Answer:

Step-by-step explanation:

there are 16 classmates in total including bess and caroline. and there chances as one person is 1 out of those 16 classmates.
Step-by-step explanation:
I hope you have a good day
Answer:
Rolf prepares four solutions using different solutes as shown in the table be❤️low.
Which solution is unsaturated?
Solution A
Solution B
Solution C
Solution D
Step-by-step explanation:
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:

Hence, the functions that produce given sequence are:
f(n) = 2n + 1
f(n) = 2(n − 1) + 3
Further explanation:
We will put n=1,2,3,4,5 to find which functions give the given sequence
<u>f(n) = 2n − 1</u>
Putting values of n

This function doesn't generate the given sequence
<u>f(n) = 2n + 1</u>
Putting values of n

This function generates the given sequence.
<u>f(n) = 2(n − 1) − 3</u>
Putting values of n

This function doesn't generate the given sequence
<u>f(n) = 2(n − 1) + 3</u>
Putting values of n

Hence, the functions that produce given sequence are:
f(n) = 2n + 1
f(n) = 2(n − 1) + 3
Keywords: Functions, Sequence
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