Given x > 0 express in simplest radical form with a rational denominator.

√336x^12/√7x^4

3 answers

Simplify the expression under the radical in the numerator:

√[336x^12] = √[(16x^6)(21x^6)] = √[16x^6] √[21x^6] = 4x^3√21

Simplify the expression under the radical in the denominator:

√[7x^4] = √[7] √[x^4] = √[7] x^2

Now we can rewrite the entire expression:

√336x^12/√7x^4 = (4x^3√21)/(√7 x^2) = 4x√(21/7) = 4x√3
A hyperbola is defined by the equation (y-4)^2/25 - (x-8)^2 = 1
what is the co-vertices,
The standard equation of a hyperbola with horizontal transverse axis is:

(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

where (h, k) is the center of the hyperbola, a is the distance from the center to each vertex along the x-axis, and b is the distance from the center to each vertex along the y-axis.

Comparing the given equation to the standard equation, we can see that this hyperbola has a vertical transverse axis (because the x term is negative). So we have:

(h, k) = (8, 4)
a^2 = 1 (from the coefficient of x^2 being -1)
b^2 = 25 (from the coefficient of y^2 being 1)

So the distance from the center to each vertex along the y-axis is b = 5. The co-vertices are the points that are distance b from the center and lie along the minor axis (i.e. along the x-axis). So we need to find the x-coordinates of these points. They are given by:

x = h ± a = 8 ± 1

Therefore, the co-vertices are the points (7, 4) and (9, 4).