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Jet001 [13]
3 years ago
15

78km into miles 32km into miles 54km into miles

Mathematics
2 answers:
Black_prince [1.1K]3 years ago
5 0

a. 48.467 miles

b. 19.8839 miles

c. 33.554 miles

1 kilometer is equal to 0.621371 miles (short = 0.62)

1 mile is equal to 1.609344 kilometers


spin [16.1K]3 years ago
4 0

48.467 ,  19.8839 , 33.554

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Your task is to build a road joining a ranch to a highway that enables drivers to reach the city in the shortest time. The perpe
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Answer:

(a)In the attachment

(b)The road of length 35.79 km should be built such that it joins the highway at 19.52km from the perpendicular point P.

Step-by-step explanation:

(a)In the attachment

(b)The distance that enables the driver to reach the city in the shortest time is denoted by the Straight Line RM (from the Ranch to Point M)

First, let us determine length of line RM.

Using Pythagoras theorem

|RM|^{2}=30^2+x^2\\|RM|=\sqrt{30^2+x^2}

The Speed limit on the Road is 60 km/h and 110 km/h on the highway.

Time Taken = Distance/Time

Time taken on the road  =\frac{\sqrt{30^2+x^2}}{60}

Time taken on the highway =\frac{50-x}{110}

Total time taken to travel, T =\frac{\sqrt{30^2+x^2}}{60}+\frac{50-x}{110}

Minimum time taken occurs when the derivative of T equals 0.

T^{'}=\frac{x}{60\sqrt{30^2+x^2}}-\frac{1}{110}\\\frac{x}{60\sqrt{30^2+x^2}}-\frac{1}{110}=0\\\frac{x}{60\sqrt{30^2+x^2}}=\frac{1}{110}\\110x=60\sqrt{30^2+x^2}\\

Square both sides

12100x^2=3600(30^2+x^2)\\12100x^2=3240000+3600x^2\\12100x^2-3600x^2=3240000\\8500x^2=3240000\\x^2=\frac{3240000}{8500} =381.18\\x=\sqrt{381.18} =19.52

The road should be built such that it joins the highway at 19.52km from the point P.

In fact,

|RM|=\sqrt{30^2+19.52^2}=35.79km

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Answer:

14 - 6n < 2(7 - 3n)

No Solution

0 < 0

work attached

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3 years ago
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Answer:18

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3 years ago
The weight of an object on Venus is about 9/10 it's weight on Earth and the weight of an object on Mars is about 2/5 it's weight
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On Venus the person is 153 lbs and on Mars it is 102 lbs.The difference is 51 lbs
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2 years ago
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For one History test, Keith had to answer 40 questions. Of these 40 questions, Keith answered 28 of them correctly. What percent
muminat

Answer:

Keith scored 70% on the History test.

Step-by-step explanation:

We have been given that for History test, Keith had to answer 40 questions. Of these 40 questions, Keith answered 28 of them correctly.

To find the percentage Keith got on History test, we will have to figure out 28 is what percent of 40.

\text{Percentage scored by Keith on History test}=\frac{28}{40}\times 100

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Therefore, Keith scored 70% on the History test.

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