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kodGreya [7K]
3 years ago
9

22. One kilometer is approximately 0.62 mile. What fraction represents this length?

Mathematics
1 answer:
bixtya [17]3 years ago
6 0

<u><em>Answer:</em></u>

One kilometer is \frac{31}{50} miles

<u><em>Explanation:</em></u>

<u>To convert a decimal to a fraction:</u>

1- Write the decimal as a fraction whose denominator is 1

2- Multiply both numerator and denominator by multiples of 10 to eliminate the decimal point

3- Simplify the fraction you have

<u>Now, for the given problem:</u>

<u>The given decimal is 0.62, following the above steps:</u>

<u>Step 1: </u>

0.62 = \frac{0.62}{1}

<u>Step 2:</u>

We have two digits after the decimal point, so to eliminate the decimal point, we will multiply the numerator and the denominator by 100

0.62 = \frac{0.62}{1} * \frac{100}{100} = \frac{62}{100}

<u>Step 3:</u>

We can note that, in the fraction obtained from step 2, both the numerator and the denominator are divisible by 2, so we simplify as follows:

\frac{62}{100} = \frac{62/2}{100/2} =\frac{31}{50}

Hope this helps :)

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Karo-lina-s [1.5K]

Answer:

y = (11x + 13)e^(-4x-4)

Step-by-step explanation:

Given y'' + 8y' + 16 = 0

The auxiliary equation to the differential equation is:

m² + 8m + 16 = 0

Factorizing this, we have

(m + 4)² = 0

m = -4 twice

The complimentary solution is

y_c = (C1 + C2x)e^(-4x)

Using the initial conditions

y(-1) = 2

2 = (C1 -C2) e^4

C1 - C2 = 2e^(-4).................................(1)

y'(-1) = 3

y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)

3 = -4(C1 - C2)e^4 + C2e^4

-4C1 + 5C2 = 3e^(-4)..............................(2)

Solving (1) and (2) simultaneously, we have

From (1)

C1 = 2e^(-4) + C2

Using this in (2)

-4[2e^(-4) + C2] + 5C2 = 3e^(-4)

C2 = 11e^(-4)

C1 = 2e^(-4) + 11e^(-4)

= 13e^(-4)

The general solution is now

y = [13e^(-4) + 11xe^(-4)]e^(-4x)

= (11x + 13)e^(-4x-4)

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