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stich3 [128]
3 years ago
7

Factor 54+27 using the GFC

Mathematics
1 answer:
alex41 [277]3 years ago
4 0
You mean GCF Greastest Common Factor
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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
lubasha [3.4K]

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

4 0
3 years ago
Please please please please please help me!!!!!​
Bond [772]

Answer:

c

Step-by-step explanation: just trust me.

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Which of the following could not represent the y-intercept of a Direct Variation graph?
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C
Sorry if I am wrong
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Angle 4 is congruent, D.
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A grocery store sold 250pounds of fruit in May. This is 5times more than it sold in January.How many pounds of fruit did the gro
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They sold 50 pounds in January.

To find this you just need to divide 250 by 5 since the amount sold in May is 5 times more.

Hope this helps :)

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3 years ago
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