Answer: 26.5cm2
Step-by-step explanation:
Answer:
The correct order is:
a
c
d
b
Step-by-step explanation:
First, let's write 1/x in a convenient way for us:
a) Substitute 1/x = p/q, to obtain x = 1/(1/x) = 1/(p/q) = q/p.
Now we assume that 1/x is rational (we want to prove that this implies that x will be also rational and because we know that x is irrational assuming that 1/x is rational will lead to an incongruence), then:
c. If 1/x is rational, then 1/x = p/q for some integers p and q with q ≠ 0. Observe that p is not 0 either, because 1/x is not 0.
Now we know that we can write x as a quotient of two integers, we need to imply that, then the next one is:
d) Observe that x is the quotient of two integers with the denominator nonzero.
And that is the definition of rational, then we end with:
b) Hence x is rational.
Which is what we wanted to get.
Step-by-step explanation:
Let (2n +1) be the larger odd number by definition, where n can be any real integer. Then (2n - 1) is the smaller consecutive odd number.
The product of the 2 odd numbers is (2n + 1)(2n - 1) = 4n^2 - 1 = 2(2n^2) - 1. Since n^2 must be an integer, 2(2n^2) - 1 is odd. (Shown)
We have been given an equation of hyperbola 
. We are asked to find the center of hyperbola.
We know that standard equation of a vertical hyperbola is in form 
, where point (h,k) represents center of hyperbola.
Upon comparing our given equation with standard vertical hyperbola, we can see that the value of h is 6.
To find the value of k, we need to rewrite our equation as:
Now we can see that value of k is 
. Therefore, the vertex of given hyperbola will be at point 
and option D is the correct choice.
