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Masteriza [31]
3 years ago
11

Given the cosine equation y = 2cos(4x) - 1, What is the midline?

Mathematics
1 answer:
pogonyaev3 years ago
6 0

Answer:

y = 2 \cos(4x)  - 1 \\ when \: y = 0 \\  \cos(4x)  =  \frac{1}{2}  \\ 4x = 60 \\ x = 15 \\ when \: x = 0 \\ y = 2 - 1 = 1 \\ intercepts =  > (15, \: 0) \: and \: (0, \: 1) \\ midpoints : ( \frac{15 + 0}{2} , \:  \frac{0 + 1}{2} ) \\  = (7.5, \: 0.5) \\ gradient =  \frac{1 - 0}{0 - 15}  \\  =  -  \frac{1}{15}  \\ y = mx + c \\ at \: (7.5, \: 0.5) \\ 0.5 =  -  \frac{1}{15}  \times 7.5 + c \\ 0.5 =  - 0.5 + c \\ c = 1 \\  \therefore \: y =  -  \frac{1}{15} x + 1 \\  =  > 15y =  - x + 15

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An alloy is composed of nickel, zinc, and copper in a 7:2:9 ratio. How many kilograms of each metal is needed to make 3.8 kg of
Tamiku [17]
Ni : Zn: Cu = 7:2:9 =7x : 2x : 9x

7x+2x+9x = 3.8
18x=3.8
x=3.8/18=1.9/9≈0.21

Ni:   7x=7*0.21=1.47 ≈1.5 kg
Zn:  2x=2*0.21=0.42≈0.4 kg
Cu: 9x=9*0.21=1.89 ≈1.9 kg

Check 1.5+0.4+1.9 =3.8 True
6 0
3 years ago
PLEASE HELP WILL MEDAL BRAINLIEST ANSWER!
babunello [35]
The amount after 7 years is given by:
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The answer is: $20,948.15
3 0
3 years ago
1/3 cup of flour is used to make 5 dinner rolls.
Sergio [31]
3 dozen = 36

1/3 ÷ x = 5 ÷ 36
1/3 × 36 = x × 5
12 = 5x
12/5 = x

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6 0
3 years ago
In a string of 12 Christmas tree light bulbs, 3 are defective. The bulbs are selected at random and tested, one at a time, until
Juliette [100K]

Using the hypergeometric distribution, it is found that there is a 0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.

In this problem, the bulbs are chosen without replacement, hence the <em>hypergeometric distribution</em> is used to solve this question.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • N is the size of the population.
  • n is the size of the sample.
  • k is the total number of desired outcomes.

In this problem:

  • There are 12 bulbs, hence N = 12.
  • 3 are defective, hence k = 3.

The third defective bulb is the fifth bulb if:

  • Two of the first 4 bulbs are defective, which is P(X = 2) when n = 4.
  • The fifth is defective, with probability of 1/8, as of the eight remaining bulbs, one will be defective.

Hence:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

P(X = 2) = h(2,12,4,3) = \frac{C_{3,2}C_{9,1}}{C_{12,4}} = 0.2182

0.2182 x 1/8 = 0.0273.

0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.

More can be learned about the hypergeometric distribution at brainly.com/question/24826394

8 0
2 years ago
A boat traveled 240 miles downstream, then 240 miles back up stream. The trip downstream took 20 hours. The trip back up stream
MaRussiya [10]

Answer:

Step-by-step explanation:

5 0
3 years ago
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