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Liula [17]
2 years ago
12

How do you eliminate the parameter theta to find a Cartesian equation of the curve: x=sin(1/2 theta), y=cos(1/2 theta), 0 is les

s than or equal to theta and theta is less than or equal to 4pi
Mathematics
1 answer:
kiruha [24]2 years ago
6 0
The answer to the problem is as follows:

x = sin(t/2) 
<span>y = cos(t/2) </span>

<span>Square both equations and add to eliminate the parameter t: </span>

<span>x^2 + y^2 = sin^2(t/2) + cos^2(t/2) = 1 </span>

<span>The final step is translating the original parameter limits into limits on x and y. Over the -Pi to +Pi range of t, x varies from -1 to +1, whereas y varies from 0 to 1. Thus we have the semicircle in quadrants I and II: y >= 0.</span>
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If
Nitella [24]

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

<h3>How to find the production level that'll maximize profit?</h3>

The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.

Next, we would differentiate the cost function, C(x) to derive the marginal cost:

C(x) = 12000 + 400x − 2.6x² + 0.004x³

C'(x) = 400 − 5.2x + 0.012x².

Also, revenue, R(x) = x × P(x)

Revenue, R(x) = x(1600 − 8x)

Revenue, R(x) = 1600x − 8x²

Next, we would differentiate the revenue function to derive the marginal revenue:

R'(x) = 1600 - 8x

At maximum profit, the marginal revenue is equal to the marginal cost:

1600 - 8x = 400 − 5.2x + 0.012x

1600 - 8x - 400 + 5.2x - 0.012x² = 0

1200 - 2.8x - 0.012x² = 0

0.012x² + 2.8x - 1200 = 0

Solving by using the quadratic equation, we have:

x = 220.40 or x = -453.73.

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

Read more on maximized profit here: brainly.com/question/13800671

#SPJ1

6 0
2 years ago
Given 11, 12, and 16 as the three
Kazeer [188]

Answer:

It is an acute triangle because all the angles are less than 90 degrees.

4 0
3 years ago
Write an equation of the line that passes through the points (2,−1) and (0,1).
Alina [70]
0,1 is the y-intercept 
5 0
3 years ago
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Sweet t has 2 orange picks for every green pick. if six of the picks are green how many are orange.
klemol [59]

There 12 orange picks because 2 x 6 = 12  

3 0
3 years ago
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225/400 in simplest form
Natali5045456 [20]
It is 9/16

divide bot by 25.
3 0
3 years ago
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