2 answers each for 8-15

Recall the half-angle identity for sine,

sin²(x/2) = (1 - cos(x))/2

Then the given equation is identical to

sin²(θ) = 1 - cos(θ)

Also recall the Pythagorean identity,

sin²(θ) + cos²(θ) = 1

Then we rewrite the equation as

1 - cos²(θ) = 1 - cos(θ)

Factoring the left side, we have

(1 - cos(θ)) (1 + cos(θ)) = 1 - cos(θ)

and so

(1 - cos(θ)) (1 + cos(θ)) - (1 - cos(θ)) = 0

and we factor this further as

(1 - cos(θ)) (1 + cos(θ) - 1) = 0

which gives

cos(θ) (1 - cos(θ)) = 0

Then either

cos(θ) = 0   or   1 - cos(θ) = 0

cos(θ) = 0   or   cos(θ) = 1

[θ = arccos(0) + 2nπ   or   θ = -arccos(0) + 2nπ]

…   or   [θ = arccos(1) + 2nπ   or   θ = -arccos(1) + 2nπ]

(where n is any integer)

[θ = π/2 + 2nπ   or   θ = -π/2 + 2nπ]   or   [θ = 0 + 2nπ]

In the interval 0 ≤ θ < 2π, we get three solutions:

• first solution set with n = 0   ⇒   θ = π/2

• second solution set with n = 1   ⇒   θ = 3π/2

• third solution set with n = 0   ⇒   θ = 0

So, the first choice is correct.

Answer:

B) [tex]-1+cos\theta[/tex]

Step-by-step explanation:

[tex](tan(\frac{\theta}{2}))(-sin\theta)[/tex]

[tex](\frac{1-cos\theta}{sin\theta})(-sin\theta)[/tex]

[tex](\frac{-sin\theta+sin\theta cos\theta}{sin\theta})[/tex]

[tex]-1+cos\theta[/tex]

Therefore, option B is correct

Helpful Tips:

Half-Angle Formula: [tex]tan(\frac{\theta}{2})= \frac{1-cos\theta}{sin\theta}=\frac{sin\theta}{1+cos\theta}=\pm\sqrt{\frac{1+cos\theta}{2}}[/tex]

Answer:

1

Step-by-step explanation:

correct on edge

sin(83 radians) * cos(7 radians)) + (cos(83 radians) * sin(7 radians)) =

0.893996664

Answer:

hope it helps

Answer:

it looks like y int is about 2550

Step-by-step explanation:

Answer:

7308 / 18

= 406

B is the answer.

Answer:

Today, Carmen out surfing for 8 hours

Step-by-step explanation:

160/100 × 5 = 8

Answer:

The price of 1 adult ticket is 12 dollars, and the price of a ticket for one student is 7 dollars

Step-by-step explanation:

Make a system of equations for the two days that the play was shown.

Let x = the price of an adult ticket

Let y = the price of a student ticket

For the first day:

For the second day:

Now, we can solve using the elimination method. Multiply the first equation by 2 and the second equation by 9. Then swap the order of the equations.

Answer: And I don’t know math

Step-by-step explanation:

Answer:

About 3 hours

Step-by-step explanation:

together, they go 13 miles in one hour. 40/13 = 3 with remainder 1

Answer:

[tex]Fourth \: option: y^2=9^2+19^2-2(9)(19) cos(41°)[/tex]

[tex]The \: law \: of \: cosines \: to \: solve \: for \: one \: side  \: is:[/tex]

[tex]c^2=a^2+b^2-2ab \: cos \: C[/tex]

We must know the other two sides (a and b) and the angle between these sides (angle C, the opposite to the side that we want to determine)

In this case c=y, a=9, b=19, and C=41°, then:

[tex]y^2=9^2+19^2-2(9)(19) \: cos \: (41°)[/tex]

Answer:

(40*4)-(32*4)=32

160-128=32

Step-by-step explanation:

Answer:

mx x 2 x1dadqd

Step-by-step explanation:

Answer:

i think that it would be 0

Answer:

É 5x3=15

Step-by-step explanation:

Answer:

94.74

Step-by-step explanation:

Hope this helps!

Answer:

94.74

Step-by-step explanation:

The stocks are worth $ 1396.29 nine months later.

Using the continuous compounding formula,

[tex]A = Pe^{rt}[/tex] where

Substituting the values of the variables into the equation, we have

[tex]A = Pe^{rt}[/tex]

[tex]A = 1200e^{0.202 X 0.75}\\A = 1200e^{0.1515}\\A = 1200(1.1636)\\A = 1396.29[/tex]

So, the stocks are worth $ 1396.29 nine months later.

Learn more about continuous compounding here:

https://brainly.com/question/24722580

Answer:

42 rats.

Step-by-step explanation:

since the ratio of mice to gerbils is 7:4, given that there are 32 gerbils, that means 32/4=8 gerbils; in other words, 56mice:32gerbils. Then, to find the # of rats, the ratio is 4:3, so you take the previous value of the # of mice and divide it by 4 to get 14(3)= 42

To understand this question, we need to know what it's asking and what's important and what is not important. Many people skip this step, but it is very important.

It is asking us to Find how many Rats there are.

This problem is defiantly reduced to the simplistic ratio

The next step is to Find clues

The clues are 32 Gerbils, 7:4 and 4:3

Now i like to make a chart but you may skip this step if you want

Gerbils=32

Mice=??

Rats=??

First, we have to find the numbers of Mice.

(Reducing Ratios divide them by a number like 2:4=1:2)

If you have 32 Gerbils and you reduced it to 4, what did you dived?

32/4=8

So, you multiply 7x8=56

There is 56 Mice.

Our table looks like this

Gerbils=32

Mice=56

Rats=??

Now we use the ratio 4:3 to find the numbers of Rats

If there are 56 mice, and it is reduced to 4, we have to do 56/4 to find out what we have to multiply 3 by to get the total numbers of rats (Inverse Operation) by. We get 14.

So now we do 3x14 in which we get 42.

Our chart now looks like this

Gerbils=32

Mice=56

Rats=42

I Hope this helped if you have any questions just tell me

Answer:

Adelina

Step-by-step explanation:

Answer:

A.  52 green beads; 39 yellow beads

Step-by-step explanation:

See the attachment.  If we take the ratios of 4, 2 , and 3, they add to 9.  The

Green (G), Blue (B), and Yellow (Y) will have 4/9, 2/9 and 3/9 each of the total beads, 117.

G:  52 Beads

B:  26 Beads

Y:  39  Beads

Answer:

The answer is 2

Step-by-step explanation:

The range of class A is 5-0 = 5

The range of class B is 3-0 = 3

the difference between 3 and 5 is 2.

Answer:

1) 9

2) 34

Step-by-step explanation:

For the first one, it would be

= (6×3)/2

= 18/2

= 9

The second one is,

= 36- (12/6)

= 36 - 2

= 34

Answer:

3x2 = 6

6-4x-7

(6-4x) - 7

2x - 7 = messi ok no xd

3.5-

Step-by-step explanation:

Answer:

[tex](3x-7)(x+1)[/tex]

Step-by-step explanation:

Use the slide-and-divide method:

[tex]3x^2-4x-7[/tex]

[tex]x^2-4x-21[/tex] <-- Multiply last term by the leading coefficient 3

[tex](x-7)(x+3)[/tex] <-- Factor

[tex](3x-7)(x+1)[/tex]

Let's simplify step-by-step.

[tex]12a^2*b^4-36a^2*b+44abc=[/tex]

There are no like terms.

Answer:

[tex]12a^2*b^4-36a^2*b+44abc=[/tex]

Answer:

all u do is take 3000×5%=150

Answer:

1.25(-xsquare - 8x + 16)

Step-by-step explanation:

pls give me brainliest

I'm not sure but I think so

Answer:

  a.  39 ft²

  c. 2x² +11x +12

  e. 35 yd²

Step-by-step explanation:

The missing vertical dimension is 5-3 = 2'. The missing horizontal dimension is 11-8 = 3'. Then the figure can be decomposed into a rectangle 11'×3' and one that is 3'×2'. The sum of those areas is ...

  total area = (11 ft)(3 ft) +(3 ft)(2 f) = (3 ft)(11 +2 ft) = (3 ft)(13 ft) = 39 ft²

__

We don't know what to make of the rectangles in each corner, so we'll assume they are distorted right-angle indicators. The area is the product of the dimensions shown:

  A = LW

  A = (2x +3)(x +4) = 2x² +11x +12 . . . area of figure

__

The shaded area is half the area of the rectangle. That is the same area you get if you use the triangle formula for the area of the shaded triangle.

  A = 1/2(14 yd)(5 yd) = 35 yd²

Answer:

C

Step-by-step explanation:

32 / 4  = 8

56 / 7 = 8

64 / 8 = 8

Check the picture below.

Answer:

Assign an identifying variable to the quantity to be found. Write a sentence stating conditions placed on the quantity. Solve the sentence for the variable.

Step-by-step explanation:

can you mark me as brainlist

Answer:

The measure of <Y = 85 degrees

Step-by-step explanation:

you can solve this problem algebraically if you know that the sum of the interior angles of a triangle is 180 degrees.

if you add all of these angles and set them equal to 180, you can find what "a" is.

a+2a+a+10=180 so 4a+10=180 so a is 42.5 (which is equal to angle x)

then looking at all of the options, it can be seen that the first two options are incorrect because angle x is equal to 42.5 degrees.

you know that angle y is equal to 2a, so multiplying "a" by two, you can find that angle y is 85 degrees.

Answer:

130

ratio of woman to man is : 5/8

5/8×208=130

Answer:

130 women

Step-by-step explanation:

3 men to 5 women:

We can add the variable x:

3x + 5x = 208

8x = 208

x = 26

3 * 26 = 78 men,

5 * 26 = 130 women.