Alright, lets get started.
A light private plane can fly 120 mph in still air.
Suppose the speed of wind = x mph
Against the wind, speed of plane will be = 120-x
With the wind, speed of plane will be = 120+x
Flying against the wind, the plane can fly 320 miles, so time taken will be
t =
With the wind, the plane can fly 640 miles, so time taken will be
Both times are given same, so
Cross multiplying
Dividing from 320
x = 40 mph
So, the speed of the wind is 40 mph. : Answer
Hope it will help :)
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Work Shown:
Let x = 5i-3
That allows us to go from (5i-3)(2i+1) to x(2i+1)
Distribute the x through: x*(2i) + x*(1) = 2i*x + x = 2i(x) + 1(x)
Now we replace every x in 2i(x) + 1(x) with 5i-3, and then we distribute a second time
2i(x) + 1(x) = 2i(5i-3) + 1(5i-3)
2i(x) + 1(x) = 2i(5i)+2i(-3) + 1(5i)+1(-3)
2i(x) + 1(x) = 10i^2 - 6i + 5i - 3
2i(x) + 1(x) = 10(-1) - i - 3
2i(x) + 1(x) = -10 - i - 3
2i(x) + 1(x) = -13 - i
Therefore, (5i-3)(2i+1) = -13 - i
The result is in a+bi form where a = -13 and b = -1.
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An alternative method is to use the box method. This is where you set up a grid that helps you multiply out (5i-3)(2i+1)
See the diagram below.
Each of the 4 red terms in the boxes represents the result of multiplying the outer blue and green terms. Example: 5i times 2i = 10i^2 in row1, column1.
This could be a parallelogram, but it also could easily be an isosceles trapezoid. A trapezoid is a figure with only one pair of parallel sides. An isosceles trapezoid is a trapezoid where the non-parallel sides are the same length. It's similar to an isosceles triangle.
Because this could be an isosceles trapezoid, this means we don't have enough information. See the attached image below for an example.
