Figure 4 shows a container in the shape of an inverted right circular cone which contains some water.


The cone has an internal radius of 2.5 m and a vertical height of 4 m.


At time t seconds, the height of the water is h m, the volume of the water is V m3 and water is modelled as leaking from a hole in the bottom of the container at a rate of h m3 s –1.


see on picture!


Given that the container was initially full of water,


(b) find an equation, in terms of h and t, to model this situation.

(3)


It takes close to 43 minutes for the container to empty.


(c) Use this information to comment on the suitability of this model.

Figure 4 Shows A Container In The Shape Of An Inverted Right Circular Cone Which Contains Some Water.The

Answers

Answer 1

Answer: a) See below; b) 2/5([tex]h^{\frac{5}{2} }[/tex]) = - [tex]\frac{1}{200}[/tex].t + 0.215

Step-by-step explanation:

a) To determine the radius (x) of the volume of water remaining, use proportionality of similar triangles:

[tex]\frac{x}{2.5} = \frac{h}{4}[/tex]

x = 0.625h

Volume is

V = 1/3.π.(0.625h)².h

V = 1/3.π.0.391.h³

Using the chain rule to determine the rate of change of height in function of t:

[tex]\frac{dV}{dt} = \frac{dV}{dh} . \frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt} = \frac{dV}{dt}/\frac{dV}{dh}[/tex]

[tex]\frac{dh}{dt} =[/tex] (π/512).[tex]\sqrt{h}[/tex] / 0.391.π.h²

[tex]\frac{dh}{dt} =[/tex] (π . [tex]\sqrt{h}[/tex]) / 512.0.391.π.h²

[tex]\frac{dh}{dt} =[/tex] [tex]\frac{h^{\frac{-3}{2} } }{200}[/tex]

[tex]h^{\frac{3}{2} }\frac{dh}{dt}=\frac{-1}{200}[/tex]

b) To find an equation:

[tex]h^{\frac{3}{2} }[/tex] dh = -(1/200) dt

∫ [tex]h^{\frac{3}{2} }[/tex] dh = -1/200 ∫dt

[tex]\frac{2.h^{\frac{5}{2} } }{5}[/tex] = [tex]\frac{-1.t}{200}[/tex] + c

It is known that it takes 43 minutes to empty the cone, so:

0 =  [tex]\frac{-1.43}{200}[/tex] + c

c = 0.215

The equation is:

[tex]\frac{2.\sqrt[5]{h^{2}} }{5}[/tex] = [tex]\frac{-t}{200}[/tex] + 0.215

c) The equation shows how height and time are inversely proportional to each other: as time goes up, height goes down. Mathematically, though, time cannot be negative. So, the model is suitable for modeling time and height but is not mathematically correct.


Related Questions

Solve: 3x
+ 4 = 5x - 4x - 8​

Answers

Answer:

3x =  - 18

Step-by-step explanation:

1. Simplify this equation in terms of what is already provided:

3x + 4 = 5x - 4x - 8 ⇒ 3x + 4 = x - 8

2. Now subtract 3x from either side, at the same time adding 8 to either side:   3x + 4 = x - 8 ⇒ 4 = -2x - 8 ⇒ 12 = -2x

3. Divide -2 on either side to isolate the x, and recieve it's value:

12 = -2x ⇒ x = 12/-2 ⇒ x = -6

4. The question demads for the value of 3x, so simply multiply the known value of x by 3, as such: x = -6 ⇒ 3x = -6 * 3 = -18

The answer is 3x=-18

(-3x + 15) + (-3x + 2)

Answers

Answer:

If you are looking for a simplified equation, then the answer is -6x + 17  

Step-by-step explanation:

(-3x + 15) + (-3x + 2)

Because you are only adding and subtracting here, you can take out the parentheses.

-3x + 15 -3x + 2

= -6x + 17  

Pls help me I give brainliest thank uu and can u do step by step

Answers

Answer:

A. 48,000

Step-by-step explanation:

60 x 20= 1200

1,200 x 40= 48,000

Plz mark brainliest .^.

Answer:

To find the volume you have to multiply all the number together in any order. The order doesn't matter.

Step-by-step explanation:

To find volume=

40*20= 800

then, 800*60= 48,000

since it's in cm and there are 3 numbers then it would be 48,000 cm cubed

what are three segments from this figure?

Answers

Answer:

AD, DA, ED, DE

Step-by-step explanation:

what is the area of a circle with the equation (x − 6)² + (y + 2)² = 17 ?

Answers

Answer:

17π

Step-by-step explanation:

Equation of a circle is:

(x − h)² + (y − k)² = r²

Area of a circle is:

A = πr²

r² = 17, so A = 17π.

A sculpture sits on a pedestal in the shape of a square prism. The side lengths of a base of the prism are 3 feet. The height of the prism is 4 feet. The museum director wants to cover all but the underside of the pedestal with foil that costs $0.22 per square foot. How much will the foil cost?

Answers

Answer:

Total cost of covering the pedestal is $12.54.

Step-by-step explanation:

The pedestal is a square prism so top and bottom are of square shape.

Hence, we have here length = width

We know that the Total Surface Area of a Prism is:

[tex]\text{Total Surface Area = } 2 (l\times w+ w \times h+ h \times l)[/tex]

Where l is length,

w is width and

h is height of prism

We know that here w = l = 3 feet

and h = 4 feet

Also, underside of pedestal is not to be covered.

The underside of pedestal is square type.

So,

[tex]\text{Required Total Surface Area = } l\times w+ 2\times w \times h+2\times h \times l[/tex]

[tex]\Rightarrow 3 \times 3 + 2 \times 3 \times 4 + 2 \times 3 \times 4\\\Rightarrow 9 + 24 + 24\\\Rightarrow 57\ ft^{2}[/tex]

Cost of cover per square foot = $ 0.22

Total cost of [tex]57\ ft^{2}[/tex]  [tex]\Rightarrow 0.22 \times 0.57 = \$12.54[/tex]

Which of the following values of t will result in a true statement when substituted into the given equation? A. t = 8 B. t = -8 C. t = 11 D. t = -12

Answers

Answer:

B

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

subtract 6066 from 294

Answers

Answer:

-5772

Step-by-step explanation:

294-6066=-5772

Answer:

The answer would be 2,772

Step-by-step explanation:

6,066 - 294 = 2,272

I hope that helps!!:)

what is the measure of angle A?

Answers

Answer:

A = 77.32

Step-by-step explanation:

sin theta = opp/ hypotenuse

sin A = 80/82

sin A = 40/41

Take  the inverse sin of each side

A = sin ^-1 (40/41)

A =77.31961651

To the nearest hundredth

A = 77.32

the price increase of a set of golf clubs is from $250 to $750. What is the percent increase?

Answers

Answer:

300%

Step-by-step explanation:

3 times 250 is 750

A shoe manufacturer was investigating the weights of men's soccer cleats. He felt that the weight of these cleats was less than the average weight of 10 ounces. After a random sample of 13 pairs of cleats, he found that sample mean was 9.63 and the standard deviation was .585. At a significance level of .05, can it be concluded that the researcher was correct?
Show work

Answers

Answer:

 The conclusion is that the researcher was correct

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 13[/tex]

    The sample mean is  [tex]\= x = 9.63[/tex]

     The standard deviation is  [tex]s = 0.585[/tex]

      The significance level is  [tex]\alpha = 0.05[/tex]

The Null Hypothesis is  [tex]H_o : \mu = 0[/tex]

The Alternative  Hypothesis  is  [tex]H_a = \mu < 10[/tex]

The test statistic is  mathematically represented as

          [tex]t = \frac{\= x - \mu }{\frac{s}{\sqrt{n} } }[/tex]

Substituting values

          [tex]t = \frac{9.63 - 10 }{\frac{0.585}{\sqrt{13} } }[/tex]

         [tex]t = - 2.280[/tex]

Now the critical value for [tex]\alpha[/tex] is  

     [tex]t_{\alpha } = 1.645[/tex]

This obtained from the critical value table

  So comparing the critical value of alpha and the test value we see that the test value is less than the critical value so the Null Hypothesis is rejected

 The conclusion is that the researcher was correct

 

 

What is the volume of this rectangular prism?(HURRY)

Answers

Answer:

295.2

Step-by-step explanation:

Answer:295.2 cm^3

Step-by-step explanation:

Length=L=15cm

Width=w=4.1cm

Height=h=4.8cm

volume of rectangular prism=L x w x h

Volume=15x4.1x4.8

Volume=295.2 cm^3

£48 is divided between Alf and Ted in the ratio of 7:9. How much does Alf receive?

Answers

So basically you add up the ratio and get 16 because 7+9.
Now you do 48 divided by 16 which is 3 to get one price. Since Alf is divided by 7 you multiply 3 with 7. So the answer would be £21

7:9=7+9=16

Alf is 7 which means 7/16*£48=6.125

A store display shows two red shirts, one blue shirt, and three shirts with red and white stripes. The display also shows two pairs of blue jeans, one pair of white pants, and one pair of white shorts. What is the probability of randomly selecting an item with white or red on it?
A) 1/4 B) 3/10 C)1/2 D) 7/10

Answers

Answer:

its 7/10

Step-by-step explanation:

The probability of randomly selecting an item with white or red on it is 3/10.

What is the probability?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

A store display shows two red shirts, one blue shirt, and three shirts with red and white stripes.

The display also shows two pairs of blue jeans, one pair of white pants, and one pair of white shorts.

The probability of randomly selecting an item with white or red on it is given by;

[tex]\rm Probability=\dfrac{Total \ number \ of \ items}{Total \ red \ or \ white \ items}\\[/tex]

Total items =  2 + 1 + 3 + 2 + 1 + 1 = 10 itens.

Substitute all the values in the formula

[tex]\rm Probability=\dfrac{Total \ number \ of \ items}{Total \ red \ or \ white \ items}\\\\\rm Probability=\dfrac{3}{10}\\\\[/tex]

Hence, the probability of randomly selecting an item with white or red on it is 3/10.

Learn more about probability here;

https://brainly.com/question/20849420

#SPJ2

What is the area of this parallelogram

Answers

Answer:

27

Step-by-step explanation:

The area of this parallelogram is its base times height. 6x4.5 is 27.

Hope this helps! (please mark me brainliest)

What is the mean of the probability distribution?

Answers

Answer:

2.0

Step-by-step explanation:

assuming this is from edge 2.0 is correct

Answer:

c

Step-by-step explanation:

Part A - find the diameter of the circle?
Part B - Find the circumference of the circle ?

Answers

Answer:

A) 16 cm

B) 50.24 cm

Step-by-step explanation:

Part A:

The diameter is double the radius

The radius is half of the diameter

To work out the diameter you would simply multiply the radius of 8 cm by 2, this gives you 16 cm. This is because the radius is half of the length of the diameter.

1) Multiply 8 by 2.

[tex]8*2=16 cm[/tex]

Part B:

The formula for the circumference of a circle is : [tex]\pi *diameter[/tex]

To work out the Circumference you would multiply the diameter of 16 cm by pi, this gives you 50.24 cm. This is because if you were to substitute the value of the diameter into the formula you would get the same result.

1) Multiply pi by 16.

[tex]\pi*16=50.24[/tex]

Pi in this case is 3.14

In the diagram below, point P is circumscribed about quadrilateral ABCD. What is the value of x? (Pls answer I give lot of point)

Answers

Answer:

D. 50

Step-by-step explanation:

130+x=180

x=50

A firm produces two types of earphones per year: x thousand of type A and y thousand of type B. The cost function (in thousands of dollars) is given by
C(x,y)=110+80x+130y
If the selling price of type A is p and the selling price of type B is q, the price-demand equations are
p=120-3x+y
q=210+x-7y
Determine how many of each type of earphone should be produced per year to maximize profit? What should be the selling prices p and q? What is the maximum profit?

Answers

Answer:

9000 A and 7000 B should be producedp = 100, q = 170$350,000 is the maximum profit

Step-by-step explanation:

We assume that "p" and "q" are given in dollars, so that the profit function (in thousands of dollars) can be written:

  P = xp +yq -C(x, y)

Profit will be maximized when the partial derivatives of P with respect to x and y are both zero:

  ∂P/∂x = p +x(∂p/∂x) +y(∂q/∂x) -∂C/∂x = 0

  (120 -3x +y) +x(-3) +y(1) -80 = 0

  -6x +2y +40 = 0

  3x -y = 20 . . . . put in standard form

and ...

  ∂P/∂y = x(∂p/∂y) +q +y(∂q/∂y) -∂C/∂y = 0

  x(1) +(210 +x -7y) +y(-7) -(130) = 0

  2x -14y +80 = 0

  x -7y = -40 . . . . put in standard form

__

The solution to these simultaneous equations can be found a variety of ways. Using Cramer's Rule, we have ...

  x = ((-1)(-40) -(-7)(20))/(-1·1-(-7)(3)) = 180/20 = 9

  y = (20(1) -(-40)(3))/20 = 140/20 = 7

9000 type A and 7000 type B earphones should be produced.

__

The corresponding selling prices are ...

  p = 120 -3(9) +7 = 100

  q = 210 +9 -7(7) = 170

The selling prices should be ...

  p = $100, q = $170

__

The maximum profit is ...

  P = xp +yq -C(x, y) = (9)(100) +(7)(170) -(110 +80(9) +130(7))

  P = 9(100 -180) +7(170 -130) -110 = 180 +280 -110

  P = 350

The maximum profit is $350,000.

A sector with an area of 11/2*pi cm^2 has radius of 3 cm. What is the central angle measure of a sector in degrees?

190
200
210
220

Answers

Answer:

Step-by-step explanation:

Area of sector = angle/360 * pi * r^2

5.5pi = angle/360 * pi * 9

5.5 = angle/360 * 9

angle = (5.5 * 360)/9 = 40 * 5.5 = 220

What is the 25th term of this arithmetic sequence?
{8, 5, 2,-1,-4, ...}
Type the correct answer in the box. Use numerals instead of words.

Answers

Answer:

Continue the pattern 24 more times by multiplying 24 terms with 3 subtracted per term

24x3=72

subtract 72 to find the term

8-72=-64

Should be -64 but we will still continue the pattern to double check

8,5,2,-1,-4,-7,-10,-13,-16,-19,-22,-25,-28,-31,-34,-37,-40,-43,-46,-49,-52,-55,-58,-61,-64

-64 is the 25th term

Hope this helps

Step-by-step explanation:

HELP ME PLEASE , ALOT OF POINTS, CHECK DOCUMENT! Show work

Answers

Answer:

x=8

Step-by-step explanation:

log4( x-6) +log4(x) = 2

We know that loga + log b = log (ab)

log4( x-6)(x) = 2

Raise each side to the base of 4

4^log4( x-6)(x) = 4^2

( x-6)(x) = 16

Distribute

x^2 -6x = 16

Subtract 16 from each side

x^2 -6x-16 = 0

Factor

(x-8) (x+2) =0

Using the zero product property

x-8=0      x+2 =0

x=8     x=-2

Checking, we cannot have the log of a negative number so -2 is not a solution

Answer:

x = 8

Step-by-step explanation:

log4(x - 6) + log4(x) = 2

log4[(x - 6) × x] = 2

x² - 6x = 4²

x² - 6x - 16 = 0

x² - 8x + 2x - 16 = 0

x(x - 8) + 2(x - 8) = 0

(x + 2)(x - 8) = 0

x = 8, -2

Log of negative numbers do not exist, so x is only 8

Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing!

Answers

Answer:

Step-by-step explanation:

B or c

Every year, census researchers collect data from 850 public and private hospitals across the United States. Which issue will invalidate the conclusion of the hypothesis test? Group of answer choices The data comes from only 850 hospitals in the U.S. when there are 5,700 hospitals in the U.S. Researchers received more data from public hospitals than from private hospitals. The data is selected by choosing the first 850 hospitals from an alphabetized list.

Answers

Answer:

Option C

Step-by-step explanation:

For a better, clear and unbiased sampling, choosing randomly might not allow for a biased sampling. Choosing in an alphabetical order might not give a representative of the whole hospitals both private and public, thus invigilator the conclusion of our hypothesis test.

Simplify (-2x^3)2•y•y^9

Answers

Answer: -4x^3 y^10
-2x^3 • 2 = 4 (because 2•2 is 4, they don’t share the same variable so you just multiply the base)
y^9 • y^1 (9+1=10)

-4x^3 y^10

Simplify (-2x^3)^2 •y•y^9       Answer 4x^6y^10

4. Kevin is using his scanner to make a smaller version of the school logo to put in the yearbook.
The original is 7 by 10 inches. The reduced image is 5.25 by 7.5 inches. What is the scale
factor of the dilation?
Math Accelerated . Chapter 11 Congruence Similarity and Transformations

How would I show my work?

Answers

Answer:

scale factor 2.5

Step-by-step explanation:

7.5% of what is 7.38?

Answers

Answer:

What =98.4

Step-by-step explanation:

Of means multiply and is means equals

7.5% * What = 7.38

Change to decimal form

.075 * what = 7.38

Divide each side by .075

.075 What /.075 = 7.38/.075

What =98.4

Answer:

the answer for this question is 98.4

you roll a cube find the probability of rolling an even number?

Answers

Answer: 1/2

Step-by-step explanation: Note that to roll an even number, we can roll a 2, 4, or 6.

So there are three ways to roll an even number.

Now let's use our ratio for the probability of an event.

P(event) = number of favorable outcomes/total number of outcomes

Since we want to find the probability of rolling a 3, the number of favorable outcomes for rolling a 3 will go on top in the ratio.

Also, remember that a number cube has six total outcomes.

So 6 will go in the bottom of our ratio

So the probability of rolling an even number is 3/6.

However, we can reduced 3/6 to 1/2.

Always reduce when finding probability.

So the probability or likelihood of rolling an even number is 1/2.

2x2+3y=-2 solve for y

Answers

Answer:

y=(-2/3)x^2-(2/3)

Step-by-step explanation:

2x^2+3y=-2

3y=-2x^2-2

y=(-2/3)x^2-(2/3)

Answer:

y= -2

Step-by-step explanation:

2x2+3y=-2

4+3y=-2

Subtract 4 from both sides

3y=-6

Divide both sides by 3

y= -2

In my case, x means multiplied by not a variable.

A certain manufacturing company has the following data on quantities shipped and unit costs for each of its four products.

Products

Base-Period
Quantities (Year 1)

Mean Shipping Cost
per Unit ($)

Year 1

Year 5

A

1,500

10.50

15.90

B

5,000

16.25

33.00

C

6,500

12.20

18.40

D

2,500

20.00

35.50

Use the price data to compute a Paasche index for the shipping cost if year 5 quantities are 4,000, 3,000, 8,000, and 3,000 for products A, B, C, and D, respectively. (Round your answer to the nearest integer.)

I5 =

Answers

Answer:

Paasche's Index=  168.63= 169

Step-by-step explanation:

Products

Base-Period                                                    Current Period

    Quantities    Mean Shipping                    Quantities    Mean Shipping

     (Year 1)         Cost per Unit ($)                  (Year 5)  Cost per Unit ($)

A         1,500         10.50                         4000                 15.90

B         5,000      16.25                            3000                 33.00

C         6,500        12.20                          8000                  18.40

D          2,500      20.00                         3000                   35.50

Paasche's Index= ∑ pn.qn/∑po.qn* 100

Where pn is the price of the current year and qn is the quantity of the current year and po. is the price of the base year and qo. is the quantity of the base year.

Paasche's Index is the percentage ratio of the aggregate of given period prices weighted by the quantities sold or consumed in the given period to the aggregate of the base period prices weighted by the given period quantities.

Multiplying the current year prices with the current year quantities and the base year price with the current year quantities we get.

Product               pn.qn                      po.qn

A                         15.90* 4000         10.50* 4000

                          = 63600                    =42000

B                       33.00*3000           16.25 * 3000  

                           = 99000                    = 48750

C                      18.40* 8000          12.20 *8000

                            =147200                 =97600

D                     35.50* 3000        20.00*3000  

                          =106500              60,000        

∑                          416300                  248350      

Paasche's Index= ∑ pn.qn/∑po.qn= 416300/ 248350 *100  =  1.676=1.68= 168.63= 169

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Whats the simplified principal square root of -36 Find the mean of 9.63, 9.75, 9.79, 9.80, 9.88, 9.94, 9.98, 11.99 A box contains cards that are numbered from 1 to 100. What is the probability of randomly selecting a number that is less than 12? 1 / 100 1 /12 11 / 100 12 / 100 What was the poet's purpose in writing the poem Escape? Please make sure you use proper grammar, capitalization, punctuation, and textual evidence in your thoughtful answer. A trapezoid was broken into a triangle and rectangle. The base of the triangle b is ______cm. Change the verb in italics to the future tense.Yo escrib una composicin interesante. determine the intercept of the line Which of the following parasites can grow more than 20 inches in length? a Coccidia b Hookworms c Whipworms d Tapeworms Decide if the verb is conjugated correctly in the following sentence.Juan y David tenen muchos amigos. (tener)The verb is conjugated correctly.O The verb is not conjugated correctly. Mike is grilling steaks for dinner. The grilling surface is shown below. Each steak requires approximately 0.25 square feet of the grill's surface. What is the maximum number of steaks that Mike can grill at the same time? 2.5 feet 2 feet 3.5 feet Please hurry its urgent. Consider the food web seen here. One member, the northern spotted owl, lives in cavities of trees in old-growth forests. Oldgrowth forests contain trees that are more than 200 years old and have not been cut, pruned, or managed. Imagine that theseforests have been heavily logged, Predict the outcome on this food web if the habitat of the owl is removedAYThe food web will collapse without this top-level consumer presentB)The niche filled by the owl will be filled by other predators like the hawkand foxThe niche filled by the owl will be empty. The other animals within thefood web will grow unchecked.Without the owl present, the empty niche will result in an overpopulationof hawks. Eventually the lower-level consumers will disappearDY Turn the following pieces into a sentences using the present progressive:1. T + tomar fotos.2. Yo + no dormir. odn and aderonke have 6:4 in 80 units of transcorp's share. how many units of this shares belong to odn Write Scheme functions to do the following. You are only allowed to use the functions introduced in our lecture notes and the helper functions written by yourself. (a) Return all rotations of a given list. For example, (rotate (a b c d e)) should return ((a b c d e) (b c d e a) (c d e a b) (d e a b c) (e a b c d)) (in some order). (b) Return a list containing all elements of a given list that satisfy a given predicate. For example, (lter (lambda (x) (< x 5)) (3 9 5 8 2 4 7)) should return (3 2 4). The wheel of a bike has a diameter of 27 inches. Find the circumference of the wheel. Round your answer to the nearest whole number. 18. The Environmental Defense Fund, The Friends of the Earth, and The Natural Defense Council, (1 point)are all divisions of The Environmental Protection Agency.TrueFalse*PLEASE HELP* Which statement is correct?The range of the graph is all real numbers less thanor equal to 0.The domain of the graph is all real numbers less thanor equal to 0.O The domain and range of the graph are the same.The range of the graph is all real numbers. How many grams is 4.2X10^24 atoms of sulfur? What is the answer to this? Please find the surface area of the sphere. Round your answer to the nearest hundredth.