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solong [7]
3 years ago
11

Which of the expressions (on the photo document I inserted) together represent all solutions to the following equation?

Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
7 0

Answer:

x =15 + 30n

Step-by-step explanation:

8cos(12x)+4=-4

Subtract 4 from each side

8cos(12x)+4-4=-4-4

8cos(12x)=-8

Divide by 8

8/8cos(12x)=-8/8

cos(12x) = -1

Take the arccos on each side

arccos(cos(12x)) = arccos(-1)

12x = 180 degrees  

But we can go around in a circle of 360 and get the same result

12 x = 180+360n  where n is an integer

Divide each side by 12

x = 180/12 +360n/12

x =15 + 30n

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The ratio of boys to girls in the Science Club is 3.5. If there are 60 girls, how many boys are there?
liubo4ka [24]

Answer:

36 boys

Step-by-step explanation:

                                                            3

Please write the ratio as 3:5 or as  --------

                                                             5

Note that 3 + 5 = 8, so that the fraction of boys in the club is 3/8 and that of girls is 5/8.  

How many are in the club altogether?  Let this count be represented by c.  Then (5/8)c = 60.

Multiplying both sides of this equation by (8/5), to isolate c, we get:

c = (8/5)(60) = 96.  Thus, there are 96 Science students altogether.

3/8 of this number are boys.  This comes out to (3/8)(96) = 36 boys.

We could also solve this problem in the following manner:

 3          b

------ = ------- , where b represents the number of boys.

  5        60

Then 5b = 180.  Dividing both sides by 5, we get b = 180/5 = 36 boys

3 0
3 years ago
A refrigerator costs $1799.99. New parts for this refrigerator cost $345, labor to repair it costs $553, and
Fynjy0 [20]

Answer: A

Step-by-step explanation: A is the best answer becauuse your whole refrigerator is covered.

4,819.99

3 0
3 years ago
I have 30 ones, 2 thousands ,4hundred thousands 60 ten, and 100 hundreds. What number am I?
swat32

Answer:402593

Step-by-step explanation:

5 0
3 years ago
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Mariah is a manager of a fitness training center that serves a certain region. She is interested in the amount of water adult re
Luden [163]
Your answer should be B
5 0
3 years ago
I NEED HELP ASAP! : An initial population of 175 quail increases at an annual rate of 22%. Write an exponential function to mode
goblinko [34]

Answer:

About 473 quails.

P=175(1.22)^t

Step-by-step explanation:

Exponential equation with P_0 as the initial amount and rate of r is:

P=P_0(1+r)^t

P=175(1+.22)^t

P=175(1.22)^t

After 5 years the population will be:

P=175(1.22)^5

P \approx 472.9739

So the population will be about 473 quails.

7 0
3 years ago
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