Consider the recursively defined set S: Basis Step: The unit circle is in S. Recursive Step: if x is in S, then x with a line th
rough any diameter is in S. (a) (4 points) Prove that: is in S. (b) ( 6 points) For an element x ∈ S, define V (x) be the number of vertices (i.e. the number of intersections of lines and arcs and lines with lines), let E(x) to be the number of edges (line segments or arcs between vertices), and let F(x) be the number of faces. Prove that for any x ∈ S that F + V = E + 1. (Please use structural induction.)
1 answer:
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Answer:
The farmer have at first <u>202</u> chickens.
Step-by-step explanation:
Given:
A farmer had twice as many chickens as ducks on his farm. After he sold 166 chickens and ducks, he had half as many chickens as ducks left.
Now, to find the chickens farmer have at first.
Let the chickens be
And, the ducks be
<em>As, the farmer had twice as many chickens as ducks on his farm.</em>
So, ......(1)
<em>As, given the farmer after selling 166 chickens and ducks, he had half as many chickens as ducks left.</em>
According to question:
Substituting the value of from equation (1) we get:
<em>By cross multiplying we get:</em>
<em>Adding both sides 332 we get:</em>
<em>Subtracting both sides by </em><em> we get:</em>
<em>Dividing both sides by 3 we get:</em>
Now, to get the number of chickens substituting the value of in equation (1):
Therefore, the farmer have at first 202 chickens.
Let
x----------> charge per hour to rent a jet sky in dollars
y----------> the total cost to rent a jet sky in dollars
we know that
<u>First Jet Sky Company</u>
---------> equation
<u>Second Jet Sky Company</u>
---------> equation
we know that
To find the number of hours for which the costs are the same
equate equation and equation
The intersection both graphs is the solution of the problem
using a graph tool
see the attached figure
the intersection point is
That means
For
the cost of the rent is in both companies
therefore
<u>the answer is</u>
