Question

The figures indicate that the higher the orbit of a satellite, the more of the earth the satellite can "see." Let θ, s, and h be as in the figure, and assume the earth is a sphere of radius 3960 miles.

Answer 1

please do not ask the same question twice, thank you

is there a picture we can see? or a question we can solve?

Answer 2

okay so for the first one

let r be the radius of 3960

the angle will be theta

theta = \[\cos^{-1} \frac{ r}{ r+h }\]

Answer 3

so plug in 3960 for r and that is the first answer

Answer 4

If a) is looking for what theta of h is equal to, wouldn't I need to get h and theta on the same side?

Answer 5

your theta is dependent on what h is, you theta is an equation of h

just like when you have y= 2x

y in an equation of x

Answer 6

So my answer would be like cos^-1(3960/3960+h)?

Answer 7

yes, for the first question

because cos(theta) = adjacent/hypotenuse

adjacent = radius
hypotenuse = radius + h

Answer 8

Okay, now part b)

Thank you btw

Answer 9

s is an arc length

the equation for arc length or a circle is radius * degree

well the degree is 2*theta

so s = radius * 2 * theta

Answer 10

(theta being in radians)

Answer 11

I don't follow, I'm sorry. My professor has not taught arc length.

Answer 12

oh, well that is how you would solve s in terms of theta :P

Answer 13

Okay so it would be like.. 3960*theta?

Answer 14

*2

Answer 15

so 7920*theta

Answer 16

"Easy" enough now for part C)

Answer 17

well we already solved for theta, so plug in your first answer in part A in for theta in part B

Answer 18

Like 7920(cos^-1(3960/3960+h))

Answer 19

yep

Answer 20

Then part d plug 100 in for h?

Answer 21

yeah that seems correct

Answer 22

Then for e... Set s equal to 3000 and solve for h?

Answer 23

exactly!

Answer 24

How would I do that with the inverse.. I haven't solved equations with an inverse yet either

Answer 25

you use a calculator if you're trying to find an exact answer. i'm assuming you haven't learned Taylor Series yet

Answer 26

No, I have not heard of It:(
Also, on part d I used my calculator and got 100924 and it was apparently wrong

Answer 27

With decimals but that was it rounded

Answer 28

it's kind of silly if they expect you to get exact answers for these questions haha

Answer 29

were the other questions correct?

Answer 30

Yes!

Answer 31

well that's good at least :P

Answer 32

are you using webassign?

Answer 33

Yes -_-

Answer 34

How would I get grid of the inverse cosines in part d I know enough algebra to solve but I'm not sure what to do with the inverse

Answer 35

\[x = \cos^{-1} (4) ---> \cos{x} = 4\]