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:
2,950 Rupees
Step-by-step explanation:
To find the simple interest, we can use the formula:
A = P(1 + rt)
Now we can simply substitute the values given in the formula.
Before anything, it is a good practice to define the values of each variable.
P = 2,500
r = 9% or 0.09
t = 2
Now we proceed to use the values in the formula.
A = 2,500(1 + (0.09 × 2))
A = 2,500(1 + 0.18)
A = 2,500( 1.18 )
A = 2,950.00 Rupees
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The answer is Troposphere