Mr. Inwood does a job in x hours while Mr. Lui can do it in y hours. How much of the job could they do it together if they were
1 answer:
If they worked for k hours, the amount of work done would be hours.
Algebraic expression involves the use of variables and their arithmetic operations.
Given that:
- Mr. Inwood does a job in x hours, while
- Mr. Lui can do it in y hours
If we have a function denoted by k (hours) indicating the work they both can do together. Then we can conclude that they can both work for:
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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: