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2 years ago

Use a double angle or half angle identity to find the exact value of each expression

Mathematics

1 answer:

inna [77]2 years ago

4 0

θ is given to be in the fourth quadrant (270° < θ < 360°) for which sin(θ) < 0 and cos(θ) > 0. This means

cos²(θ) + sin²(θ) = 1 ==> sin(θ) = -√[1 - cos²(θ)] = -3/5

Now recall the double angle identity for sine:

sin(2θ) = 2 sin(θ) cos(θ)

==> sin(2θ) = 2 (-3/5) (4/5) = -24/25

You might be interested in

[|(x-4)÷(x+5)|]\leq[4]

Katena32 [7]

Answer:

Solutions are;

x = -8

x = -3.2

Step-by-step explanation:

Here, we want to solve the given equation for x

|(x-4)/(x + 5)| = 4

From what we have, this is an absolute value equation and thus, we are going to have two solutions

These are;

x-4/x+ 5 = 4

x-4 = 4(x + 5)

x-4 = 4x + 20

x-4x = 20 + 4

-3x = 24

x = -24/3

x = -8

secondly;

x-4/x+5 = -4

x-4 = -4(x + 5)

x-4 = -4x - 20

x + 4x = -20 + 4

5x = -16

x = -16/5

x = -3.2

3 0

3 years ago

You need to paint a decorative garden ornament that is in the shape of pyramid with a square base

KATRIN_1 [288]

Step-by-step explanation:

Total Surface area of a pyramid is given as

= Lateral surface area + area of base.

Lateral surface area = 1/2×perimeter of base×slant height

given the base is square with side 9 in , and slant height of 12 inches.

therefore, LSA = 1/2(9*4)×12 = 216 in^2

Now, TSA = LSA + Base area = 216+9^2 = 297 in^2

a) It is given that the pyramid is smaller therefore, it will require lesser paint than the original pyramid ( The TSA of the smaller pyramid cannot be calculated as its dimentions are not given).

b) It can not be solved as dimensions are missing in the question.

However, the logic has been explained in the soluion one easily put values to find the solution.

7 0

3 years ago

Ellie's Bakery is having a grand opening sale. All pastries are being discounted by 25%. Let x represent the regular price of an

Sindrei [870]

a) The expression to find the sale price of pastry = 0.75 x

b) The regular price of the pastry bought by Kimberly = $2.70

Step-by-step explanation:

Step 1 :

Let x be the regular price of the pastry in the bakery

Percentage of discount = 25%

Amount of discount = 0.25 x

The expression to find the sale price of pastry = x - 0.25 x = 0.75 x

Step 2 :

Sale price of the pastry bought by Kimberly = $2.03 = 0.75 x

To find the regular price

0.75x = 2.03

x = $\frac{2.03}{0.75}$ = 2.70

Regular price of the pastry bought by Kimberly = $2.70

Step 3 :

Answer :

a) The expression to find the sale price of pastry = 0.75 x

b) The regular price of the pastry bought by Kimberly = $2.70

8 0

3 years ago

Write an equation of the line that is perpendicular to the line y = 1 2 x + 8 that passes through the point (4,6).

Harlamova29_29 [7]

B.

This is because perpendicular lines have opposite and flipped slopes.

4 0

2 years ago

NEED HELP. Show example too

user100 [1]

Answer:

Step-by-step explanation: antimay

6 0

3 years ago