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2 years ago

Solve for x by completing the square: x2 - 12x + 11 = 0

Mathematics

1 answer:

sineoko [7]2 years ago

6 0

Answer:

Step-by-step explanation:

x² - 12x + 11 = 0 ( subtract 11 from both sides )

x² - 12x = - 11

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 6)x + 36 = - 11 + 36

(x - 6)² = 25 ( take square root of both sides )

x - 6 = ± $\sqrt{25}$ = ± 5 ( add 6 to both sides )

x = 6 ± 5

Then

x = 6 - 5 = 1 ⇒ (1, 0 )

x = 6 + 5 = 11 ⇒ (11, 0 )

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Answer:

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2 years ago

Charles is walking arounda fountain that has a circumference of 124ft .what is the diameter of the fountain?

Dovator [93]

Hello.

To find the diameter you use this equation:
Radias<span>cm x 2/pie
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3 years ago

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the sum of the first n terms of a sequence is 20 - 10 / 2 ^ n - 1 find the sum of the first five terms

Travka [436]

Answer:

$S_5=\dfrac{170}{9}$

Step-by-step explanation:

Given that,

The sum of first n term of a sequence is $S_n=20-\dfrac{10}{2n-1}$

We need to find the sum of the first 5 terms.

Put n = 5,

$S_5=20-\dfrac{10}{2(5)-1}\\\\=20-\dfrac{10}{10-1}\\\\=20-\dfrac{10}{9}\\\\=\dfrac{170}{9}$

So, the sum of first 5 terms is equal to $\dfrac{170}{9}$ .

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2 years ago

Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(

Temka [501]

The particular quadratic solution to the ODE is found as follows:

$x=at^2+bt+c$
$x'=2at+b$

$(2at+b)+2(at^2+bt+c)=t^2+4t+7$
$2at^2+(2a+2b)t+(b+2c)=t^2+4t+7$

$\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4$

Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

$x'+2x=0\implies r+2=0\implies r=-2$

so that $x_c=Ce^{-2t}$ is a characteristic solution to the ODE, and the general solution would be

$x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4$

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3 years ago