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kozerog [31]
2 years ago
14

Use the power reduction formulas to rewrite the expression. (Hint: Your answer should not contain any exponents greater than 1.)

Mathematics
1 answer:
WINSTONCH [101]2 years ago
8 0

The formulas in question are

sin²(x) = (1 - cos(2x))/2

cos²(x) = (1 + cos(2x))/2

Then

sin⁴(4x) = (sin²(x))²

… = ((1 - cos(2x))/2)²

… = (1 - 2 cos(2x) + cos²(2x))/4

… = (1 - 2 cos(2x) + (1 + cos(4x))/2)/4

… = 1/4 - 1/2 cos(2x) + (1 + cos(4x))/8

… = 3/8 - 1/2 cos(2x) + 1/8 cos(4x)

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The product of 6 and a number, x, is twice the<br> difference of x and 5.
11Alexandr11 [23.1K]

Answer:

2(x-5)=6x

Step-by-step explanation:

8 0
3 years ago
Which of the following shows the numbers in the box below listed in increasing order?
Anarel [89]

9514 1404 393

Answer:

  (A) -2, 3/7, 1/2, 1.2

Step-by-step explanation:

The numbers are in increasing order when they are listed left-to-right as they appear on the number line.

The only numbers that may give you trouble are 3/7 = 6/14 and 1/2 = 7/14.

The negative number is less than any positive number. 1.2 is greater than any fraction that is less than 1.

The correct ordering is found in choice A.

5 0
2 years ago
3 = x/12 - 4 what is x
alexgriva [62]

Answer:

x=84

Step-by-step explanation:

Add 4 on both sides

3=x/12-4

7=x/12

Multiply both sides by 12

(12)7=x/12(12)

84=x

Hope this helps! :)

3 0
3 years ago
Read 2 more answers
A bottle of la belle bœuf contains 3/8 ounces of perfume. How many ounces of perfume would 4 1/2 bottles contain?
dusya [7]

ANSWER

1 \frac{11}{16} ounces

EXPLANATION

It was given that,a bottle of la belle bœuf contains 3/8 ounces of perfume.

We want to find how many ounces of perfume would 4 1/2 bottles contain.

If 1 bottle contains 3/8 ounces;

Then 4½ bottles should contain more ounces.

If more less divides.

4½ bottles contain

\frac{4 \frac{1}{2} \times  \frac{3}{8}  }{1}

=  \frac{27}{16}

=1.6875 ounces.

3 0
3 years ago
gabriella wants to tile a room with an area of 320 square feet. the width of the room is 4/5 its length. what are the length and
Salsk061 [2.6K]
Assuming the shape of the room is a rectangle :

Area = Width x Length.

Let's call width "w" and length "l" . Now if, the width is 4/5 of the length that means 4/5 times length gives us the width, like this :

w=\frac { 4 }{ 5 } \cdot l

As given in the question, area of the rectangle is 320 square feet. And as I said before area of a rectangle can be found by multiplying its length and width. 

w.l=320

w=\frac { 4 }{ 5 } \cdot l , we can plug w's value in the previous equation to find "l". 

\frac { 4 }{ 5 } \cdot l\cdot l=320\\ \\ \frac { 4 }{ 5 } \cdot { l }^{ 2 }=320\\ \\ { l }^{ 2 }=320\cdot \frac { 5 }{ 4 } \\ \\ { l }^{ 2 }=\frac { 320\cdot 5 }{ 4 } \\ \\ { l }^{ 2 }=\frac { 1600 }{ 4 } \\ \\ { l }^{ 2 }=400\\ \\ \sqrt { { l }^{ 2 } } =\sqrt { 400 } \\ \\ l=20

Let's plug "l"s value in the equation.

w.l=320\quad \Longrightarrow \quad w\cdot 20=320\quad \Longrightarrow \quad w=\frac { 320 }{ 20 } \quad \Longrightarrow \quad w=16

The length is 20 feet and the width is 16 feet.


6 0
3 years ago
Read 2 more answers
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