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3 years ago

Write the equation of a vertical ellipse with a major axis of 20, a minor axis of 12, and a center of (6, 3)

Mathematics

1 answer:

kupik [55]3 years ago

6 0

Answer:

The answer to your question is

Standard form

$\frac{(x - 6)^{2} }{12^{2}} + \frac{(y - 3)^{2} }{20^{2}} = 1$

General form

400x² + 144y² - 4800x - 864y - 41904 = 0

Step-by-step explanation:

Data

Vertical ellipse

Mayor axis = a = 20

Minor axis = b = 12

Center = (6, 3)

Formula

$\frac{(x - h)^{2} }{b^{2}} + \frac{(y - k)^{2} }{a^{2}} = 1$

Substitution and standard form

$\frac{(x - 6)^{2} }{12^{2}} + \frac{(y - 3)^{2} }{20^{2}} = 1$

General equation

400(x - 6)² + 144(y - 3)² = 57600

400(x² - 12x + 36) + 144(y² - 6y + 9)² = 57600

400x² - 4800x + 14400 + 144y² - 864y + 1296 = 57600

400x² + 144y² - 4800x - 864y +14400 + 1296 - 57600 = 0

400x² + 144y² - 4800x - 864y - 41904 = 0

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Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker sys

il63 [147K]

Answer:

a) $P(x)=-0.042x^2+530x-18000$

b) $P'(x)=-0.084x+530$

$P'(4000)=194$

$P'(9500)=-268$

Step-by-step explanation:

We know that Revenue is our total income and cost is our total cost. Thus, profit is what's left after cost is subtracted from Income (revenue). Thus, we can say:

P(x) = R(x) - C(x)

Finding Profit Function (P(x)):

$P(x) = R(x) - C(x)\\P(x) = -0.042x^2+800x-(270x+18000)\\P(x)=-0.042x^2+800x-270x-18000\\P(x)=-0.042x^2+530x-18000$

This is the profit function.

The marginal profit is the profit earned when ONE ADDITIONAL UNIT of the product is sold. This is basically the rate of change of profit per unit. We find this by finding the DERIVATIVE of the Profit Function.

Remember the power rule for differentiation shown below:

$\frac{d}{dx}(x^n)=nx^{n-1}$

Now, we differentiate the profit function to get the marginal profit function (P'):

$P(x)=-0.042x^2+530x-18000\\P'(x)=2(-0.042)x^1+530x^0-0\\P'(x)=-0.084x+530$

This is the marginal profit function , P'.

We need to find P'(4000) and P'(9500). So we basically put "4000" and "9500" in the marginal profit function's "x". The value is shown below:

$P'(x)=-0.084x+530\\P'(4000)=-0.084(4000)+530\\P'(4000)=194$

and

$P'(x)=-0.084x+530\\P'(9500)=-0.084(9500)+530\\P'(9500)=-268$

6 0

2 years ago

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nalin [4]

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2 years ago

Find the measure of the arc or angle indicated. or find the value of x

bonufazy [111]

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