Please Help me On this And explain please show ur work
2 answers:
This can be done using long division that we have learned with numbers, except that each digit in the numeric long division is replaced with a number that can exceed 10.
Thus we can write the division as where the right most digit represent a number, and each number to the left represent an increasing power of x.
________________________
1 +2 +1 | 1 +10 +13 + 39
We will use a first quotient digit of 1 and begin the division
_1______________________
1 +2 +1 | 1 +10 +13 + 39
1 +2 +1 (subtract)
8 12 39
After that, we have a multiplier of 8 and continue
_1___8___________________
1 +2 +1 | 1 +10 +13 + 39
1 +2 +1 (subtract)
8 12 39
8 16 8 (subtract)
-4 31
This means that we have a quotient of (x+8) with a remainder of -4x+31
thus the final expression looks like
Thus we can write the division as where the right most digit represent a number, and each number to the left represent an increasing power of x.
________________________
1 +2 +1 | 1 +10 +13 + 39
We will use a first quotient digit of 1 and begin the division
_1______________________
1 +2 +1 | 1 +10 +13 + 39
1 +2 +1 (subtract)
8 12 39
After that, we have a multiplier of 8 and continue
_1___8___________________
1 +2 +1 | 1 +10 +13 + 39
1 +2 +1 (subtract)
8 12 39
8 16 8 (subtract)
-4 31
This means that we have a quotient of (x+8) with a remainder of -4x+31
thus the final expression looks like
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Answer:
Let's define East as the positive x-axis and North as the positive y-axis.
If Michelle's initial position is (0, 0)m
We know that Nathasha is 50m due East of Michelle.
Then the position of Natasha is (50, 0)m
Now we know that Natasha walks 20m due North, then the new position of her's is:
(50, 0 + 20)m = (50, 20)m
While Michelle walks 10m due South (South would be the negative y-axis, then we subtract 10 meters)
Michelle's new position will be:
(0, 0 - 10)m = (0, -10)m
Now we want to know the distance and bearing of Michelle from Natasha.
First, remember that the distance between two points (a, b) and (c, d) is given by:
Distance = √( (a - c)^2 + (b - d)^2)
Then the distance between Michelle and Natasha is:
Distance = √( (50m - 0m)^2 + (20m - (-10m))^2)
Distance = √( (50m)^2 + (30m)^2) = 58.31m
Now to find the bearing you can see the image below:
Point B is Michelle's position and point A is Natasha's position.
To find the bearing, we can make a triangle rectangle as the one shown in the image:
Also remember the relation:
Tan(a) = (opposite cathetus)/(adjacent cathetus).
Where the opposite cathetus is the difference between the x-values of each position, this is:
opposite cathetus = 50m - 0m = 50m
And the adjacent cathetus is the difference between the y-values, this is:
adjacent cathetus = 20m - (-10m) = 30m
Then:
Tan(a) = 50m/30m
Tan(a) = 5/3
Now if we apply the inverse Tan function to both sides, Atan(x) we get:
Atan(Tan(a)) = Atan(5/3)
a = Atan(5/3) = 59°
So the bearing is of 59°.
