Answer:
length = 11 yard
width = 5 yard
Step-by-step explanation:
Area of a rectangle = L W
where A = 55 yard
L = 3W - 4
find: Length
width
solution:
A = L W
55 = (3W - 4) W
55 = 3W² - 4W
3W² - 4W - 55 = 0
use quadratic equation to solve for W:
W = <u> - (-4) ± √(-4)² - 4(3)-55 </u>
2(3)
W = 5, W = -11/3
substitute W=5 to equation L = 3W - 4 to solve for L
L = 3W - 4
L = 3(5) - 4
L = 15 - 4
L = 11
therefore, the dimensions of a rectangle:
length = 11 yard
width = 5 yard
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
Answer:
x=12
Step-by-step explanation:
(9x-4)+(5x+16)=180
14x+12=180
-12 -12
14x=168
then devide both sides by 14
x=12
