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aliina [53]
3 years ago
11

I’m not sure how to complete this if anyone can solve it for me

Mathematics
1 answer:
finlep [7]3 years ago
5 0

Answer:  AD = 108

               BD = 105

             ADB = 213

             ABC = 182

<u>Step-by-step explanation:</u>

If no radius is given, assume it is length 1.

Then, the length of the arc is equal to the central angle.

Reminder that a circle is 360°

\bold{\underline{\stackrel\frown{AD}:}}

The central angle = 108°, so the arc length = 108

\bold{\underline{\stackrel\frown{BD}:}}

BD = BC + CD

     = 35° + 70°

     = 105°

The central angle = 105°, so the arc length = 105

\bold{\underline{\stackrel\frown{ADB}:}}

ADB = AD + CD + BC

     = 108° + 70° + 35°

     = 213°

The central angle = 213°, so the arc length = 213

\bold{\underline{\stackrel\frown{ABC}:}}

First, find the angle of AB.

AB = 360° - ADB  

     = 360° - 213°      

     = 147°

ABC = AB + BC

     = 147° + 35°

     = 182°

The central angle = 182°, so the arc length = 182

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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
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Answer:

a) p(x) = 300 - 3

b) P(x) = -3 x² + 285 x

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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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