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Thepotemich [5.8K]
3 years ago
10

Frances has piano lessons every fourth day.

Mathematics
1 answer:
Fiesta28 [93]3 years ago
7 0

Answer: ask your teacher I’m not that smart

Step-by-step explanation:

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Cos x cos (-x) -sin x sin (-x) = 1. Verify the Identity. Please Show All Steps.
umka21 [38]

Answer:

cos x cos (-x) -sin x sin (-x) = 1 ⇒ proved down

Step-by-step explanation:

* Lets revise the angles in the four quadrants

- If angle x is in the first quadrant, then the equivalent angles to it are

# 180 - x ⇒ second quadrant (sin (180 - x) = sin x , cos (180 - x) = -cos x

  tan (180 - x) = -tan x)

# 180 + x ⇒ third quadrant (sin (180 - x) = -sin x , cos (180 - x) = -cos x

  tan (180 - x) = tan x)

# 360 - x ⇒ fourth quadrant (sin (180 - x) = -sin x , cos (180 - x) = cos x

  tan (180 - x) = -tan x)

# -x ⇒fourth quadrant (sin (- x) = -sin x , cos (- x) = cos x

  tan (- x) = -tan x)

* Lets solve the problem

∵ L. H .S is ⇒ cos x cos (-x) - sin (x) sin (-x)

- From the rules above cos x = cos(-x)

∴ cos x cos (-x) = cos x cos x

∴ cos x cos (-x) = cos² x

- From the rule above sin (-x) = - sin x

∴ sin x sin (-x) = sin x [- sin x]

∴ sin x sin (-x) = - sin² x

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x - (- sin² x)

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x + sin² x

∵ cos² x + sin² x = 1

∴ R.H.S = 1

∴ L.H.S = R.H.S

∴ cos x cos (-x) -sin x sin (-x) = 1

8 0
2 years ago
The area of a circle is 39.62cm2.<br> Find the length of the radius rounded to 2 DP.
Shkiper50 [21]

Using the formula for area of a circle:

Area = pi x radius^2

Replace area with the given value:

39.62 = pi x radius^2

Divide both sides by pi

Radius^2 = 39.62/pi

Radius^2 = 12.62

Solve for radius by taking the square root of both sides

Radius = sqrt(12.62)

Radius = 3.55 cm

4 0
2 years ago
For the line segment whose endpoints are R(1, 2) and S(6, 7), find the y value for the point located 3 ov`er 4 the distance from
Mrac [35]

Answer:

23/4

Step-by-step explanation:

This means that it is 3/4 of the distance in the x <u>and</u> y coordinates, so it is 3/4 of the way from 2 to 7, and since this is a difference of 7-2=5, then it is 2 + (5 * 3/4) or 2 + 15/4 or 23/4.

7 0
3 years ago
A bag contains 5 yellow marbles and 10 blue marbles. If a representative sample contains 2 yellow ​marbles, then how many blue m
Dmitry [639]

Answer:

There will be 4 blue marbles

Step-by-step explanation:

Yellow to blue marbles is in a ratio of:

5:10

the representative sample is:

2:x

simplee cross multiplication can be aplied

5x = 2*10

5x = 20

divide both sides by 5

x = 4

there should be four blue marbles

4 0
3 years ago
Read 2 more answers
Find the greatest common factor
timama [110]

<u>answers to 1 - 4:</u>

1.<em> </em><em>GCF: </em>2

2. <em>GCF:</em> 3

3. <em>GCF : </em>7

4.<em> GCF:</em> 3


4 0
3 years ago
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