45-21 over 5-2 which would be 4 because it shows it
Yes, you made an algebraic error. By multiplying 18 x 4, you messed up on order of operations.
(x+9)(x+2)*4
becomes:
(x^2+11x+18)*4
= 4x^2 + 44x + 72
anyway, this is how I would do this problem:
(x+9)(x+2)(4) = 912
(x+9)(x+2) = 228
x^2 + 11x + 18 = 228
x^2 + 11x - 220 = 0
(x+21)(x-10) = 0
x = -21 or 10
The dimensions can't be negative, so we only use x = 10
The dimensions are then 10+9, 10+2, 4
or 19, 12, 4
The first solution is quadratic, so its derivative y' on the left side is linear. But the right side would be a polynomial of degree greater than 1, so this is not the correct choice.
The third solution has a similar issue. The derivative of √(x² + 1) will be another expression involving √(x² + 1) on the left side, yet on the right we have y² = x² + 1, so that the entire right side is a polynomial. But polynomials are free of rational powers, so this solution can't work.
This leaves us with the second choice. Recall that
1 + tan²(x) = sec²(x)
and the derivative of tangent,
(tan(x))' = sec²(x)
Also notice that the ODE contains 1 + y². Now, if y = tan(x³/3 + 2), then
y' = sec²(x³/3 + 2) • x²
and substituting y and y' into the ODE gives
sec²(x³/3 + 2) • x² = x² (1 + tan²(x³/3 + 2))
x² sec²(x³/3 + 2) = x² sec²(x³/3 + 2)
which is an identity.
So the solution is y = tan(x³/3 + 2).
Answer:
Not gonna lie i don't understand that on either
8/10 is close to 1(8/10 = 0.8 and 5 and up you round up)
4/9 is close to 0 (4/9 = 0.44 and 4 and down you round down!)
