Answer:
-dx/dy = (1 + x) √(1 − x²)
Step-by-step explanation:
y = √((1 − x) / (1 + x))
Squaring both sides:
y² = (1 − x) / (1 + x)
Take derivative of both sides (use power rule and chain rule on the left, and quotient rule on the right):
2y dy/dx = [(1 + x)(-1) − (1 − x)(1)] / (1 + x)²
2y dy/dx = (-1 − x − 1 + x) / (1 + x)²
2y dy/dx = -2 / (1 + x)²
y dy/dx = -1 / (1 + x)²
Substitute the expression for y:
√((1 − x) / (1 + x)) dy/dx = -1 / (1 + x)²
Multiply both sides by 1 + x:
√((1 − x) (1 + x)) dy/dx = -1 / (1 + x)
√(1 − x²) dy/dx = -1 / (1 + x)
Solve for dy/dx:
dy/dx = -1 / [ (1 + x) √(1 − x²) ]
The gradient of the normal is the slope of the perpendicular line:
-dx/dy = (1 + x) √(1 − x²)
Here's a graph:
desmos.com/calculator/kbglyjdzaj
Answer:
$13200
Step-by-step explanation:
All we have to do is set up a proportion.
1200/100=x/1100
Thathat means that
100x=1,320,000
x= 13200
it would still be 5 units. translations do not change the length
Because ΔCDF is similar to ΔBDE, the corresponding sides are proportional
CD:BD=FD:ED
(3.63+5.19):5.19=(x+4.45):4.45
5.19(x+4.45)=(3.63+5.19)*4.45
5.19x+5.19*4.45=3.63*4.45+5.19*4.45
5.19x=3.63*4.45=16.1535
x≈3.11
you can also do DB:BC=DE:EF. You'll get the same result.
Answer:
F (X-3) =4X-18
Step-by-step explanation: