Multiply the original DE by xy:
xy2(1+x2y4+1−−−−−−−√)dx+2x2ydy=0(1)
Let v=xy2, so that dv=y2dx+2xydy. Then (1) becomes
x(y2dx+2xydy)+xy2x2y4+1−−−−−−−√dxxdv+vv2+1−−−−−√dx=0=0
This final equation is easily recognized as separable:
dxxln|x|+CKxvKx2y2−1K2x4y4−2Kx2y2y2=−dvvv2+1−−−−−√=ln∣∣∣v2+1−−−−−√+1v∣∣∣=v2+1−−−−−√+1=x2y4+1−−−−−−−√=x2y4=2KK2x2−1integrate both sides
The preimage WXYZ is to undergo a rotation of 90° in the clockwise direction.
A 90° clockwise rotation leads to the following change in the coordinates;
(x,y) -> after rotation (y,-x)
this rule applies for all the vertices in the preimage
W - (3,-5) --> W' (-5,-3)
X - (1,-3) ---> X' (-3,-1)
Y - (-1,-5)---> Y' (-5,1)
Z - (1,-7) ---> Z' (-7,-1)
therefore the new coordinates are W' (-5,-3), X' (-3,-1), Y' (-5,1) and Z' (-7,-1)
The answer is 36 I'm pretty sure
Answer:
Step-by-step explanation:
Using the given expressions, we can write the area as ...
A = BH
42 = (2x +1)(x +3) = 2x^2 +7x +3
2x ^2 +7x -39 = 0
(x -3)(2x +13) = 0
x = 3 or -6.5 . . . . . these values make the factors be zero
In order for the parallelogram to have positive dimensions, the value of x must be 3. So, the base and height are ...
base = 2(3) +1 = 7
height = 3 +3 = 6
There are 490 workers
3/4 = 210/x
Cross multiply, 210x4 and 3x
You're then left with 3x = 840, divide both sides by 3
This answer is 280 and represents the amount of female workers
Then just add 210 and 280, your answer is 490. Hope that helps!
