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olga nikolaevna [1]
3 years ago
15

If your car can drive 433 miles on a full tank of gas, find the miles per gallon if your gas tank holds 17.2 gallons? How much d

oes it cost to fill your tank if gas is $2.85 per gallon?
Mathematics
1 answer:
just olya [345]3 years ago
6 0

Answer:

-25.17 miles per gallon.

-It costs $49.02 to fill your tank.

Step-by-step explanation:

-To find the miles per gallon, you can use a rule of three:

17.2 gallons →  433 miles

    1 gallon   →        x

x=(1*433)/17.2= 25.17

If your gas tank holds 17.2 gallons, you car can drive 25.17 miles per gallon.

-To find the cost to fill your tank, you have to multiply the price per gallon for the amount of gallons that the tank can hold:

$2.85*17.2=$49.02

It costs $49.02 to fill your tank.

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Find three positive numbers whose sum is 140 and whose product is a maximum. (Enter your answers as a comma-separated list.)
Paladinen [302]

Answer:

\frac{140}{3}, \frac{140}{3}, \frac{140}{3}

Step-by-step explanation:

Let the numbers be x, y\ and\ z.

Such that:

x + y + z = 140

Make z the subject

z = 140 -x - y

For their product to be maximum, we have:

f(x,y,z) = xyz

Substitute z = 140 -x - y in f(x,y,z) = xyz

f(x,y) = xy(140 - x - y)

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f(x,y) = 140xy - x^2y - xy^2

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f_x=140y - 2xy - y^2

f_y=140x - x^2 - 2xy

Since the products are maximum, then f_x = f_y = 0

For f_x=140y - 2xy - y^2

140y - 2xy - y^2 = 0

Factorize:

y(140 - 2x - y) = 0

Split

y = 0\ or\ 140 - 2x - y = 0

Make y the subject

y = 0\ or\ y = 140 - 2x

For f_y=140x - x^2 - 2xy

140x - x^2 - 2xy = 0

---------------------------------------------------

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---------------------------------------------------

Substitute y = 140 - 2x

140x - x^2 - 2xy = 0

140x - x^2 - 2x(140 - 2x) = 0

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Re-arrange

4x^2 -x^2 +140x - 280x = 0

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Factor x out

x(3x - 140) = 0

Divide through by x

3x - 140 = 0

3x = 140

x = \frac{140}{3}

Recall that: y = 140 - 2x

y = 140 - 2 * \frac{140}{3}

y = 140 - \frac{280}{3}

Take LCM

y = \frac{140*3-280}{3}

y = \frac{140}{3}

Recall that:

z = 140 -x - y

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Take LCM

z =  \frac{3 * 140- 140 - 140}{3}

z =  \frac{140}{3}

Hence, the numbers are:

\frac{140}{3}, \frac{140}{3}, \frac{140}{3}

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