We often use functions to model or represent situations and relationships. These representations can be as equations, graphs, ta
1 answer:
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Step-by-step explanation:
Consider the provided information.
For the condition statement or equivalent "If p then q"
- The rule for Converse is: Interchange the two statements.
- The rule for Inverse is: Negative both statements.
- The rule for Contrapositive is: Negative both statements and interchange them.
Part (A) If it snows tonight, then I will stay at home.
Here p is If it snows tonight, and q is I will stay at home.
Converse: If I will stay at home then it snows tonight.
Inverse: If it doesn't snows tonight, then I will not stay at home.
Contrapositive: If I will not stay at home then it doesn't snows tonight.
Part (B) I go to the beach whenever it is a sunny summer day.
Here p is I go to the beach, and q is it is a sunny summer day.
Converse: It is a sunny summer day whenever I go to the beach.
Inverse: I don't go to the beach whenever it is not a sunny summer day.
Contrapositive: It is not a sunny summer day whenever I don't go to the beach.
Part (C) When I stay up late, it is necessary that I sleep until noon.
P is I sleep until noon and q is I stay up late.
Converse: If I sleep until noon, then it is necessary that i stay up late.
Inverse: When I don't stay up late, it is necessary that I don't sleep until noon.
Contrapositive: If I don't sleep until noon, then it is not necessary that i stay up late.
Answer:
volume V of the solid
Step-by-step explanation:
The situation is depicted in the picture attached
(see picture)
First, we divide the segment [0, 5] on the X-axis into n equal parts of length 5/n each
[0, 5/n], [5/n, 2(5/n)], [2(5/n), 3(5/n)],..., [(n-1)(5/n), 5]
Now, we slice our solid into n slices.
Each slice is a quarter of cylinder 5/n thick and has a radius of
-k(5/n) + 5 for each k = 1,2,..., n (see picture)
So the volume of each slice is
for k=1,2,..., n
We then add up the volumes of all these slices
Notice that the last term of the sum vanishes. After making up the expression a little, we get
But
we also know that
and
so we have, after replacing and simplifying, the sum of the slices equals
Now we take the limit when n tends to infinite (the slices get thinner and thinner)
and the volume V of our solid is
