Mathematics, 21.03.2020 05:11 jmallory3031

A boat traveled 252 miles downstream and back. The trip downstream took 12 hours. The trip back took 84 hours. Find the speed of the boat in still water and the speed of the current.

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Answer from: 109077

the speed of the boat in still water is 12 mph and the speed of the current is 9 mph.

Step-by-step explanation:

Let x represent the speed of the boat in still water.

Let y represent the speed of the current.

The boat travelled 252 miles downstream and the same distance upstream.

The trip downstream took 12 hours. Assuming the boat travelled with the wind when going downstream, the total speed would be (x + y) mph.

Distance = speed × time

The expression for distance travelled downstream is

252 = 12(x + y)

Dividing through by 12, it becomes

21 = x + y- - - - - - - - - - 1

The trip back took 84 hours. Assuming the boat travelled against the wind when going back(upstream), the total speed would be (x - y) mph.

The expression for distance travelled upstream is

252 = 84(x - y)

Dividing through by 84, it becomes

3 = x - y- - - - - - - - - - 2

Adding equation 1 to equation 2, it becomes

24 = 2x

x = 24/2

x = 12 mph

Substituting x = 12 into equation 1, it becomes

21 = 12 + y

y = 21 - 12

y = 9 mph

Answer from: Quest

there are lots of ways. pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula. the area is half the sum of the cross products of the sides.

a(-2,6) -2(2)-6(-5) = 26

b(-5,2) -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3) 4(3) - (-3)(5) = 27

e(5,3) 5(3) - 3(1) = 12

f(1,3) 1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 + 18 + 27 + 12 + 12) = 57

that checks!

Find the area of the following shape. you must show all work to receive credit. need asap timed tes

Answer from: Quest

the answer is d

the answer is in the first quadrant, which make the y-int positive.

since the dots are going down, therefore the correlation is negative

i hope it is right.

Poloma believes that the equation of the line of best fit for the following scatterplot is y=5/6x-31

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A boat traveled 252 miles downstream and back. The trip downstream took 12 hours. The trip back took...

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