there are 60 minutes per hour
99/60 = 1.65 km per minute
1.65 x 2 = 3.3 km in 2 minutes
Divide the number that islf can divide by like 2 or 3 or 4 for exaples
Answer:
0.25
Step-by-step explanation:
The answer would be b. THis is becuse the second choice has less than or equal to and just less than signs. This is what is shown on the graph. The open circles are the less than sides, and the closed circles mean less than or equal to. Hope this helps.
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).
