A. The amount of water in a tank t minutes after it has started to drain is given by = 100( − 15) 2 . I. At what rate is the water running out at the end of 5 minutes? Ii. What is the average rate at which the water flows out during the first 5 minutes?

Answers

Answer 1

Answer:

a)-2000

b)-2500

Step-by-step explanation:

Given:

W(t) = 100(t-15)²

applying derivation on both sides

W'(t) = 200(t-15)

->a) At what rate is the water running out at the end of 5 minutes?

Evaluating at t=5

W'(5)= 100(5-15) =>200(-10)

W'(5)=-2000

->b) What is the average rate at which the water flows out during the first 5 minutes?

[tex]\frac{W(5)-W(0)}{5-0} =\frac{100(5-15)^2*100(0-15)^2}{5} =>\frac{10000-22500}{5}[/tex]

=>-2500


Related Questions

You pick one card from each set and find the sum. How many different sums are possible?

Answers

Answer:

24 possibilities

Step-by-step explanation:

2*2*6=24

24 possibilities

The number of different sums possible is 24 possibilities.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We have been given that pick one card from each set and find the sum.

Therefore, we need to find the number of different sums that are possible;

2 x 2 x 6=24

24 possibilities

Hence, the number of different sums possible is 24 possibilities.

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can someone help? 25 points

Answers

Answer:

8 hours

Step-by-step explanation:

HE has to pay $7 an hour.

8*7=56

He has a descount of $3, so

$56-$3=$53.

Which is the exat amount of money that Tony has.

Answer:

The answer is 46

Because he wants to spend less so you would do

7x7=49

He could only rent the boat for 7 hours because that would be less than 53$

Now you do 49-3=46

Because he had a discount

So the answer is 46

Step-by-step explanation:

Hope this helped!

how do I simplify this algebraic expression 3x+2a-4x

Answers

Start by changing the -4x to + -4x.

So we have 3x + 2a + -4x.

To simplify, we can only combine what are called our like terms and in this problem, we have a pair of like terms in our x terms.

3x + -4x simplifies to -x.

So our answer is -x + 2a.

Note that if you wrote your answer as -1x + 2a, it means the same thing. However, as we move farther into math, we usually tend to drop the -1 or 1 that is in front of a variable since it's implied

Jackson and Xavier are both solving the multiplication 0.8 x 5. Jackson gets 4 as a solution, and Xavier gets 0.4. Xavier said to Jackson, "Your answer of 4 can't be right for 0.8 x 5. You need a decimal point because a product always has the same number

Answers

Answer:

Jackson

0.8×5=4

Xavier

0.8×5=0.4

If Xavier said to Jackson that his answer of 4 can't be right.

Jackson needs a decimal point because a product always have the same answer.

Then,

Xavier is right with his sayings but wrong with the answer of 0.4

The correct answer is 4.0

The decimal point should be counted from the back not from the front as Xavier did

Given a school supply store sells pencils for $2, pens for $4, and markers for $5. Write an expression for the total cost of 3 pencils, 2 pens, and 3 markers

Answers

Answer: 29

Step-by-step explanation:

3x2= 6

4x2=8

3x5=15

6+8+15= 29

hoped I helped you a bit! Good luck! :)

Tue or False? The first distribution shown below had a smaller mean than does the second distribution

Answers

Answer:

the answer id true

i hope that helps

What are the roots of the graph below?

Answers

Answer:

-2,-1,1,2

Step-by-step explanation:

The term root is just another name for the x intercept so just look at where your line crosses the x axis and you will have your answer. Remember the y axis is not involved so it cannot be a co-ordinate.

The art club had an election to select a president. 75% of the 68 members of the club voted in the election. How many members voted?

Answers

Answer:

51 members voted of the 68 members

The area of a circle is 4π x 2 + 12πx + 9π.
a. What is an expression for the radius of the circle?
b. What is the least possible integer value of x for the circle to exist? Explain.

Answers

Answer:B D

Step-by-step explanation:

I just got it right

A copy machine makes 231 copies in 5 minutes and 15 seconds. How many copies does it make per minute?

Answers

Put 5 min 15 sec into seconds (315 seconds) and set up a ratio to find how many copies are made every 60 seconds.

The solution is 44 copies

The number of copies the copy machine makes in one minute is 44 copies

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The number of copies the copy machine makes = 231 copies

Time required by the to make 231 copies = 5 minutes 15 seconds

5 minutes = 5 x 60 seconds

5 minutes = 300 seconds

5 minutes 15 seconds = 300 + 15 seconds

5 minutes 15 seconds = 315 seconds

So , Time required by the to make 231 copies = 315 seconds

Now , number of copies in 1 minute = 60 x ( The number of copies the copy machine makes / Time required by the to make 231 copies )

Substituting the values in the equation , we get

Number of copies in one minute A = 60 x ( 231 / 315 )

Number of copies in one minute A = 60 x 0.733

Number of copies in one minute A = 44 copies

Therefore , the value of A is 44 copies

Hence , the number of copies is 44 copies

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a knife is 3 times the cost of spoon
9 spoons and 12 knives cost £82.80

Answers

Answer:

5 .52

Step-by-step explanation:

do the math. aaaaaaaaaaaaaaaaaaaannnnnnnnnnnnnnnnnddddddd this is the best appppp evvvvver

Solve the following system of equations {4x−6y=105x+6y=−55

Answers

Answer:

31557778998765432

Step-by-step explanation:

is it impossible

what is -4 {2 - y} + 3y = 3 {y - 4}

Answers

-8+4y+3y=3y-12
7y-8=3y-12
7y-3y= -12+8
4y= -4
Y= -1

Which expression represents the volume of a rectangular prism that is not occupied by the cylinder.

Answers

Answer:

The volume of the prism not occupied by the cylinder is (150 - 25*pi)*h.

Step-by-step explanation:

In order to calculate the volume of the rectangular prism that is not occupied by the cylinder we need to calculate the total volume of the rectangular prism and subtract it by the volume of the cylinder. We have:

Rectangular prism:

Volume prism = length*height*width

Volume prism = 15*h*10 = 150*h

Cylinder:

Volume cylinder = pi*r²*h = pi*5²*h = 25*pi*h

The volume of the prism that is not occupied by the cylinder is:

volume not occupied = volume prism - volume cylinder

volume not occupied = 150*h - 25*pi*h = (150 - 25*pi)*h

The volume of the prism not occupied by the cylinder is (150 - 25*pi)*h.

The city limits of Las Pythagoras form a perfect shape of an isosceles right triangle whose legs are both 25 2525 kilometers long. The population in Las Pythagoras is 100 , 000 100,000100, comma, 000 people. What is the population density of Las Pythagoras?

Answers

320

Step-by-step explanation:

DESPERATE GEOMETRY HELP!!!

Answers

Answer:

b. 3

Step-by-step explanation:

pi * r^2 * h = 162 pi

plug in 18 ft for h

pi * r^2 * (18) = 162 pi

simplifies to r^2 = 9

r=3

James has g amount of games. Samuel, his friend, has 4 times as many games as James. Write an algebraic expression to represent how many games James has and how many games Samuel has in terms of g.

Answers

Answer: The answer is given below

Step-by-step explanation:

From the question, we are told that James has a lot of games and his friend Samuel, has 4 times as many games as James.

So let the number of games that James has be denoted by g.

Since Samuel has 4 times as the number of games that James has, then Samuel's game will be

= 4 × g

= 4g

Therefore, the expression for James will be g and the expression for the number of games Samuel has is 4g.

4. A plane was flying at an altitude of 55,000 feet when it began the descent toward the airport. The airplan
descends at a rate of 825 feet per minute.

A. What is the function rule that describes this situation?

B. What is the altitude of the plane after it has descended for 13 minutes? Show your work

C. Use the function in Part A to determine how long it takes for the plane to land if it descends at a
continuous rate.

Answers

Answer:

Step-by-step explanation:

A Descent rate,

B 10725ft,

C 25min

I think the anser is c:::::::::::::::::)

Describe in your own words what a hyperbola is.

Answers

Answer:

A conic section that can be thought of as an inside-out ellipse

Step-by-step explanation:

Hyperbola is a two-branched open curve-conic section.

What is a hyperbola?

Hyperbola is the locus of all those points in a plane such that the difference in their distances from two fixed points in the plane is a constant.

For the given situation,

We need to describe about a hyperbola.

A hyperbola is two curves that are like infinite bows. It is a two-branched open curve, a  conic section produced by the intersection of a circular cone and a plane that cuts both nappes of the cone.

The standard equation of hyperbola is

                     [tex][\frac{x^{2} }{a^{2} }-\frac{y^{2} }{b^{2} }]=1[/tex]

where,[tex]b^2 = a^2 (e^2 -1)[/tex]

a,b are the points on the plane and e is the eccentricity.

Hence we can conclude that hyperbola is a two-branched open curve-conic section.

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Timothy makes reduced copies of a photograph that has an actual length of 8 in. Each time he presses the reduce button on the copier, the copy is reduced by 12%. What formula shows the pattern for the size of each copy of the photograph as it is reduced? What is the length of the photograph’s copy if Timothy presses the reduce button 5 times? Round to the nearest tenth.

Answers

Answer:

length of the photograph will be 4.2 in. after pressing the button 5 times.

Step-by-step explanation:

By pressing the button, every time size of the photograph gets reduced by 12%.

Therefore, the sequence formed by the reduced sizes of the photo will be a geometric sequence and the formula for the size of the reduced image will be,

L = [tex]l(1-\frac{12}{100})^{n}[/tex]

Where l = Actual length of the photograph

L = length of the reduced image

n = Number of times the button has been pressed

For l = 8 in. and n = 5

L = [tex]8(1-0.12)^{5}[/tex]

  = [tex]8(0.88)^{5}[/tex]

  = 4.22 in

L ≈ 4.2 in.

Therefore, length of the photograph will be 4.2 in. after pressing the button 5 times.

The length of the photograph's copy when the button is pressed the 5th times is 4.2 inches

The question is an illustration of an exponential function.

An exponential function is represented as:

[tex]y = ab^x[/tex]

Where:

a represents the initial value i.e. a = 8b = 1 - r; and r represents the rate. i.e. r = 12%.

So, the function becomes

[tex]y = 8 \times (1 - 12\%)^x[/tex]

Express 12% as decimal

[tex]y = 8 \times (1 - 0.12)^x[/tex]

This gives

[tex]y = 8 \times 0.88^x[/tex]

When the button is pressed the 5th times, we have:

[tex]y = 8 \times 0.88^5[/tex]

[tex]y = 4.2[/tex]

Hence, the length of the photograph's copy is 4.2 inches

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What is the slope of the line that passes through (1,-19) and (-2,-7)?

Answers

The formula for the slope of a line is m = (y2 - y1) / (x2 - x1).

Point 1 = (1, -19)

Point 2 = (-2, -7)

m = (-7 - -19) / (-2 - 1)

m = (-7 + 19) / (-2 - 1)

m = 12 / -3

m = -4

Hope this helps! :)

plzzzzzzzzzzzzzzaaaaaaaaaa

Answers

Answer:

A

Step-by-step explanation:

[tex]3x^2+5x+2=0[/tex]

[tex]x=\dfrac{-5\pm \sqrt{5^2-4(2)(3)}}{6}=\dfrac{-5\pm 1}{6}=-\dfrac{2}{3}, -1[/tex]

Therefore, the answer is choice A. Hope this helps!

In ΔHIJ, the measure of ∠J=90°, IJ = 47 feet, and HI = 68 feet. Find the measure of ∠H to the nearest degree.

Answers

Answer:

44

Step-by-step explanation:

Solve
8 - (2x - 9) = 17-24

Answers

Answer:

x=12

Step-by-step explanation:

8-(2x-+9)=17-24

8-2x=17-24-9

8-2x=-7+-9

8-2x=-16

-2x=-16-8

-2x=-24

x=-24/-2

x=12

8-(2x-9)=17-24
8 - 2x -+9 = -7
-2x+17=-7
-17 -17
-2x = -24
/-2. /-2

x = 12

Melissa needs to wrap a gift box that is shaped like a rectangular prism. The length is 6 inches, the width is 6 inches and the height is 8 inches. How much wrapping paper does she need to cover the whole box

Answers

Answer:

A=264

Step-by-step explanation:

VX
Does choosing a blue marble represent the complement
event of choosing a red marble? Explain.
B
Р
В

Answers

Answer:

red marble

Step-by-step explanation:

i did this yw

what is the percent change between 6 to 3?

Answers

The percentage change is 50%

Answer:

50% = percent chang

Step-by-step explanation:

6 ÷ 50%

6 × .50 = 3

3 ÷ .50 = 6

2. Express as a unit rate.
a) Betty drives her car 150 km in 2 h.
150 km/2 =

Answers

Answer:

75 km per hour.

Step-by-step explanation:

150km/2hr divided by two is 75 km/hr

A bag contains marbles of four different colors listed below. What is the probability of picking a BLUE marble at random out of the bag?
8 blue marbles, 24 red marbles, 16 green marbles, 4 yellow marbles.
~
1) 8/100
2) 2/13
3) 6/13
4) 4/13

Answers

Step-by-step explanation:

Total marbles = 24 + 8 + 16 + 4 = 52

Probability of blue marble = 8/ 52 = 4 / 26 = 2 / 13

Option 2 is the correct answer

Idk what it is plz help me

Answers

Answer:

1) Starting height is 6.25

2) after 20 years it would be 30

1.25(20)=25+5=30

3) 76 years

Answer:

a) 5 feet

b) 30 feet

c) 76 years

Step-by-step explanation:

a) 5 feet. If t is 0, it'll still be 5 feet

b) 30 feet

1.25*20+5=

25+5=

30

c) 76 years

100 = 1.25t+5

1.25t=95

t=76

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