9514 1404 393
Answer:
- maximum: 15∛5 ≈ 25.6496392002
- minimum: 0
Step-by-step explanation:
The minimum will be found at the ends of the interval, where f(t) = 0.
The maximum is found in the middle of the interval, where f'(t) = 0.
![f(t)=\sqrt[3]{t}(20-t)\\\\f'(t)=\dfrac{20-t}{3\sqrt[3]{t^2}}-\sqrt[3]{t}=\sqrt[3]{t}\left(\dfrac{4(5-t)}{3t}\right)](https://tex.z-dn.net/?f=f%28t%29%3D%5Csqrt%5B3%5D%7Bt%7D%2820-t%29%5C%5C%5C%5Cf%27%28t%29%3D%5Cdfrac%7B20-t%7D%7B3%5Csqrt%5B3%5D%7Bt%5E2%7D%7D-%5Csqrt%5B3%5D%7Bt%7D%3D%5Csqrt%5B3%5D%7Bt%7D%5Cleft%28%5Cdfrac%7B4%285-t%29%7D%7B3t%7D%5Cright%29)
This derivative is zero when the numerator is zero, at t=5. The function is a maximum at that point. The value there is ...
f(5) = (∛5)(20-5) = 15∛5
The absolute maximum on the interval is 15∛5 at t=5.
Answer:
A. -500
Step-by-step explanation:
Find the slope using rise over run (change in y / change in x)
Find the change in the y values (height of the plane):
24,000 - 18,000
= 6,000
Find the change in the x values (miles from the airport)
(60 - 72)
= -12
Divide 6000 by -12:
6000/-12
= -500
So, the slope of the plane's path is A. -500
Answer:

Step-by-step explanation:
We do not have enough information for slope intercept form. But we can use the point-slope formula to find the information. The formula is
where we substitute a point (x,y) for
.
We have m=3/4 and (4, 1). We input m and
.

We now simplify the parenthesis and solve for y.

We convert -4 into a fraction with 1 as the denominator.

We add 1 to both sides to isolate y,

This is slope intercept form. The line as slope 3/4 and y-intercept (0,2) or b=2.
Answer:The first one is a line segment the second one is a ray and the 3rd one is a line
Step-by-step explanation:
Answer: (6^-4)^-4 , (6^-2)^-8, (6^8)^2
Step-by-step explanation:
When there is a number with an exponent in a parenthesis raised to another exponent, you multiply the two exponents together. So, in this case we are looking for 2 exponents that give us a product of 16.