Kevin weighed his loaded truck at a weigh station. It weighed 14 tons 500 lbs 9 oz. His empty truck weighed 2 tons 600 lbs 12 oz
. What was the weight of his load?
1 answer:
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The incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3
<h3>What is a logarithm? </h3>It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
2ln(x) = In(3x) - [In(9) - 2ln(3)]
In(x²) = In(3x) - [In(9) - In(9)]
ln(x²) = ln(3x) - 0
ln(x²) = ln(3x/0) (incorrect step)
ln(x²) = ln(3x)
x² = 3x (correct step)
x² - 3x =0
x(x - 3) = 0
x = 0, 3
Thus, the incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3
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If points D, E, F and G make a rectangle with the given coordinates for each point then the area of the rectangle is 150 sq. units
How to find distance between two points?
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by D = √((x₂ – x₁)² + (y₂ – y₁)²)
This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
According to the given question:
The four vertices are D(-1,-3), E(-9, -9), F(-18, 3) and G(-10, 9) check the attachment below.
Distance between two points D = √((x₂ – x₁)² + (y₂ – y₁)²)
Side DE = √((-9 – (-1))² + (-9 – (-3))²) = √100 = 10 units
Side EF = √((-18 – (-9))² + (3 – (-9))²) = √225 = 15 units
Side FG = √((-10 – (-18))² + (9 – 3)²) = √100 = 10 units
Side GD = √((-1 – (-10))² + (-3 – 9)²) = √225 = 15 units
∴ Area of rectangle = l x b = DE . EF
Area = 10 x 15 = 150 sq. units
Hence the area of rectangle with the given coordinates is 150 sq. units
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