Outline a proof of the following statement by writing the “starting point” and the “conclusion to be shown” in a proof of the statement.
? real numbers r and s, if r and s are rational then r ? s is rational.
That is, complete the sentences below.
Proof: Suppose __________.
We must show that __________.
Proof: Suppose r and s, are any [particular but arbitarily chosen] rational numbers.
We must show that r ? s is rational.
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Parametrize the surface S.S is the portion of the plane -8x - 8y + 6z = 3 that lies within the cylinder 
.
What will be an ideal response?
Provide an appropriate response.Years ago, people used fountain pens. The ink was very "wet" and so a blotter was used to absorb "wet" ink left on the surface of the paper. Suppose you have a single sheet of graph paper and that you have just used your fountain pen to graph the one-to-one function f. Explain how, if the ink is "wet", you could now obtain the graph of f-1 using only your sheet of graph paper. (Hint: Fold the sheet of graph paper.)
What will be an ideal response?
Find the standard form of the equation of the following conic section.center (5.9, 0); r = 8
A. (x + 5.9)2 + y2 = 64 B. (x - 5.9)2 + y2 = 8 C. (x - 5.9)2 + y2 = 64 D. (x + 5.9)2 + y2 = 8
Complete the identity.sin ? [sin(5?) + sin 7?)] = ?
A. 
cos ? [cos(5?) + cos(7?)]
B. cos ? [cos(5?) + cos(7?)]
C. 
cos ? [cos(5?) - cos(7?)]
D. cos ? [cos(5?) - cos(7?)]