The circle is centered at the origin and the length of its radius is three. What is the circles equation

Mathematics

1 answer:

Vlad [161]2 years ago

7 0

Answer:

x^2 + y^2 = 3^2

Step-by-step explanation:

Use the standard equation of a circle with center at (h, k) and radius r:

(x - 0)^2 + (y - k)^2 = 3^2, or

x^2 + y^2 = 3^2

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What is lim x→3 x^2 - x - 6/ x - 3

Kisachek [45]

<h3>Answer: D) 5</h3>

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Explanation:

If we plugged x = 3 into the expression, then we'd get x-3 = 3-3 = 0 in the denominator. That's not allowed. But we can simplify first

x^2-x-6 factors to (x-3)(x+2). The key here is that (x-3) is a factor. It cancels with the x-3 in the denominator

So, $\frac{x^2-x-6}{x-3} = \frac{(x-3)(x+2)}{x-3} = x+2$

Allowing us to say,

$\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}\frac{(x-3)(x+2)}{x-3}\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}(x+2)\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 3+2\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 5\\\\\\$

5 0

3 years ago

Find the ratio. Than find and interpret the value of the ratio

shepuryov [24]

Answer:

The ratio is 3/4: 2

The value of the ratio is 3/8

The amount of club soda is 3/8 times the amount of white grape juice

3 0

3 years ago

In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected for a

Softa [21]

Answer:

95% Confidence interval = (23.4,26.2)

Step-by-step explanation:

In this problem we have to develop a 95% CI for the mean.

The sample size is n=49, the mean of the sample is M=24.8 and the standard deviation of the population is σ=5.

We know that for a 95% CI, the z-value is 1.96.

The CI is

$M-z*\sigma/\sqrt{n}\leq\mu\leq M+z*\sigma/\sqrt{n}\\\\24.8-1.96*5/\sqrt{49}\leq\mu\leq 24.8+1.96*5/\sqrt{49}\\\\ 24.8-1.4\leq\mu\leq 24.8+1.4\\\\23.4\leq\mu\leq 26.2$