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3 years ago

Is the square root of 1,815 rational?

Mathematics

2 answers:

Masja [62]3 years ago

4 0

Answer:

It is not

Step-by-step explanation:

8_murik_8 [283]3 years ago

3 0

<h3>Answer: No, it is not rational</h3>

Explanation:

Using a calculator, we find that

sqrt(1815) = 42.6028168082816

which is not a whole number. The decimal numbers go on forever without any known pattern. Therefore, this number is irrational. This means it is not rational.

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What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

telo118 [61]

Answer:

$f(x)=-\frac{1}{8}(x-3)^2+3$

Step-by-step explanation:

We want to find the equation of the parabola with a focus of $(3,1)$ and directrix $y=5$ .

Considering the directrix, the quadratic graph must open downwards.

The equation of this parabola is given by the formula,

$(x-h)^2=4p(y-k)$ , where $(h,k)$ is the vertex of the parabola.

The axis of this parabola meets the directrix at $(3,5)$ .

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$h=\frac{3+3}{2}=3$ and $k=\frac{5+1}{2}=3$ .

The equation of the parabola now becomes,

$(x-3)^2=4p(y-3)$ .

Also $|p|$ is the distance between the vertex and the directrix.

$|p|=2$

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$p=-2$ .

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We make y the subject to get,

$y=-\frac{1}{8}(x-3)^2+3)$ .

This is the same as

$f(x)=-\frac{1}{8}(x-3)^2+3)$ .

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3 years ago