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3 years ago

Charlie buys a $23,000 mustang in 2006

Mathematics

1 answer:

vladimir1956 [14]3 years ago

8 0

Answer:

ANd?

Step-by-step explanation:

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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

Does 12 tenors : 16 basses form a proportion

astra-53 [7]

Answer:

Yes I’m pretty sure

Step-by-step explanation:

8 0

2 years ago

Yeah, im clueless please help;-;

svetlana [45]

Answer:

Starting from the left, top to bottom. first answer is 8, second is 21.3, third is 64, 204.8. Right side is essentially y=x to a power, the answers are from top to bottom, 8,27,64,125

Step-by-step explanation:

Essentially, its just asking you to divide the given y values by the x values.

7 0

2 years ago

Finding area of a sector

katen-ka-za [31]

The smaller sector is 360-255=105 degree
it is 105/360 portion of the whole circle, and the area of the whole circle is πr², r is 14
so the area of the smaller sector is (105/360)*π*14²
run those numbers through your calculator, use 3.14 for π, you get 179.5

if you are looking for area of the larger sector, it would be
(255/360)*π*14²=435.94

3 0

2 years ago

The weight of an elephant is 10^3 times the weight of a cat. If the elephant weighs 14,000 pounds,how many pounds does the cat w

Ket [755]

Answer:

14 pounds.

Step-by-step explanation:

10 cubed is 1000.

14000/1000=14

6 0

2 years ago