Answer:
Using either method, we obtain: 
Step-by-step explanation:
a) By evaluating the integral:
![\frac{d}{dt} \int\limits^t_0 {\sqrt[8]{u^3} } \, du](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5Cint%5Climits%5Et_0%20%7B%5Csqrt%5B8%5D%7Bu%5E3%7D%20%7D%20%5C%2C%20du)
The integral itself can be evaluated by writing the root and exponent of the variable u as: ![\sqrt[8]{u^3} =u^{\frac{3}{8}](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bu%5E3%7D%20%3Du%5E%7B%5Cfrac%7B3%7D%7B8%7D)
Then, an antiderivative of this is: 
which evaluated between the limits of integration gives:
and now the derivative of this expression with respect to "t" is:
b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then
is continuous on [a,b], differentiable on (a,b) and 
Since this this function 
is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:
Answer:1.5 pints
Step-by-step explanation: I only want Brainliest and 5 star. Thank u
The total cost of the customers order is s/2 + 1.50 dollars.
<u>Explanation:</u>
Let s represent the cost of sandwich
Cost of pretzels = 1.50 dollars
Special offer by deli lunch = Half of the cost of sandwich + bag of pretxel
Cost of offer. = s/2 + 1.50 dollars
Original order = 1 sandwich
Originial cost = s dollars
Well if you get 60 dollars every day we can represent that as 60d
We can set that equal to 289999 to solve for days, d.
289999 = 60d
289999/60 = d
4,833.3166667 = d
So 4,834 total days
Answer:
27 and 29
Step-by-step explanation:
let A and B the expected numbers
assuming B = A + 2, the problem can be written as follows
¼(A + A + 2) = 14
4*¼(A + A + 2) = 4*14
(A + A + 2) = 56
2A + 2 = 56
A + 1 = 28
A = 27
B = 27 + 2 = 29
