C. we multiply the equation by 3
Answer:
V = 904.32 ft^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The radius is 6 and pi = 3.14
V = 4/3 ( 3.14) (6)^3
V = 904.31999 ft^3
Rounding to the hundredths place
V = 904.32 ft^3
Answer:
n = 5.5
Step-by-step explanation:
4n - 10 = 12
4n = 12 + 10
4n = 22
n = 22/4
n = 5.5
Answer:
$114.75
Step-by-step explanation:
You have to multiply the hours by the wage. Looking at the time that the worker was in during the morning, it was a total of 4 hours. Since the wage is $13.50/hr, we would multiply 13.50 by 4.
13.50 * 4 = 54.00
So, now we have to add together the total hours in the afternoon. If we count the time, we get 4 1/2 hours. So, now we multiply 13.50 by 4.5.
13.50 * 4.5 = 60.75
Now, to find the total pay for that day, we add both the morning and the afternoon pay together.
54.00 + 60.75 = 114.75
Therefore, the pay for this day is $114.75.
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).
