A pizza chef begins to spin a constant volume of dough to make a pie by spinning and tossing the dough into the air, such that the dough takes on a cylindrical shape. The dough's radius increases while the height decreases, but the dough remains a cylinder. At time t = tı, the height of the dough is 1/2 inch, the radius of the dough is 16 inches, and the radius of the dough is increasing at a rate of 2 inches per minute.

Required:
a. At time tı, at what rate is the area of the "top" of the pizza (the part with the toppings) increasing with respect to time? Show the computations that lead to your answer, and indicate units of measure.
b. At time tı, at what rate is the height of the dough decreasing with respect to time?

Answers

Answer 1

Answer:

a ) dAt/dt  =  50,24 in/min

dh/dt  =  -  0,125 in/min

Step-by-step explanation:

The area of the top is At :

At = π*r²

a)  Tacking derivatives with respect to time:

dAt/dt  =  2* π*r * dr/dt

At   t  =  t₁      r  = 16 in     and  dr/dt =  0,5

Then

dAt/dt  =  2*3,14*16*0,5   in/min

a ) dAt/dt  =  50,24 in/min

b) The volume of the cylinder is:

Vc =  π*r²*h     ( where h is the heigh of the cylinder )

Tacking derivatives with respect to time

dVc/dt  =  2* π*r*h*dr/dt  +  π*r²*dh/dt

But  dVc/dt  = 0  since the volume remains constant, then:

π*r²*dh/dt  = -  2* π*r*h*dr/dt

r*dh/dt  =  -  2*h*dr/dt

dh/dt  = - 2*0,5*2/16  in/min

dh/dt  =  -  0,125 in/min


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Lee and Marisol are conducting a science experiment to identify different kinds of macromolecules in food. They prepare the following table to help them remember the chemical reactions that indicate the presence of each type of macromolecule they are studying.

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Answer:

Step-by-step explanation:

Three times the number of polar bears is more than
twice the number of polar bears plus 45.
a. Write an inequality to model this situation.
b. Which of the following could possibly be the
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A. 38
B. 40
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D. 48

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Answer:

a. [tex]3x>2x+45[/tex]  b. [tex]48[/tex]

Step-by-step explanation:

For b the number of polar bears must be greater than 45 in order for there to be more on the left side.

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Which number line shows -3, -2, 1, and 3 correctly plotted?

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Answer:

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Step-by-step explanation:

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Answer:

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An estimated 3 out of every 25 men are left-handed.
What percent of men are lert-handed?

Answers

Answer:

12%

Step-by-step explanation:

3 / 25 = 0.12

Move the dot 2 places to the right to get a percentage.

Answer:

12%

Step-by-step explanation:

3/25 * x/100

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Answer:

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Step-by-step explanation:

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In Mona’s new video game she earns 30 points for each fish caught and 80 points for each octopus captured, but she loses 15 points every time she captures a crab. Which expression represents the total number of points Mona will earn if she catches x fish, y octopi, and z crabs?
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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classify which numbers are rational or irrational


The given numbers are:
5/4
√100
7.3
0.00247
√4/9
√2/24
0.01 with the line above the 1

Answers

Answer:

5/4 = rational   √100 = rational 7.3 =rational 0.00247 = rational √4/9 = irrational √2/24 = irrational 0.01 (with the line) = irrational

Step-by-step explanation:

an irrational number is an infinitely repeating number that can not be written as a fraction, instead it must be written as a decimal. A rational number is a number that can be made by dividing two integers (an integer is a number with no fractional part).

The numbers are,

a. 5/4 = Rational

b. √100 = Rational

c. 7.3 = Rational

d. 0.00247  = Rational

e. √4/9  = Irrational

f. √2/24  = Irrational

g. 0.01 (with the line above the 1) = Irrational

What is Number system?

A system of writing to express the number is called number system.

Given that;

The numbers are,

5/4, √100 , 7.3 , 0.00247, √4/9 , √2/24 , 0.01 with the line above the 1.

Now,

Check the numbers as;

5/4  = 1.25

So, The number is a Rational number.

√100 = 10

So, The number is a Rational number.

7.3 = 7.3

So, The number is a Rational number.

0.00247 = 247/100000

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√4/9 = 2/3 = 0.666.......

So, The number is a Irrational number.

√2/24

So, The number is a Irrational number.

0.01 with the line above the 1

So, The number is a Irrational number.

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a. 5/4 = Rational

b. √100 = Rational

c. 7.3 = Rational

d. 0.00247  = Rational

e. √4/9  = Rational

f. √2/24  = Irrational

g. 0.01 (with the line above the 1) = Irrational

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Enter the midpoint of the segment whose endpoints are (8, 7) and (-2, 16).​

Answers

Answer:

(3, 11.5)

Step-by-step explanation:

The coordinates of midpoint are ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )

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Answer:

(3, 11.5)

Step-by-step explanation:

midpoint=X1 + X2 , y1+y2

2 2

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Use the drop-down menus to label the points on the number line.

Answers

Answer:

Step-by-Use the drop-down menus to label the points on the number line.

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Coordinate geometry is the study of geometry using the points in space.

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Answers

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Answer:

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Step-by-step explanation:

License plates are made using letters followed by digits. How many plates can be made if repetition of letters and digits is​ allowed

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Given f(x) = X-2 and g(x)= 1/x-2 which of the following values is not in the domain of (fog)(x)?

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Answers

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Answer:

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Step-by-step explanation:

Edge 2021

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Answers

Answer:

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Step-by-step explanation:

3x7+2^3/(3+1) <----- Here is the original problem.

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21+2^3/4 <----- Do your multiplication (in the front)

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Answers

Answer:

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Step-by-step explanation:

4a(3b+5)+2b

Substitution

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Order of operations (PEMDAS)

4(6)[21+5]+2(7)

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Answers

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Step-by-step explanation:

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Learning Task No. 3: Solve the following equation. Then compare
your answer by writing <, > and = in your notebook.
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Answers

Answer:

(1)   <

(2)  <

(3)   =

(4)   <

Step-by-step explanation:

[tex]By \ applying \ the \ rule \ of \ BODMAS \ (i.e. \ Bracket, \ of, \ Division,\ Multiplication, \ Addition,[/tex][tex]\ and \ Subtraction).[/tex]

(1)

5 + 8 - 2 -7 = 13 × 10 - 17

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(2)

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(3)

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

The mean of a set of data is 4.68 and its standard deviation is 2.83. Find the z score for a value of 9.38

Given that :

Mean (m) = 4.68

Standard deviation (s) = 2.83

Value of x = 9.38

Zscore = (x - mean) / standard deviation

Zscore = (9.38 - 4.68) / 2.83

Zscore = 4.7 / 2.83

Zscore = 1.6607773

Hence, Zscore for a value of 9.38 is 1.66

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

The dispersion among sample means is less than the dispersion among the sampled items themselves because:______

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Step-by-step explanation:

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Answer:

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Answer:

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