Answer:
The magnitude is 
The direction is 
i.e toward the x-axis
Step-by-step explanation:
From the question we are told that
The function is 
The point considered is 
Generally the maximum rate of change of f at the given point and the direction is mathematically represented as
![\Delta f(x,y) = [\frac{\delta f(x,y)}{\delta x } i + \frac{\delta f(x,y)}{\delta y } j ]](https://tex.z-dn.net/?f=%5CDelta%20f%28x%2Cy%29%20%3D%20%20%5B%5Cfrac%7B%5Cdelta%20%20f%28x%2Cy%29%7D%7B%5Cdelta%20x%20%7D%20i%20%2B%20%5Cfrac%7B%5Cdelta%20%20f%28x%2Cy%29%7D%7B%5Cdelta%20y%20%7D%20j%20%20%5D)
![\Delta f(x,y) = [\frac{\delta (9sin(xy))}{\delta x} i + \frac{\delta (9sin(xy))}{\delta y} i ]](https://tex.z-dn.net/?f=%5CDelta%20f%28x%2Cy%29%20%3D%20%20%5B%5Cfrac%7B%5Cdelta%20%20%289sin%28xy%29%29%7D%7B%5Cdelta%20x%7D%20i%20%20%2B%20%5Cfrac%7B%5Cdelta%20%20%289sin%28xy%29%29%7D%7B%5Cdelta%20y%7D%20i%20%20%20%5D)
![\Delta f(x,y) = [9y cos (x,y) i + 9xcos (x,y) j]](https://tex.z-dn.net/?f=%5CDelta%20f%28x%2Cy%29%20%3D%20%5B9y%20cos%20%28x%2Cy%29%20i%20%2B%20%209xcos%20%28x%2Cy%29%20j%5D)
At
![\Delta f (0,8) = [9(8) cos(0* 8)i + 9(8) sin(0* 8)j ]](https://tex.z-dn.net/?f=%5CDelta%20%20f%20%280%2C8%29%20%3D%20%20%5B9%288%29%20cos%280%2A%208%29i%20%20%2B%209%288%29%20sin%280%2A%208%29j%20%20%5D)
Answer:
(10; -1)
the x-coordinate of the other endpoint is (x;y)
because the segment has midpoint at (3;0)
=> x - 4 = 3.2 = 6
y + 1 = 0.2 = 0
<=> x = 10
y = -1
=> the other endpoint is (10; -1)
So I think maybe the example for the first problem created some confusion, and you may want to have your child take another look.
If we numbered the top half 1 to 9 going from left to right, numbers 1, 2, 6, 7 and 8 are right. They worked because the top number (numerator) perfectly fit into the bottom number (denominator). This is not true for the rest.
The key is to find the largest number that you can think of that will go into BOTH the top and the bottom evenly.
So for number 3: 18/24; 18 does not fit evenly into 24. The highest number that will fit into both is 6, so you divide both top and bottom by 6 and your answer is 3/4.
Number 4: 45/54; the highest number that goes into both is 9, so you divide both top and bottom by 9 and your answer is 5/6.
Number 5: 55/66; the highest number that can go into both is 11, so the answer is 5/6.
Is this making sense?
The bottom, numbering 1 to 9 from left to right. The correct ones are 1, 6 and 9.
For 2: 14/41 is about 15/40. Both can be divided by 5, so the answer is 3/8.
For 3: 20/81 is about 20/80, and 2/8 is close, but can still be divided by 2, so the answer is 1/4.
For 4: 24/49 is closer to 25/50 than 20/50. 25/50 can be divided by 25, so the answer is 1/2.
For 5: it was all correct, but the answer can be further reduced from 2/8 to 1/4.
For 7: 23/72 is about 25/75, and 25 goes into both, so it reduces to 1/3.
For 8: 13/21 is about 15/20, and 5 goes into both, so the answer is 3/4.
As your child continues to learn this, remember that if he or she gets an answer like 2/6 or 6/12, they should ask themselves if they can further reduce the fractions- 2/6 reduces to 1/3, and 6/12reduces to 1/2. I know it's confusing, but they do get the hang of it with practice
Answer:
The Area of the parallelogram = 144 m²
Step-by-step explanation:
<u><em>Formula</em></u>:
Area of a parallelogram = b × h
Where , b is the base of the parallelogram
and h is its height.
………………………………
In our case :
b = 12 ; h = 12
Then
The Area of the parallelogram = 12 × 12 = 144 m²
