Question

Write a loop that displays all possible combinations:

a) Nested loop
b) For loop
c) While loop
d) If-else loop

Answer 1

C. y = e^3x / (3x + 9)

Step-by-step explanation:

To show that y₀³y = x has a solution y = e^3x / (3x + 9), we can substitute this solution into the given equation and demonstrate its validity.

Starting with y = e^3x / (3x + 9), we raise it to the power of 3:

y³ = (e^3x / (3x + 9))³

Simplifying the expression:

y³ = e^9x / (3x + 9)³

Now, if we multiply y³ by (3x + 9), we get:

y³(3x + 9) = e^9x / (3x + 9)

Canceling out the common factor of (3x + 9) on both sides:

y³ = e^9x

Now, we substitute this expression back into the original equation:

y₀³y = (e^3x)³ * (e^9x / (3x + 9)) = e^9x = x

This demonstrates that y = e^3x / (3x + 9) is indeed a solution to the given equation, and the correct option is C.