Melinda has a goal of donating at least $300 to charity this year. Her mother and father each gave her $25 to help and she is se
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Answer:
Using either method, we obtain:
Step-by-step explanation:
a) By evaluating the integral:
The integral itself can be evaluated by writing the root and exponent of the variable u as:
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:
<h2>The factory needs to sell 327 packbacks to make at least 9,800 per week.</h2>Step-by-step explanation:
We know that each backpacks is sold for $40.00.
The goal is to make at least $9,800 per week. With this information we can define the inequality
Where represents backpacks. Notice that this inequality is about profits, that's why we subtract the cost from the sell price, in this case, the profid margin is $30.00 per backpack, so
Solving for
Therefore, the factory needs to sell 327 packbacks to make at least 9,800 per week.