Which is an equation of a circle with center (2, -1) that passes through the point (3, 4)?

1 answer:

5 0

Let A be (2,-1) & B be (3,4). The radius of the circle is AB. Let's calculate it

AB =√{(3-2)²+(4+1)²] = √26

Now the standard form of the equation of a circle:

(x-h)²+(y-k)² = R²

(x-2)²+(y-1)² = 26

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1.7. Use a calculator, bud.

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Write three different examples of the sum of a quadratic trinomial and a cubic monomial.

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Answer:

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Step-by-step explanation:

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3 years ago

A moving company charges $840 plus $17 per hour. Another moving company charges $760 plus $22 per hour.how long is job that cost

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1. Make an equation.
Moving company #1: y = 17x + 840
Moving company #2: y = 22x + 760

2. Put the equations together and solve
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3 years ago

Consider the infinite geometric series (∞/Σ/n=1) * -4(1/3)^{n-1}.

raketka [301]

The first four terms of the series probably refer to the first four partial sums.

$\displaystyle\sum_{n=1}^1-4\left(\frac13\right)^{n-1}=-4\left(\frac13\right)^{1-1}=-4$
$\displaystyle\sum_{n=1}^2-4\left(\frac13\right)^{n-1}=-\frac{16}3$
$\displaystyle\sum_{n=1}^3-4\left(\frac13\right)^{n-1}=-\frac{52}9$
$\displaystyle\sum_{n=1}^4-4\left(\frac13\right)^{n-1}=-\frac{160}{27}$

which you can compute either by adding one term at a time, or using the well-known formula,

$\displaystyle\sum_{n=1}^kar^{n-1}=a\frac{1-r^{k+1}}{1-r}$

(I can provide a link to a derivation I gave in a nearly identical question in the comments)

The series converges as $k\to\infty$ if and only if $|r|$ , which is certainly the case here, since $-1$ .

Extrapolating from the formula above, the sum of the convergent series is

$\displaystyle\sum_{n=1}^\infty ar^{n-1}=\frac a{1-r}$

so the sum for this series is $\dfrac{-4}{1-\frac13}=-6$ .