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3 years ago

9

The scale on a map shows that 200 miles is represen by 5 inches on a map. Which proportion can be used to find the distance on t

he map,x, that represents 50 miles?

1 answer:

Mandarinka [93]3 years ago

4 0

Answer:

1.25 inches

Step-by-step explanation:

200 miles/ 50 miles = 5 inch / x

x = (50 x 5) / 200 = 250 / 200 = 1.25

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Calculate the area of a rectangle if its dimensions are listed below:

Marizza181 [45]

Answer:

Length=10x

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Area=10x×7x

=70x²

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2 years ago

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At pretend highschool there are 325 boys and 275 girls.

RideAnS [48]

Answer:

13:11

Step-by-step explanation:

325:275

If divided by 5 all through, you get 65:55, then by 5 again you get 13:11

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What is the Laplace Transform of 7t^3 using the definition (and not the shortcut method)

Leokris [45]

Answer:

Step-by-step explanation:

By definition of Laplace transform we have

L{f(t)} = $L{{f(t)}}=\int_{0}^{\infty }e^{-st}f(t)dt\\\\Given\\f(t)=7t^{3}\\\\\therefore L[7t^{3}]=\int_{0}^{\infty }e^{-st}7t^{3}dt\\\\$

Now to solve the integral on the right hand side we shall use Integration by parts Taking $7t^{3}$ as first function thus we have

$\int_{0}^{\infty }e^{-st}7t^{3}dt=7\int_{0}^{\infty }e^{-st}t^{3}dt\\\\= [t^3\int e^{-st} ]_{0}^{\infty}-\int_{0}^{\infty }[(3t^2)\int e^{-st}dt]dt\\\\=0-\int_{0}^{\infty }\frac{3t^{2}}{-s}e^{-st}dt\\\\=\int_{0}^{\infty }\frac{3t^{2}}{s}e^{-st}dt\\\\$

Again repeating the same procedure we get

$=0-\int_{0}^{\infty }\frac{3t^{2}}{-s}e^{-st}dt\\\\=\int_{0}^{\infty }\frac{3t^{2}}{s}e^{-st}dt\\\\\int_{0}^{\infty }\frac{3t^{2}}{s}e^{-st}dt= \frac{3}{s}[t^2\int e^{-st} ]_{0}^{\infty}-\int_{0}^{\infty }[(t^2)\int e^{-st}dt]dt\\\\=\frac{3}{s}[0-\int_{0}^{\infty }\frac{2t^{1}}{-s}e^{-st}dt]\\\\=\frac{3\times 2}{s^{2}}[\int_{0}^{\infty }te^{-st}dt]\\\\$

Again repeating the same procedure we get

$\frac{3\times 2}{s^2}[\int_{0}^{\infty }te^{-st}dt]= \frac{3\times 2}{s^{2}}[t\int e^{-st} ]_{0}^{\infty}-\int_{0}^{\infty }[(t)\int e^{-st}dt]dt\\\\=\frac{3\times 2}{s^2}[0-\int_{0}^{\infty }\frac{1}{-s}e^{-st}dt]\\\\=\frac{3\times 2}{s^{3}}[\int_{0}^{\infty }e^{-st}dt]\\\\$

Now solving this integral we have

$\int_{0}^{\infty }e^{-st}dt=\frac{1}{-s}[\frac{1}{e^\infty }-\frac{1}{1}]\\\\\int_{0}^{\infty }e^{-st}dt=\frac{1}{s}$

Thus we have

$L[7t^{3}]=\frac{7\times 3\times 2}{s^4}$

where s is any complex parameter

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2 years ago

There are 10 books on a shelf of which 4 are paperbacks

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3 years ago

An airplane on autopilot took 5 hours to travel 3 comma 510 kilometers. What is the unit rate for kilometers per hour?

loris [4]

Answer:

702 kilometers per hour.

Step-by-step explanation:

3,510 divided by 5 = 702.

Since 5 is the number of hours it took to travel 3,510 kilometers, and we need to find the kilometers per hour, simply divide 3,510 by 5.

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2 years ago