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Alex777 [14]
3 years ago
14

Complete the parametric equations for the given rectangular equation.

Mathematics
1 answer:
Mama L [17]3 years ago
6 0

Answer:

1) x = 5√(1-sin^2t)

2) y = = -2+3t

Step-by-step explanation:

1)

Given rectangular equation:

x^2/25 + y^2 =1

Parametric equations y=-sint and x=?

Find parametric equation for x

Substituting value of y =-sint in given rectangular equation, we get

x^2/25 + (-sint )^2 =1

x^2/25 + sin^2t =1

x^2 + 25sin^2t = 25

x^2 =25 - 25sin^2t

taking square root on both sides

x= √(25 - 25sin^2t)

  = √25(1-sin^2t)

   = 5√(1-sin^2t)

2)

Given rectangular equation:

y=-3x+4

Parametric equations x=2-t and y=?

Find parametric equation for y

Substituting value of x=2-t  in given rectangular equation, we get

y= -3(2-t) +4

 = -6+3t+4

 = -2+3t !

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stepladder [879]

Answer:

15;9;-8

Step-by-step explanation:

1. 5/3x-3=2/3x+12

x=15 once you combine like terms

2. 5x+35-3x+12=7x+2

2x+47=7x+2

5x=45

x=9

3. 12x+20-3=9x-7

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2 years ago
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topjm [15]
The answer is 4/5 because there are 20 in total squared and circles but the total shapes is 25 so simplify the fraction 20/25=4/5
6 0
2 years ago
A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in t
Zinaida [17]

Answer:

a) p(x) = 300 - 3

b) P(x) = -3 x² + 285 x

c) Price of per room per day  = $ 157.5

when Number of rooms occupied , x = 47.5

Step-by-step explanation:

Given - A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in the charge per room per day, one more room is vacant. Each occupied room costs an additional $15 per day to maintain.

To find - a) Find the demand function, expressing p, the price charged for each room per day, as a function of x, the number of rooms occupied.

             b) Find the profit function P(x).

             c) Find the price of per room per day the motel should charge in order to maximize its profit.

Proof -

a)

Let

(x, y) be the point

where x represents number of rooms occupied

and y represents price of room per day.

Now,

Given that,

a room is priced at $60 per day, all 80 rooms of the motel are occupied.

So, point becomes (80, 60)

And  given that For every $3 rise in the charge per room per day, one more room is vacant.

So, point becomes (79, 63)

Now, we have two points (80, 60), (79, 63)

Let us assume that,

p(x) be the price charged for each room per day

Now,

By using point - slope formula , we get

p -60 = \frac{(63 - 60}{(79 - 80)} (x - 80)

⇒p -60 = (-3)(x-80)

⇒p-60 = 240 -3 x

⇒p(x) = 240 + 60 -3 x

⇒p(x) = 300 - 3 x

b)

Given that,

Each occupied room costs an additional $15 per day to maintain.

Let C(x) be the cost function,

Then C(x) =15 x

now,

Revenue function,

R(x) =x*p

      = x*(300 -3 x )

      = 300 x - 3 x²

⇒R(x) = 300 x - 3 x²

Now,

We know

Profit function = Revenue function - Cost function

⇒P(x) = R(x)-C(x)

⇒P(x) = (300 x -3 x²) -15 x

⇒P(x) = -3 x² + 285 x

c)

P'(x) = -6 x +285

For Maximize profit , Put P'(x) = 0

⇒-6 x+ 285 =0

⇒6 x= 285

⇒x = \frac{285}{6}

⇒x= 47.5

∴ we get

Maximize profit is when price, p = 300 - 3x

                                                      = 300 -3(47.5)

                                                      = $157.5

⇒Price of per room per day  = $ 157.5

when Number of rooms occupied , x = 47.5

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Hello!


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2 years ago
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106.666667



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