Geometry Question!!!!!!!!

Audrey has $111 to spend on a tennis racket and lessons. The racket costs $55 and the lessons cost $14 per hour. Define a variab

Mnenie [13.5K]

Answer:

Audrey can afford 4 hours of lesson.

Step-by-step explanation:

Given that:

Amount Audrey has to spend = $111

Cost of racket = $55

Cost per lesson = $14

Let,

y be the total cost

x be the number of hours

According to given statement;

y = 14x + 55

111 = 14x + 55

111 - 55 = 14x

14x = 56

Dividing both sides by 14

$\frac{14x}{14}=\frac{56}{14}\\x=4$

Hence,

Audrey can afford 4 hours of lesson.

7 0

3 years ago

An office supply company produces yellow document envelopes. The envelopes come with a variety of sizes, but the length is alway

IceJOKER [234]

P= 2(2w+4)+2w
P=4w+8+2w
P= 6w+8 is the answer

6 0

3 years ago

These Questions is worth 20 Points. No Explanation Required.

avanturin [10]

13. five plus y equal to negative two. y = -7

14. eight plus h equal to twelve. h = 4

15. negative thirteen plus four equal n. n = -9

7 0

3 years ago

Find a parametric representation for the part of the cylinder y2 + z2 = 49 that lies between the planes x = 0 and x = 1. x = u y

sweet-ann [11.9K]

Answer:

The equation for z for the parametric representation is $z = 7 \sin (v)$ and the interval for u is $0\le u\le 1$ .

Step-by-step explanation:

You have the full question but due lack of spacing it looks incomplete, thus the full question with spacing is:

Find a parametric representation for the part of the cylinder $y^2+z^2 = 49$ , that lies between the places x = 0 and x = 1.

$x=u\\ y= 7 \cos(v)\\z=? \\ 0\le v\le 2\pi \\ ?\le u\le ?$

Thus the goal of the exercise is to complete the parameterization and find the equation for z and complete the interval for u

Interval for u

Since x goes from 0 to 1, and if x = u, we can write the interval as

$0\le u\le 1$

Equation for z.

Replacing the given equation for the parameterization $y = 7 \cos(v)$ on the given equation for the cylinder give us

$(7 \cos(v))^2 +z^2 = 49 \\ 49 \cos^2 (v)+z^2 = 49$

Solving for z, by moving $49 \cos^2 (v)$ to the other side

$z^2 = 49-49 \cos^2 (v)$

Factoring

$z^2 = 49(1- \cos^2 (v))$

So then we can apply Pythagorean Theorem:

$\sin^2(v)+\cos^2(v) =1$

And solving for sine from the theorem.

$\sin^2(v) = 1-\cos^2(v)$

Thus replacing on the exercise we get

$z^2 = 49\sin^2 (v)$

So we can take the square root of both sides and we get

$z = 7 \sin (v)$

4 0

3 years ago

PLEASE ANSWER THESE TWO QUESTIONS ASAP!!!!!!!!!!!!!!!!

nikdorinn [45]

1. Separate the composite figure into two shapes whose area can be indentified, and then add the areas together.

4 0

3 years ago