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Colt1911 [192]
3 years ago
15

john made two candles in the shape of rectangular prisms. The first candle is 12cm high, 4 cm long, and 6 cm wide. The second ca

ndle is 4 cm higher, but has the same length and width. How much additional wax was needed to make the taller candle?
Mathematics
1 answer:
anzhelika [568]3 years ago
6 0

Answer:

96cm^3

Step-by-step explanation:

To determine how much additional wax was needed to make the taller candle, we determine the volume of each of the candles and find the difference in their volumes

<u>First Candle</u>

  • Height=12cm
  • Length=4 cm
  • Width= 6 cm

Volume=Height X Length X Width

=12 X 4 X 6

=288cm^3

<u>Second Candle</u>

The second candle is 4cm higher

  • Height=12+4=16cm
  • Length=4 cm
  • Width= 6 cm

Volume=Height X Length X Width

=16 X 4 X 6

=384cm^3

Difference in Volume = 384-288 =96cm^3

Therefore, 96cm^3 of additional wax was used to make the second candle.

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Answer:

Apples = 24

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Step-by-step explanation:

Let u be the unit of fruit in the basket,

number of apples: 3u +7

number of pears: 5u -9

now to find u, we equate the two equations.

3u+7=5u-9

Now simplify.

5u-3u=7+9

2u=16

u=8

Now we can find the original number of apples and pears by substituting u.

so original number of apples = 3u = 3(8) = 24

and original number of pears = 5u = 5(8) = 40

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Find the slope and then an equation for each line.
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Which represent geometric sequences? A marathon runner runs half of a race, then runs half the distance left to the finish line,
dimulka [17.4K]

Answer:

Step-by-step explanation:

1). Let the length of a marathon race = x miles

   Marathon runner runs this race in the sequence formed as,

   \frac{x}{2},\frac{x}{4},\frac{x}{8}.........

  Common ratio = \frac{\frac{x}{4}}{\frac{x}{2}}

                           = \frac{x}{4}\times \frac{2}{x}

                           = \frac{1}{2}

  Therefore, it's a geometric sequence.

2). First movie rental cost = $2

  Followed by each additional movie rental cost = $1

  Therefore, rental of movies will be in the form of a linear equation,

  y = 2x + 1

  where x = number of movies

  And y = Rental of movies

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3). 10, 1, 0.1, 0.01.......

  Ratio in 2nd and 1st term = \frac{1}{10}=0.1

  Ratio in 3rd and 2nd term = \frac{0.1}{1}=0.1    

  Therefore, ratio in each term is common.

  Sequence formed will be a geometric sequence.

4). \sum_{k=1}^{7}4(0.2)^{k-1}

   Expression represents a common ratio of 0.2,

  Therefore, expression given will represent a geometric sequence.

5). -4, 20, -100, 500, ...........

   Ratio of 2nd and 1st term = \frac{20}{-4} = -5

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   Therefore, it's a geometric sequence.

6). -1, 5, 11, 17.........

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   Ratio of 3rd and 2nd term = \frac{11}{5}=2.2

   -5 ≠ 2.2

   Therefore, sequence is not a geometric sequence.

7). -500, 100, -20, 4........

   Ratio of 2nd and 1st term = \frac{100}{-500}=-\frac{1}{5}

   Ratio of 3rd and 2nd term = \frac{-20}{100}=-\frac{1}{5}  

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