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mart [117]
3 years ago
10

Geometry help please

Mathematics
1 answer:
Ghella [55]3 years ago
7 0
If we know the three corresponding sides form the same ratio, then we can use the SSS similarity theorem

If we know that 2 pairs of angles are congruent, then we can use the AA similarity theorem

Finally, if we know that two sides are proportional with the congruent angles between the two sides, then we can use the SAS similarity theorem

See the attached for the final answers

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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
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

5 0
2 years ago
Which circle will have the largest circumference?
Dmitriy789 [7]
7383829bshsbnebsbbwben
4 0
3 years ago
Rewrite the radical as a rational exponent. the fourth root of 7 to the fifth power
Verdich [7]
7^5/4 would be the answer to the question I think you are asking
7 0
3 years ago
Read 2 more answers
Thomas invests $50,000 in an account that compounds interest continuously and earns 15%. How long will it take for his money to
WARRIOR [948]

Answer:

It will take about 7.3 years for his money to triple.

Step-by-step explanation:

Identify the variables in the formula.

A = 150,000

P = 50,000

r = 0.15

t = ?

A = Pe^rt

Substitute the values into the formula.

150,000 = 50,000e^0.15*t

Solve for t. Divide each side by 50,000.

3 = e^0.15*t

Take the natural log of each side.

ln 3 = ln e^0.15*t

Use the power property and then simplify.  

ln 3 = 0.15*t ln e

ln 3 = 0.15-t

Divide each side by 0.15.

(ln 3) /(0.15) = t

Approximate the answer.

t ≈ 7.3

4 0
3 years ago
Read 2 more answers
6. Find the measure of each<br> marked angle.
Katyanochek1 [597]
ANSWER : both angles are 60 degrees and x is equal to 8.
10x - 20 = 7x + 4
Move the terms
3x = 24
x= 8
Sub back in to find the value:
80 - 20 = 60
56 + 4 = 60

Please mark as brainliest
8 0
3 years ago
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