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gtnhenbr [62]
3 years ago
5

What value is added to both sides of the equation x2 − 4x = −2 in order to solve by completing the square? 4, 2 , −2 , −4

Mathematics
1 answer:
Fiesta28 [93]3 years ago
6 0
X^2 - 4 x = -2
Add 4 to both sides:
x^2 - 4 x + 4 = 2
Write the left-hand side as a square:
(x - 2)^2 = 2
Take the square root of both sides:
x - 2 = sqrt(2) or x - 2 = -sqrt(2)
Add 2 to both sides:
x = 2 + sqrt(2) or x - 2 = -sqrt(2)
Add 2 to both sides:
Answer:  x = 2 + sqrt(2) or x = 2 - sqrt(2)
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8 0
2 years ago
For the function given below, find a formula for the Riemann sum obtained by dividing the interval (0, 3) into n equal subinterv
Viktor [21]

Splitting up [0, 3] into n equally-spaced subintervals of length \Delta x=\frac{3-0}n = \frac3n gives the partition

\left[0, \dfrac3n\right] \cup \left[\dfrac3n, \dfrac6n\right] \cup \left[\dfrac6n, \dfrac9n\right] \cup \cdots \cup \left[\dfrac{3(n-1)}n, 3\right]

where the right endpoint of the i-th subinterval is given by the sequence

r_i = \dfrac{3i}n

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Then the definite integral is given by the infinite Riemann sum

\displaystyle \int_0^3 2x^2 \, dx = \lim_{n\to\infty} \sum_{i=1}^n 2{r_i}^2 \Delta x \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac6n \sum_{i=1}^n \left(\frac{3i}n\right)^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3} \sum_{i=1}^n i^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3}\cdot\frac{n(n+1)(2n+1)}6 = \boxed{18}

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2 years ago
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ycow [4]

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Since your circle has diameter of 12, then its radius is 6.  Then r^{2} =36

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If you want to move the location of the center, but keep it on the x-axis, then add or subtract a number to the x, such as this:

(x+4)^{2} +y^{2} =36

The center of this circle would be (-4, 0) which is still on the x-axis.

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3 years ago
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Firdavs [7]

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Step-by-step explanation:

30 - 2(7+2)- 1        Distribute or  solve parentheses

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