The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.) cm2 (b) What is the relative error

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 = [tex]\frac{(63 - 60}{(79 - 80)} (x - 80)[/tex]

⇒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 = [tex]\frac{285}{6}[/tex]

⇒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

Answer:

Umm can you please rewrite that

Step-by-step explanation:

its not really anything to simplfy

Answer:

1. <

2.>

3.>

Step-by-step explanation:

Answer:

Since the value of y is always the double of x, the relationship (0,0) (2,4) (4,8) (6,12) can be considered proportional.

Since the division of y by x gives different values, the relationship (0,1) (2,5) (3,9) (4,10) is not proportional.

Step-by-step explanation:

A relationship (x,y) can be considered proportional if the division of x by y is always the same.

Is this relationship proportional? (0,0) (2,4) (4,8) (6,12)

Why?

The double of 0 is 0

The double of 2 is 4.

The double of 4 is 8

The double of 6 is 12.

Since the value of y is always the double of x, the relationship (0,0) (2,4) (4,8) (6,12) can be considered proportional.

Is this relationship proportional? (0,1) (2,5) (3,9) (4,10)

Why?​

Here, we cannot estabilish a relation, which means that they are not proportional.

Since the division of y by x gives different values, the relationship (0,1) (2,5) (3,9) (4,10) is not proportional.

Answer:

17.3

Step-by-step explanation:

Answer:

B) 103.25

Step-by-step explanation:

Area of rectangle:

A = bh

A = (16)(4)

A = 64

Area of a semi-circle:

r = d/2 = 5

A = (πr²)/2

A = (3.14 * 5²)/2

A = (3.14 * 25)/2

A = (78.5)/2

A = 39.25

Combined:

64 + 39.25 = 103.25

Answer: 103.25

Step-by-step explanation:

area of the rectangle is 4*16= 64

The area of the complete circle is [tex]\pi r^{2}[/tex]

r=d/2

r=10/2

r=5

[tex]25\pi[/tex] is the area of the full circle

[tex]\frac{25\pi }{2}[/tex] is the area of the semi- circle

area of the figure

[tex]64+\frac{25\pi }{2}[/tex]=103.27

Answer:

12a+20b-12

Step-by-step explanation:

Answer:

In math, 4 to 7 = 4/7and 7 to 4 = 7/4so they are NOT equal.

Step-by-step explanation:

Answer: No.

Step-by-step explanation: YOU ALREADY HAVE THE ANSWER

Answer:

[tex]m\angle PUQ = 43\textdegree[/tex]

Step-by-step explanation:

[tex]\angle PUQ[/tex], [tex]\angle QUR[/tex], [tex]\angle RUS[/tex], and [tex]\angle RUT[/tex] all form a straight line, so their measures add up to [tex]180 \textdegree[/tex]. Therefore, [tex]m\angle PUQ = 180 \textdegree - m\angle QUR - m\angle RUS - m\angle RUT[/tex] [tex]=180\textdegree - 49\textdegree - 52\textdegree - 36 \textdegree = \bold 4 \bold3\bold\textdegree[/tex]. Hope this helps!

Math isn't my best subject, but I beleive its 43.

49+52+36=137

137-180= 43.

Sorry if it's correct, but I believe 43 is the answer.

Answer:

Evaluate the expression 6 x ( 4 + 3 x 2) + 100. ... mixed numbers) by replacing given fractions with equivalent fractions in such a ... What is the quotient expressed as a.

Answer:

40 (forty) is the natural number following 39 and preceding 41.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

2002 - 2003

Step-by-step explanation:

Answer:

The answer is 2003-2004 I think?

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

y = 3x + 3

Step-by-step explanation:

Rise: 3   Run: 1

slope (m) = 3/1 = 3

y intercept (b) = 3

y = mx + b = 3x + 3

Answer: $8.75 for 250 vitamins.

Step-by-step explanation:

To find how much each vitamin costs we can divide $5.25 by 150.

5.25/150 = 0.035. So each vitamin is equal to $0.035.

We can then multiply the cost of 1 vitamin by 250.

0.035 x 250 = 8.75 or $8.75.

We can also make an equation for this problem. Let the total cost be equal to y and each vitamin equal to x.

y = 0.035x

So the equation above states that the total cost, y, is the amount of vitamins that are bought.

Answer:

Population of the 48th generation will be 4469.

Step-by-step explanation:

Recursive formula by which the population is increasing,

[tex]L_{n+1}=L_n+95[/tex]

L₀ = 4

Common difference 'd' = 95

Recursive formula represents a linear growth in the population.

Therefore, explicit formula for the given sequence will be,

[tex]L_n[/tex] = L₀ + (n - 1)d [Explicit formula of an Arithmetic sequence]

Here n = Number of terms

L₄₈ = L₀ + (48 - 1)(95)

     = 4 + 4465

     = 4469

Therefore, population of the 48th generation will be 4469.

Answer:

c

Step-by-step explanation:

The answer is c

Answer:

5/8 * ? = 2 1/2

Step-by-step explanation:

x is the height of tower when finished.

We know that Priya takes a break when the tower is 2 and 1/2 feet tall, which is 5/8 off the height of the tower she wants to build.

This means that 5/8 of x equals 2 and 1/2 Let us represent this information in an equation.

5/8 × x = 2 and 1/2

Convert our given mixed fraction into improper fraction.

5/8 × x = 5/2

Multiply both sides of our equation by 8/5.

(8/5 × 5/8) × x = (5/2 × 8/5)

x = 8/2

x = 4

4 feet

Answer:

so let's call the unknown number x.

-5/4 x X = 7/2

by changing the subject, X = 7/2 / -5/4

to divide fractions, we turn the fraction we're dividing by upside down and change the sign to multiplication. so X = 7/2 x 4/-5

after multiplying, X =>28/-10

simplified, X = 14/-5

Answer:

(5x3m) + (5x2) = 15m + 10

Step-by-step explanation:

multiply 5 to 3m plus 5 to 2 which is equivalent to 15m + 10

Answer:

12

Step-by-step explanation:

Answer:

[tex]\displaystyle 4^{4}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{4^{-4}}{4^{-8}}[/tex]

Step 2: Rewrite