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3 years ago

35 students planned to walk in a fund raiser. The ratio of girls to boys is 5 to 2. How many boys are there?

Mathematics

1 answer:

Molodets [167]3 years ago

5 0

Answer:

Step-by-step explanation:

2/35

2 {

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1 5

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2cos5xcos3x+sinx=cos8x

harkovskaia [24]

It looks like your equation (it's not an identity) is

2 cos(5x) cos(3x) + sin(x) = cos(8x)

Recall that

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==> 2 cos(x) cos(y) = cos(x + y) + cos(x - y)

so that

2 cos(5x) cos(3x) = cos(8x) + cos(2x)

Then the equation simplifies to

cos(8x) + cos(2x) + sin(x) = cos(8x)

cos(2x) + sin(x) = 0

Also recall that

cos(2x) = 1 - 2 sin²(x)

so the equation is quadratic in sin(x) and can be factorized:

1 - 2 sin²(x) + sin(x) = 0

2 sin²(x) - sin(x) - 1 = 0

(2 sin(x) + 1) (sin(x) - 1) = 0

Solve for x :

2 sin(x) + 1 = 0 or sin(x) - 1 = 0

sin(x) = -1/2 or sin(x) = 1

[x = arcsin(-1/2) + 2nπ or x = π - arcsin(-1/2) + 2nπ] or x = arcsin(1) + 2nπ

(where n is any integer)

x = -π/6 + 2nπ or x = -5π/6 + 2nπ or x = π/2 + 2nπ

4 0

3 years ago

PLEASE HELP!!!! Use the table below to match the slopes to the lines.

skelet666 [1.2K]

Answer: Check out the filled out chart below.

Row 1: 1/4, 1/4, -4

Row 2: -2, -2, 1/2

Row 3: 3, 3, -1/3

=========================================

Explanation:

Parallel lines have equal slopes. So if the original line has slope 1/4, then any parallel line will also have slope 1/4. The only thing different is the y intercept.

Perpendicular slopes multiply to -1 assuming neither line is vertical. For row 1, the perpendicular slope is -4 which multiplies with the original slope 1/4 to get -1.

Put another way, the perpendicular slope is the negative reciprocal of the original slope. For row 2, the perpendicular slope is 1/2 because we flip the fraction and the sign for the original slope -2 = -2/1

4 0

4 years ago

Scatter plots answers and explained pleaseee!!

dlinn [17]

Answer:

The point means that when the player's shoe size was 12, their height was 74 inches

Step-by-step explanation:

7 0

3 years ago

Your chemistry textbook has 936 pages and weighs 4.2 pounds. your calculus textbook has 1368 pages and weighs 6.0 pounds. these

Zarrin [17]

Let the number of chemistry books be x and the number of calculus books be y
total number of books in each case is:
x+y=24
x=24-y.....i

Weight of each case:
2707.2/20
=135.36
thus
4.2x+6.0y=135.36..ii substituting i in ii
4.2(24-y)+6y=135.36
100.8-4.2y+6y=135.36
hence
1.8y=34.56
y=19.2
hence
x=24-19.2
x=4.8
thus the number of chemistry books was 4.8*20=96 number of calculus was
19.2*20
=384 books

4 0

3 years ago

What is greater 413,005 or 62,910

Reika [66]

412,005 and 62,910 the number you are looking for is greater than them is 1112,9328 is greater than 413,005 and 62,910

6 0

4 years ago