Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inv
1 answer:
The statement "<span>The rate of change of y with respect to x is inversely proportional to y^4" can be written mathematically as dy/dx = k/y^4
To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
![y= \sqrt[5]{Bx+C}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%5B5%5D%7BBx%2BC%7D%20)
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To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
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Binomial expansion is used to factor expressions that can be expressed as the power of the sum of two numbers.
The proof that (1.01)^12 exceeds (1.02)^6 by 0.0007 is
The expressions are given as:
A binomial expression is represented as:
Express 1.01 as 1 + 0.01
So, we have:
Apply the above formula
This gives
Similarly,
Express 1.02 as 1 + 0.02
So, we have:
Apply
This gives
Calculate the difference as follows:
The above equation means that:
(1.01)^12 exceed the value of (1.02)^6 by 0.0007
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