Given:
Expression is

To prove:
If r is any rational number, then
is rational.
Step-by-step explanation:
Property 1: Every integer is a rational number. It is Theorem 4.3.1.
Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.
Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.
Let r be any rational number.
We have,

It can be written as

Now,
3, -2 and 4 are rational numbers by property 1.
is rational by Property 3.
are rational by Property 3.
is rational by property 2.
So,
is rational.
Hence proved.
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Sum of the interior angles of any triangle is 180° .
Thus ;


Subtract sides 138°


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The tangent line to the curve can be determined by implicitly differentiating the equation of the curve. In this case, with the equation <span>y sin 12x = x cos 2y, (π/2, π/4), the implicit differentiation is 12 y cos 12x dx + sin 12 x dy = -2x sin 2y dy + cos 2y dx; dx (12 y cos 12x - cos 2y) = dy (</span><span>-2x sin 2y - sin 12x). Hence
y' = (</span>12 y cos 12x - cos 2y) / (<span>-2x sin 2y - sin 12x)</span>
Answer:
B B B B B
B B B B
B B B B B B B B BB
B B B B B B B B B B B B B
70 is a composite number because it can be divided by numbers other than one and itself.