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svlad2 [7]
3 years ago
10

Determine which equation is belongs to the graph of the limacon curve below.

Mathematics
1 answer:
JulsSmile [24]3 years ago
8 0

Answer: Option C.

Step-by-step explanation:

We have functions of r(θ)

In our graph, we can see that the minimum value of r is when θ = 0°, and the maximum value is when θ = 180°.

We also know that the graph is in the square (-5, 5)x(-5, 5) and you can see that the maximum radius is almost less than 5.

Then let's analyze the options:

A) r = 3 - 2*cos(θ)

the maximum is at the right angle, but the maximum is:

r = 3 -2*(-1) = 5, so this maximum value is bigger than the one in the graph.

B) r = 3 - sin(θ)

For the sin functions, the maximum and minimum do not correspond with the values i write earlier, so we can discard this option.

C) r = 3 - cos(θ)

The maximum is: r = 3 - (-1) = 4, so this may be the correct answer.

the minimum is r = 3 - 1 = 2,

this is a possible equation for our circle.

D) r = 2 - 2*cos(θ)

Here, when θ = 0, we have: r = 2 - 2*1 = 0, but in the graph we can see that the radius is not 0 when θ = 0, so we can discard this option.

So the only option that makes sense is option C.

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The sum of two numbers is 66. The larger number is 6 more than the smaller number. What are the numbers?
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The two numbers are 30 and 36. I know this because when I did 10 and 16, I realized that if I went up 10 for each number, the sum would go up by 20. So I did 20 and 26, and got 46. Then I did 30 and 36, and the sum was 66.

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8 0
3 years ago
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Jason jumped of a cliff into the ocean . His height as a function off time could be models as h(t)=16tsquared + 16t + 480 where
Karo-lina-s [1.5K]

I see that you are in high school, and I'm hoping that you've been introduced
to differential calculus, because I don't know how to answer this question without
using it.

We're told that Jason's height above the water is  <em>H(t) = -16t² + 16t + 480 .</em>
We can observe many things from this equation:
-- Up is the positive direction; down is the negative direction.
-- The acceleration of gravity is 32 ft/sec² .
-- Jason jumps upward from the cliff, at 16 ft/sec .
-- The cliff is 480-ft above the water.
(This tells us why the question is only concerned with his maximum height,
and then it ends ... 480-ft is one serious cliff, and what happens after the
peak of his arc is too gruesome to contemplate.)

In any case, his vertical velocity is the first derivative, with respect to time,
of his height above the water.

         V = -32 t + 16

At the peak of his arc, where gravity takes over, his velocity changes from
upward to downward, and it's momentarily zero.

                                           0 = -32t + 16

Add  32t  to each side:    32t = 16

Divide each side by  32:    <em>  t = 1/2 second</em>

His height at that instant is     H(0.5) = -16(0.5)² + 16(0.5) + 480 =

                                           <em>4-ft above the cliff,  484-ft above the water</em>,

and then he begins falling from that altitude.

The duration of his dive is      484 = 16 t²
                                                   t = √(484/16) = <em>5.5 seconds</em>

and he hits the water at      V = a t = (32) x (5.5) = 176 ft/sec = <em>exactly 120 mph </em>

Jason was good man ... a good student, and always kind to everyone he met.
He will certainly be missed.


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maw [93]

Answer:

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