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3 years ago

Solve the system of equations: 6x/5 + y/5 = 2.3 x/10 − 2y/3 = 1.2

Mathematics

2 answers:

mario62 [17]3 years ago

5 0

(X,Y)= (266/123, -121/82)

solniwko [45]3 years ago

3 0

The answer is 32x+24y I think

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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

4 years ago

A bucket is put under a leaking ceiling. the amount of water in the bucket doubles every minute. after 8 minutes, the bucket is

frosja888 [35]

4 minutes because 4 is half of 8

7 0

3 years ago

Read 2 more answers

SOMEONE HELP ME WITH THIS

Alexandra [31]

Answer:

X=7 and y=6

Step-by-step explanation:

Y=-2x + 20.......eq(i)

6x-5y=12.....eq(ii)

Now, putting y= - 2x +20 in eq (ii)

6x - 5(-2x + 20)=12

6x + 10x - 100 = 12

16x=12+100

X=112 /16

X=7

Then, putting x=7 in eq (i)

Y=-2*7 +20

=-14 +20

8 0

3 years ago

An urn contains 17 white balls and 18 red balls. A sample of four balls is selected at random from the urn. What is the probabil

erik [133]

Answer:

c. 0.3974

Step-by-step explanation:

Given;

number of white balls, W = 17

number of red balls, R = 18

Total number of balls, T = 35

The number of ways the event will occur is given by

= P(2 whites) and P(2 reds)

= P(2whites) x P(2 reds)

= 17C2 x 18C2

= 136 x 153

= 20,808

The total number of possible outcome

= 35C4

= 52,360

The probability = 20,808 / 52,360

= 0.3974

The correct option is "C"

6 0

3 years ago

What does the infinity symbol mean in intermediate math

TiliK225 [7]

That means the decimal is repeatative

7 0

3 years ago