The popcorn in a vending machine costs $0.75 per bag. Which function rule describes the situation?

Evaluate the six trigonometric functions of the angle 0.

Arturiano [62]

Given:

Right triangle

To find:

The six trigonometric functions of θ

Solution:

Hypotenuse = 18

Adjacent side to θ = 10

Opposite side to θ = ?

Using Pythagoras theorem:

$\text {Hypotenuse}^2 = \text{adjacent}^2+\text{opposite}^2$

$18^2 =10^2+\text{opposite}^2$

$324=100+\text{opposite}^2$

Subtract 100 from both sides.

$224=\text{opposite}^2$

Taking square root on both sides.

$4\sqrt{14}=\text{opposite}$

Using trigonometric ratio formula:

$$\sin\theta =\frac{\text{opposite }}{\text{hypotenuse}}$

$$\sin\theta =\frac{4\sqrt{14} }{18}$

$$\csc\theta =\frac{\text{hypotenuse}}{\text{opposite }}$

$$\csc\theta =\frac{18}{4\sqrt{14} }$

$$\cos \theta=\frac{\text { adjacent side }}{\text { hypotenuse }}$

$$\cos \theta=\frac{10}{18}$

$$\sec \theta=\frac{\text { hypotenuse }}{\text { adjacent side }}$

$$\sec \theta=\frac{18 }{10}$

$$\tan \theta=\frac{\text { opposite side }}{\text { adjacent side }}$

$$\tan \theta=\frac{4\sqrt{14} }{10}$

$$\cot \theta=\frac{\text { adjacent side }}{\text { opposite side }}$

$$\cot \theta=\frac{10}{4\sqrt{14} }$

8 0

3 years ago

For a moving object,When. The force acting on the object varies directly with the object's acceleration. When a force of 64 N ac

Tems11 [23]

Answer:

72 N

Step-by-step explanation:

From the question.

Force is directly proportional to acceleration, with the mass of the object constant.

F α a

F = ka

F₁/a₁ = F₂/a₂....................... Equation 1

Where F₁ = Initial force, a₁ = initial acceleration. F₂ = final force, a₂ = Final acceleration.

make F₂ the subject of the equation

F₂ = (F₁/a₁)a₂................ Equation 2

Given; F₁ = 64 N, a₁ = 8 m/s², a₂ = 9 m/s²

Substitute these values into equation 2

F₂ = (64/8)(9)

F₂ = 72 N

5 0

3 years ago

Someone help pls :,)

Semenov [28]

Answer:

W = 87 degrees

Step-by-step explanation:

First we can rearrange the question so that W is isolated on the left side, which we do by dividing both sides by tan:

tanW/tan = 19.0811/tan

W = 19.0811/tan

Now we can use the inverse tan function on the calculator ( $tan^{-1}$ ) to calculate it:

W = 19.0811 x $tan^{-1}$

W = 87 degrees

Hope this helped!

8 0

3 years ago

On Saturday, you spend $33, give $15 to a friend, and receive $20 for mowing your neighbor’s lawn. You have $21 left. Use two me

tia_tia [17]

21+20-15-33=x

x=-7

Hope this helped☺☺

8 0

3 years ago

Find the y? 3x + 6y = 12

kari74 [83]

Could you give Brainliest please???

Answer:

y = 2 - 1/2x

Step-by-step explanation:

So we are given the equation 3x + 6y = 12 and are ask to find y.

To find y you must isolate it first.

3x + 6y = 12

(Subtract 3x to isolate the y term)

6y = 12 - 3x

(Divide both sides by 6 to isolate the variable)

y = 2 - 3/6x

(Simplify)

y = 2 - 1/2x

And that is your answer since there is a second variable.

5 0

3 years ago