Solve for m (8m+4) 38 degrees
1 answer:
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It is true that the product of two consecutive even integers are always one less than the square of their average.
<u>Step-by-step explanation</u>:
Let the two consecutive odd integers be 1 and 3.
- The product of 1 and 3 is (1
3)=3
- The average of 1 and 3 is (1+3)/2 =4/2 = 2
- The square of their average is (2)² = 4
∴ The product 3 is one less than the square of their average 4.
Let the two consecutive even integers be 2 and 4.
- The product of 2 and 4 is (2
- The average of 2 and 4 is (2+4)/2 =6/2 = 3
- The square of their average is (3)² = 9
∴ The product 8 is one less than the square of their average 9.
Thus, It is true that the product of two consecutive even integers are always one less than the square of their average.
The displacement is 18.03 steps, and the direction is 47.25°
<h3>How to get the displacement?</h3>
We know that displacement is the difference between the final position and the initial position.
We assume the initial position (0, 0). Let's define the positive x-axis as the east and the positive y-axis as the north.
First, the student moves 8 steps east, so she is at:
(0 + 8, 0)
Then she moves 6 steps northeast, so the new position is:
(6*cos(45°) + 8, 6*cos(45°))
Finally, she moves 9 steps due north, so we have:
(6*cos(45°) + 8, 6*cos(45°) + 9)
Then the final position is:
(12.24, 13.24)
So the displacement is:
D = (12.24, 13.24) - (0, 0) = (12.24, 13.24)
The magnitude of the displacement is:
So the magnitude is 18.03 steps.
And the direction is given by the arctangent of the quotient between the y-component and the x-component:
If you want to learn more about displacements:
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