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andriy [413]
4 years ago
12

Samantha drove her car with a full tank of gas 268 miles to her friends town for an average of 22.68 miles/gallons and then refi

lled her car with gas. How much gas was used by the car on the trip?
Mathematics
1 answer:
Greeley [361]4 years ago
4 0

Answer:

23.64 gallons

Step-by-step explanation:

Given:

Samantha drove her car with a full tank of gas 268 miles to her friends town

for an average of 22.68 miles/gallons and then refilled her car with gas.

Question asked:

How much gas was used by the car on the trip ?

Solution:

<u><em>By unitary method:</em></u>

<u>As  average of car is given 22.68 miles/gallons:</u>

For 22.68 miles, number of gallons of gas used = 1

For 1 mile, number of gallons of gas used = \frac{1}{22.68}

For 268 mile, number of gallons of gas used = \frac{1}{22.68}\times268

                                                                           = \frac{268}{22.68} =11.82

Now, to find total gas used in whole trip :-

11.82 + 11.82 = 23.64 gallons of gas

Thus, 23.64 gallons of gas used by the car on the trip.

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The cost of the least expensive fence is $3200

Step-by-step explanation:

The given is:

  • A fence must be built to enclose a rectangular area of 20,000 ft²
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We need to find the cost of the least expensive fence

Assume that the length of each side opposite to North or South is x feet and the length of each other sides  is y feet

∵ The length of the rectangle = x feet

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- Divide both sides by x to find y in terms of x

∴ y=\frac{20,000}{x}

The fence's length is equal to the perimeter of the rectangular area

∵ Perimeter of the rectangle = 2 length + 2 width

∴ Perimeter of the rectangle = 2x + 2y

∵ Fencing material costs $4 per foot for the two sides facing

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∴ x costs $4 per foot

∵ The cost of the other two sides is $8 per foot

∴ y costs $8 per feet

The cost of the fence is the sum of the products of 4 , 2x and 8 , 2y

∵ The cost of the fence (C) = 4(2x) + 8(2y)

∴ C = 8x + 16y

- Substitute y by its value above

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∵ \frac{320,000}{x} can be written as 320,000x^{-1}

∴ C=8x+320,000x^{-1}

∵ \frac{dC}{dx}=8(1)x^{1-1}+320,000(-1)x^{-1-1}

∴ \frac{dC}{dx}=8-320,000x^{-2}

- Equate \frac{dC}{dx} by zero

∴ 8-320,000x^{-2}=0

∵ -320,000x^{-2}=-\frac{320,000}{x^{2}}

∴ 8-\frac{320,000}{x^{2}}=0

- Subtract 8 from both sides

∴ -\frac{320,000}{x^{2}}=-8

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∴ - 320,000 = - 8x²

- Divide both sides by -8

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- Take √  for both sides

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∵ C=8(200)+\frac{320,000}{(200)}

∴ C = 1600 + 1600

∴ C = 3200

The cost of the least expensive fence is $3200

Learn more:

You can learn more about the differentiation in brainly.com/question/4279146

#LearnwithBrainly

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