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2 years ago

13

Mr. phill stopped to fill his car with gas on the way to New York. It took 1 ¼ minutes to fill a 15 liters of gas in his tank. A

t this rate, how long will it take to fill his 50 liter gas tank?

1 answer:

KatRina [158]2 years ago

4 0

Answer:

4 1/6 min or 4 min 10 sec

Step-by-step explanation:

<u>Filling rate is:</u>

15 ÷ 1 1/4 = 15 ÷ 5/4 = 15 × 4/5 = 12 l/min

<u>Total volume is 50 l, time required to fill is:</u>

50/12 = 4 2/12 = 4 1/6 min or 4 min 10 sec

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Kofi has 4 meters of fabric that he wants to cut into 5 equal-sized pieces. What is true about the length of each piece of the f

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3 years ago

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Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

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Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

<em>Hence, the smallest sum is 2</em>

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3 years ago

240 is 240% of what number?

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3 years ago

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