It's easy to show that 
is strictly increasing on ![x\in\left[0,\frac\pi8\right]](https://tex.z-dn.net/?f=x%5Cin%5Cleft%5B0%2C%5Cfrac%5Cpi8%5Cright%5D)
. This means
and
Then the integral is bounded by
Answer: The roses costed $9
Step-by-step explanation:
3 multiplied by 3 equals 9
1 multiplied by 6 equals 6
9+6=15
Answer:
Z - score = 2.83
Step-by-step explanation:
Given the following :
Number of samples (N) = 60
Sample mean (x) = 41.9mg
Population mean (μ) = 40mg
Population standard deviation (sd) = 5.2
Using the relation :
Z = (x - μ) / (sd / √N)
Z = (41.9 - 40) / (5.2 / √60)
Z = 1.9 / (5.2 / 7.7459666)
Z = 1.9 / 0.6713171
Z = 2.8302570
Therefore, the z-score = 2.83
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:
12km
Step-by-step explanation:
this really is actually kind of simple so it takes shawn 6 hours to get there at a speed of 2 kilometer per hour so you take the time and you X it by the speed therefor 6 X 2 = 12 and that would be your answer
