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elixir [45]
3 years ago
6

A boat travels 2km upstream and 2km downstream. The total time of the trip is 1 hour. The speed of the stream is 2km/h. What is

the speed of the boat in still water?
Mathematics
1 answer:
scoray [572]3 years ago
7 0
2 = ( v + 2 ) × t1 ;
2 = ( v - 2 ) × t2 ;
t1 + t2 = 1 ;
where v is the speed of the boat in still water ; t1 is the time upstream ; t2 is the tome downstream ;
Then, v + 2 = 2 / t1 and v - 2 = 2 / t2 ;
v = 2 / t1   -  2  and v = 2 / t2  +  2 ;
2 / t1 - 2 = 2 / t2 + 2 ;
2 / t1 - 2 / t2 = 4 ;
1 / t1 - 1 / t2 = 2 ;
t2 - t1 = 2t1t2 ;
But, t2 = 1 - t1 ;
1 - t1 - t1 = 2t1( 1 - t1 ) ;
1 - 2t1 = 2t1 - 2t1^2 ;
2t1^2 - 4t1 + 1 = 0 ; quadratic equation ;
solving this equation , 
t1 ≈ 0.29 hour ;
v ≈ 2 / 0.29 - 2;
v ≈ 4.89 km/h ;

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Answer:

Step-by-step explanation:

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{Distribute  (-1) to the second expression}

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{Combine like terms}

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3 years ago
Write the equation, in point-slope form, that contains the point (3, -6) with a slope of 2.
maria [59]

Answer:

y+6=2(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-6)=2(x-3)

y+6=2(x-3)

3 0
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Ilya [14]

The answer is

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C is the point on the line y = 2x + 1 where x = 2<br> Find the co-ordinates of the mid-point of BC.
inysia [295]

Based on the calculations, the coordinates of the mid-point of BC are (1, 4).

<h3>How to determine coordinates of the mid-point of BC?</h3>

First of all, we would determine the initial y-coordinate by substituting the value of x into the equation of line that is given:

At the origin x₁ = 0, we have:

y = 2x + 1

y₁ = 2(0) + 1

y₁ = 2 + 1

y₁ = 3.

When x₂ = 2, we have:

y = 2x + 1

y₂ = 2(2) + 1

y₂ = 4 + 1

y₂ = 5.

In order to determine the midpoint of a line segment with two (2) coordinates or endpoints, we would add each point together and divide by two (2).

Midpoint on x-coordinate is given by:

Midpoint = (x₁ + x₂)/2

Midpoint = (0 + 2)/2

Midpoint = 2/2

Midpoint = 1.

Midpoint on y-coordinate is given by:

Midpoint = (y₁ + y₂)/2

Midpoint = (3 + 5)/2

Midpoint = 8/2

Midpoint = 4.

Therefore, the coordinates of the mid-point of BC are (1, 4).

Read more on midpoint here: brainly.com/question/4078053

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2 years ago
Why would a railway be important to either side in the civil war?
GaryK [48]

Answer:

Either side would have been improved by a railway so they could get more ammo in and get food in and also get the sick and wonded out to get medical attention

Step-by-step explanation:

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