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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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From families with four children a family is chosen at random. Let X be the number of boys in the family. Calculate and sketch t
alisha [4.7K]

Solution :

Given :

X = the number of boys in a family of four children

Families having four children are chosen randomly.

The gender distribution in the four child family are equally probable.

Thus,

 X                P(X)                                          CDF

0             ^4C_0 (1/2)^{4}        = 1/16                     \frac{1}{16}

1               ^4C_1 (1/2)^{4}       = 1/4                       \frac{5}{16}

2                ^4C_2 (1/2)^{4}      = 3/8                      \frac{11}{16}

3                ^4C_3 (1/2)^{4}      = 1/4                       \frac{15}{16}

4                  ^4C_4 (1/2)^{4}    = 1/16                      1

4 0
3 years ago
How many atoms are in the given sample 214.1 g of Vanadium
lord [1]

Answer:

The atomic weight (or atomic mass) of Vanadium is 50.9415 which means that a "mole" of Vanadium atoms (6.02 x 10^23 atoms) will have a mass of 50.9415 grams.  So, 214.1 grams of Vanadium would have

(214.1 / 50.9415) * (6.02 x 10^23) = 2.530 x 10^24 atoms



Step-by-step explanation:


6 0
3 years ago
Twice the sum of a number and 3 is equal to three times the difference of the number and 3
lana66690 [7]
<span>Twice the sum of a number and 3 = 2(n + 3)
</span><span>three times the difference of the number and 3 = 3(n - 3)
so
</span><span>Twice the sum of a number and 3 is equal to three times the difference of the number and 3:
</span>2(n + 3) = 3(n - 3)
2n + 6 = 3n - 9
n = 15

answer
2(n + 3) = 3(n - 3)
n = 15
7 0
3 years ago
Read 2 more answers
Solve for x.<br> logo(x-2) + log(x + 3) = 2
amid [387]

Answer:

x=-1-5√17/2

Step-by-step explanation:

logo((x-2)(x+2))=2

logo(x²+3x-2x-6)=2

x²+3x-2x-6=10²

x²+x-6=100

x²+x-106=0

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5 0
2 years ago
Your drapery business has just gotten a new client who needs 4 drapes made. Each one will need to be 8 feet by 5 feet and you mu
UNO [17]

22 because 6 inches on top and bottom means you need 12 inchesw each drape and you have 4 drapes so 48 inches therefor rounding that you get 1 yard each added onto the 8 feet and 5 feet for each drape.

6 0
3 years ago
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