka midline)

A = Max - Midline

   = 10 - 4

   = 6

The max to the midpoint is π/4

⇒ 1/4 P = π/4

⇒ P = π

B = 2π/P    

  = 2π/π

  = 2

C = 0 because there is no phase shift

D = 4 (given)

Input A = 6, B = 2, C = 0, and D = 4 into the cosine function:

y = 2 cos (2x - 0) + 4

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3 years ago
-8x+2y=-2<br> 4x+4y=-4<br> What is the solution to the system
pickupchik [31]

The solution to system is x = 0 and y = -1

<em><u>Solution:</u></em>

<em><u>Given system of equations are:</u></em>

-8x + 2y = -2 ----------- eqn 1

4x + 4y = -4 ---------- eqn 2

We have to solve the system of equations

We can solve the equations by elimination method

<em><u>Multiply eqn 2 by 2</u></em>

8x + 8y = -8 ------ eqn 3

<em><u>Add eqn 1 and eqn 3</u></em>

-8x + 2y = -2

8x + 8y = -8

( + ) ---------------

0x + 2y + 8y = -2 - 8

10y = -10

Divide both sides by 10

y = -1

<em><u>Substitute y = -1 in eqn 1</u></em>

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x = 0

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3 0
3 years ago
In Rivertown High School, about 30% of the students buy a raffle ticket. Given that a student buys a raffle ticket, there is a 1
lesya [120]

The probability that that a randomly selected student will buy a raffle ticket and win a prize = 0.03

Step-by-step explanation:

Step 1 :

Given,

The percentage of students buying the raffle ticket = 30%

The percentage that the student who bought the ticket wins the prize = 10%

We need to determined the probability that randomly selected student will buy a raffle ticket and win a prize.

Step 2 :

The probability that a student buys the raffle ticket =  \frac{30}{100}  = \frac{3}{10}

The probability that a student wins a prize = \frac{10}{100} = \frac{1}{10}

The probability that a student who buys the ticket wins a price can be computed by taking the product of the above 2 probabilities.

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Step 3 :

Answer :

The probability that that a randomly selected student will buy a raffle ticket and win a prize = 0.03

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3 years ago
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erik [133]

Answer:

15.38%

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There are 4 7's in a deck of 52 cards.

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