1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Amanda [17]
3 years ago
12

Unit 6 lesson 9: linear functions sample work

Mathematics
1 answer:
loris [4]3 years ago
4 0

Answer:

Initially, you have 2573 pieces.

You use 5 pieces each minute.

Right when you start, you have 2573 pieces.

One minute after that, you have 2573 - 5 pieces.

Another minute after, you have 2573 - 2*5 pieces.

Another minute after, you have 2573 - 3*5 pieces.

And so on.

You can see the pattern here, and with this, we can find the linear equation that represents the number of pieces that you have as a function of time.

Then, if the variable t represents the number of minutes that passed since you started, we can write the equation:

f(t) = 2573 - 5*t

That represents the number of pieces that you have after t minutes.

You might be interested in
Eighteen subtracted from half a number is 38.<br> Find the number.
Andrews [41]

Answer:

x=112

Step-by-step explanation:

x/2-18=38

first add +18

x/2=56

now multiply by 2

x=112


6 0
3 years ago
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must h
mestny [16]

Answer:

Radius =6.518 feet

Height = 26.074 feet

Step-by-step explanation:

The Volume of the Solid formed  = Volume of the two Hemisphere + Volume of the Cylinder

Volume of a Hemisphere  =\frac{2}{3}\pi r^3

Volume of a Cylinder =\pi r^2 h

Therefore:

The Volume of the Solid formed

=2(\frac{2}{3}\pi r^3)+\pi r^2 h\\\frac{4}{3}\pi r^3+\pi r^2 h=4640\\\pi r^2(\frac{4r}{3}+ h)=4640\\\frac{4r}{3}+ h =\frac{4640}{\pi r^2} \\h=\frac{4640}{\pi r^2}-\frac{4r}{3}

Area of the Hemisphere =2\pi r^2

Curved Surface Area of the Cylinder =2\pi rh

Total Surface Area=

2\pi r^2+2\pi r^2+2\pi rh\\=4\pi r^2+2\pi rh

Cost of the Hemispherical Ends  = 2 X  Cost of the surface area of the sides.

Therefore total Cost, C

=2(4\pi r^2)+2\pi rh\\C=8\pi r^2+2\pi rh

Recall: h=\frac{4640}{\pi r^2}-\frac{4r}{3}

Therefore:

C=8\pi r^2+2\pi r(\frac{4640}{\pi r^2}-\frac{4r}{3})\\C=8\pi r^2+\frac{9280}{r}-\frac{8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{24\pi r^2-8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{16\pi r^2}{3}\\C=\frac{27840+16\pi r^3}{3r}

The minimum cost occurs at the point where the derivative equals zero.

C^{'}=\frac{-27840+32\pi r^3}{3r^2}

When \:C^{'}=0

-27840+32\pi r^3=0\\27840=32\pi r^3\\r^3=27840 \div 32\pi=276.9296\\r=\sqrt[3]{276.9296} =6.518

Recall:

h=\frac{4640}{\pi r^2}-\frac{4r}{3}\\h=\frac{4640}{\pi*6.518^2}-\frac{4*6.518}{3}\\h=26.074 feet

Therefore, the dimensions that will minimize the cost are:

Radius =6.518 feet

Height = 26.074 feet

5 0
3 years ago
In the data set below, what are the lower quartile, the median, and the upper quartile. 13, 16, 16, 17, 51, 57, 62, 72, 92, 97
FinnZ [79.3K]

Answer:

I'm rusty on this but I believe:

the median is 54

the lower quartile = 16

the upper quartile is 72

5 0
3 years ago
Which of the following represents a major difference between the Incas and the Phoenicians?
max2010maxim [7]

Answer:

B

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
A mixture of gasoline and oil is supposed to contain K ounces of oil for every gallon of gasoline.
Masteriza [31]

1,K

i have ttm and plus im smart

4 0
3 years ago
Other questions:
  • a car travels 83 7/10 miles on 2 1/4 gallons of fuel. which is the best estimate of the car travels on one gallon of fuel
    15·1 answer
  • The weight of water is 62 1/2 lb per cubic foot water that weighs 300 lb will fill how many cubic feet
    12·1 answer
  • Within a given population, 22 percent of the people are smokers, 57 percent of the people are males, and 12 percent are males wh
    11·1 answer
  • Write the ordered pair that represents MP. Then find the magnitude of MP.
    15·1 answer
  • For this item, any answers that are not whole numbers should be entered as decimals, rounded to the hundredth. Marissa's Fashion
    14·2 answers
  • Please help meee! :&lt; An author receives $0.60 for each hardcover book or paperback book that is sold. There were x hardcover
    5·1 answer
  • HELLO!! I REALLY NEED SOME HELP WOTH THIS QUESTION, ITS DUE SOON AND IF YOU CAN SHOW WORK THAT WOULD REALLY HELP THX!!
    9·2 answers
  • A box contains
    10·2 answers
  • A triangle has a side lengths of 34in., 28in., and 42in. is the triangle an acute, right, or obtuse?
    10·2 answers
  • Suppose I have Rs 1000 and I put it in the bank. What will be the amount I have after 5 years if Interest is 5% per annum?​
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!