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skad [1K]
3 years ago
11

An empty cylindrical vase with a radius of 8 cm and a height of 9 cm is filled with 6 cm^3 of sand every 15 seconds. At the same

time 8cm^3 of sand is taken out of the vase every minute. After how many minutes will the base be half filled with sand?
Mathematics
1 answer:
Andru [333]3 years ago
6 0

General Idea:

The volume of cylinder is given by \pi r^{2} h, where r is the radius and h is the height of the cylinder.

Applying the concept:

Step 1: We need to find the volume of full cylinder with the given dimensions using the formula.

Volume of full cylinder =\pi r^{2} h=\pi* 8^{2} *9=576\pi cm^{3}

Volume of half cylinder =\frac{576\pi }{2} =288\pi cm^{3}

Step 2: Let x be the number of minutes of filling the sand.

6 cm^{3} of sand filled every 15 seconds, there are four 15 seconds in a minute.

So volume of sand filled in 1 minute= 6*4 cm^{3} = 24 cm^{3}.

8 cm^{3} of sand taken out of cylindrical vase every minute.

Net volume of sand filled in 1 minute = Volume of sand filled in the vase in one minute - Volume of sand taken out in 1 minute

Net volume of sand filled in 1 minute=24 cm^{3} - 8cm^{3}=16cm^{3}

Volume of sand filled in x minutes = 16x.

We need to set up an equation to find the number of minutes need to fill half the volume in cylindrical vase.

16x = 288\pi \\ \\ x=\frac{288\pi}{16}  \\ \\ x=18\pi \\ \\ x=57 minutes

Conclusion:

The number of minutes required for the base be half filled with sand is 57

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Ali Clara and Shane raise money for new books for the school library all Ellie rays 20% more than Clara and $58 more than Shan C
Vikki [24]

Answer:

a. $435

b. 33.33%

Step-by-step explanation:

P.S - The exact question is -

Let Clara raised money = x

As given,

Ali raised 20% more than Clara

⇒Ali raised money =  x + \frac{20}{100}x = x + \frac{1}{5} x = \frac{6}{5}x

Also given,

Clara raised \frac{1}{4} times more than Shan

Clara raised money = Shan raise money + \frac{1}{4} times shan raired money

⇒Clara raised money = \frac{5}{4}  Shan raised money

⇒Shan raised money =  \frac{4}{5} times Clara

⇒Shan raised money = \frac{4}{5} x

As given,

Ali raised $58 more than shan

⇒\frac{6}{5}x = \frac{4}{5}x + 58

⇒\frac{6}{5}x -\frac{4}{5} x = 58

⇒\frac{2}{5}x = 58

⇒x = (29)(5) = $145

∴ we get

Clara raised money = x = $145

Ali raised money = \frac{6}{5}x = $174

Shan raised money =\frac{4}{5} x  = $116

a.)

Total raised money = $145 + 174 + 116 = $435

b.)

Percentage of money Clara raised = \frac{145}{435}×100% = \frac{1}{3}×100% = 33.33%

3 0
3 years ago
A number x plus 23 is fewer than 24
pychu [463]

Answer:

Step-by-step explanation:

To translate statements into expressions and equations:

1) Identify __KEY__ __WORDS____ that indicate the operation. 2) Write the numbers/variables in the correct order.

The SUM of _____5_______ and ______8______: _____5 + 8_____ The DIFFERENCE of ___n_____ and ____3______ : _____n – 3______ The PRODUCT of ____4______ and ____b – 1____: __4(b – 1)___

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                                  1.thesumof8andt 8+t 3.theproductof5andb 5b

LESS THAN

MORE THAN

2.thequotientofgand15 4.thedifferenceof32andx 32-x

SWITCH THE the first number subtracted

                ORDER OF THE TERMS!

from the second! 5. Eightmorethanx _x-8_

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6. Sixlessthanp __p-6___

   Key Words five dollars less than Jennifer earned Variable Let d represent # of $ Jennifer earned Expression d–5 6. 14lessthanf f-14

8. 3 more runs than Pirates scored P + 3 10. Arthur is 8 years younger than Tanya

7.pmorethan10 10+p

9. 12 less than some number n – 12

11. Kelly’s test score is 6 points higher than Mike’s

              IS,

equals,

is equal to

Substitute with equal sign. 8. The product of 7 and b is equal to 63.

7b = 63

10. The quotient of x and 7 is equal to 13. x/7 =13

 7. 5 more than a number is 6. n+5=6

9. The sum of r and 45 is 79. r+45=79

               TWICE = DOUBLE = 2 times a number = multiply by 2

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     Expression

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     Expression

   8 more than a number

The sum of 8 and a number x increased by 8

the total of x and 8

 x+8

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r decreased by 6

6 less than a number

6 subtracted from a number

 r-6

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     Expression

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     Expression

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The product of 2 and n

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 The quotient of z and 3 A number divided by 3 The ratio of z and 3

        Practice: Underline key words. Write each phrase as an algebraic expression or equation.

 11.

13.

15.

18.

20.

Translate each expression or equation into a word expression or statement.

22) 23) 24)

9y the product of 9 and number y________________ x – 8 = 14 _8 less than a number is 14.__

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  Nine times a number decreased by four

9n–4

Five times the sum of six and some number

5(6+n)

Twice the difference of y and three

2 ( y – 3)

The sum of 5 and product of 7 and x

5+7x 9–

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7. Five less than twice a number is 7. __2n – 5 = 7____

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9. Ten more than the quotient of a number and 3 is 12. + 10 = 12__________

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YOU MUST USE PARENTHESES for · or ÷ THE (SUM) or (DIFFERENCE)!

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– 9

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7 0
3 years ago
Read 2 more answers
the equation I=prt solves for the amount of simple interest a bank account receives after a certain period of time. I stands for
Dominik [7]

Answer:

The percentage rate is 4.5%.

Step-by-step explanation:

The given formula for simple interest is I=prt where I=simple interest, p=principle, r = percentage rate and t=time.  In the problem, we are told that after six years (t=6), $7000 (p=7000) earns $1890 (I=1890).  We can then substitute in the values for three of our variable to get the following:  1890 = (7000)(6)r.  Multiplying 7000x6 = 42000 giving us 1890 = 42000r.  Using inverse operations, we divide both sides of the equation by 42000 to get 0.045 = r.  Since r = percentage rate, we need to multiply our decimal by 100 to find the percentage.  0.045 x 100 = 4.5%.

5 0
3 years ago
Consider the graph with four lines below. On a coordinate plane, line a has a positive slope and goes through points (negative 1
yan [13]

Answer:

The correct option is;

line a and line b

Step-by-step explanation:

Lina a passes through (-1, 0) and (1, 2)

Line b passes through (2, 2) and (-1, -1)

Line c passes through (0, 3) and (1, 0)

Line d passes through y = 1

An equation that has no solution

By examination, from the plot of the coordinates using an online tool, the system that would have no solution is the system of line a and line b because they are parallel lines and cannot meet or have a point where there is a common solution, therefore, there are no solutions when the equations of the two lines are combined in one equation

Slope of line a = -2/-2 = 1

Slope of line b = 3/3 = 1

The slopes of lines a and b are equal, therefore, line a and line b are parallel.

5 0
3 years ago
HELPPP ASAP PLEASEEE THANK YOU
ahrayia [7]

Step 1: Find the slope

Slope formula = (y2 - y1) / (x2 - x1)

---You can choose any two points when finding the slope!

Point 1 = (-2,-10)

Point 2 = (-1,-3)

Slope = (-3 - - 10) / (-1 - - 2)

Slope = 7 / 1

Slope = 7

Step 2: Find the y-intercept

Now that we have the slope, we'll plug that and one point into slope-intercept form. Then, we'll solve for b.

Slope-Intercept Form: y = mx + b

---m is the slope, b is the y-intercept

Point = (-1, -3)

Slope = 7

-3 = 7(-1) + b

-3 = -7 + b

b = 4

Step 3: Put it all together

Now that we know the slope and y-intercept, all that's left to do is plug them into slope-intercept form.

Slope-Intercept Form: y = mx + b

Slope = 7

Y-Intercept = 4

Line: y = 7x + 4

Correct Answer: A

Hope this helps!

5 0
2 years ago
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