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3 years ago

use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine . . sin^6 x

1 answer:

andrey2020 [161]3 years ago

4 0

1/128 (3 - 4 Cos[4 x] + Cos[8 x])( sin^2(x) )^2 cos^4(x)

( (1 - cos^2(x) )^2 cos^4(x) 

(1 - 2cos^2(x) + cos^4(x) ) cos^4(x) 

cos^4(x) - 2cos^6(x) + cos^8(x) 

( cos^2(x) )^2 - 2( cos^2(x) )^3 + ( cos^2(x) )^4 <==> knowing the identity; cos^2(x) = (1/2) * (1 + cos(2x)) 

( (1/2) * (1 + cos(2x)) )^2 - 2( (1/2) * (1 + cos(2x)) )^3 + ( (1/2) * (1 + cos(2x)) )^4 

( (1/4) * (1 + 2cos(2x) + cos^2(2x) )) - 2( (1/8) * (cos^3(2x) + 3cos^2(2x) + 3cos(2x) + 1) + ( (1/16) * cos^4(2x) + 4cos^3(2x) + 6cos^2(2x) + 4cos(2x) + 1)

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The answer is B) which is letter E . hope this helps <3

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3 years ago

I need to know if this number is any of the following:

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It is rational/irrational

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Find the perimeter of the triangle.

ch4aika [34]

Answer:

3x +2x-5+(-7x+8)=

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Step-by-step explanation:

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Ava is buying paint from Amazon. Ava

irina [24]

Answer:

2.625 cups or 21 ounces

Step-by-step explanation:

Ava needs 3/4 cup of blue paint for every 1 cup of white paint. So, the ratio is 0.75 : 1.

She has 28 ounces of white paint. But, you have to convert ounces to cups.

1 cup = 8 ounces

28 ounces ÷ 8 ounces/cup = 3.5 cups

Now set up a ratio.

$\frac{0.75}{1} = \frac{x}{3.5}$

X (how much blue paint is needed) is over 3.5 cups (the amount of white paint she has)

Cross multiply and divide.

$\frac{0.75}{1} = \frac{x}{3.5}$

x = 0.75 × 3.5

x = 2.625 cups

To convert to ounces, multiply by 8.

2.625 cups × 8 ounces = 21 ounces

Therefore, Ava needs 2.625 cups or 21 ounces of blue paint.

Hope that helps.

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3 years ago

Miguel is a golfer, and he plays on the same course each week. The following table shows the probability distribution for his sc

aivan3 [116]

1) 4.55

2) Short hit

Step-by-step explanation:

The table containing the score and the relative probability of each score is:

Score 3 4 5 6 7

Probability 0.15 0.40 0.25 0.15 0.05

Here we call

X = Miguel's score on the Water Hole

The expected value of a certain variable X is given by:

$E(X)=\sum x_i p_i$

where

$x_i$ are all the possible values that the variable X can take

$p_i$ is the probability that $X=x_i$

Therefore in this problem, the expected value of MIguel's score is given by:

$E(X)=3\cdot 0.15 + 4\cdot 0.40 + 5\cdot 0.25 + 6\cdot 0.15 + 7\cdot 0.05=4.55$

In this problem, we call:

X = Miguel's score on the Water Hole

Here we have that:

- If the long hit is successfull, the expected value of X is

$E(X)=4.2$

- Instead, if the long hit fails, the expected value of X is

$E(X)=5.4$

Here we also know that the probability of a successfull long hit is

$p(L)=0.4$

Which means that the probabilty of an unsuccessfull long hit is

$p(L^c)=1-p(L)=1-0.4=0.6$

Therefore, the expected value of X if Miguel chooses the long hit approach is:

$E(X)=p(L)\cdot 4.2 + p(L^C)\cdot 5.4 = 0.4\cdot 4.2 + 0.6\cdot 5.4 =4.92$

In part 1) of the problem, we saw that the expected value for the short hit was instead

$E(X)=4.55$

Since the expected value for X is lower (=better) for the short hit approach, we can say that the short hit approach is better.

8 0

3 years ago