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2 years ago

Solve for x over the complex numbers.

Mathematics

2 answers:

Grace [21]2 years ago

8 0

Answer:

Step-by-step explanation:

Given x^2+4x+13=0, find the complex roots. The best approach here is to use the quadratic formula. Note that a = 1, b = 4 and c = 13.

Thus, the discriminant, b^2 - 4ac, is (4)^2 - 4(1)(13) = 16 - 52 = -36, and the square root of that is plus or minus i√36, or plus or minus 6i.

plus or minus i√

AysviL [449]2 years ago

8 0

Answer:

x = - 2 + 3i or x = - 2 - 3i

Step-by-step explanation:

Given quadratic equation,

$x^2 + 4x + 13=0$

By the quadratic formula,

$x=\frac{-4\pm \sqrt{4^2 - 4\times 1\times 13}}{2\times 1}$

$x=\frac{-4\pm \sqrt{16-52}}{2}$ '

$x=\frac{-4\pm \sqrt{-36}}{2}$

$x=\frac{-4\pm 6i}{2}$

$x=-2\pm 3i$

Hence, the solution of the given equation,

x = - 2 + 3i or x = - 2 - 3i

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Answer:

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Step-by-step explanation:

First multiply both side 1000: 1000C=Wtc

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3 years ago

What is the circumference of a circle with a diameter of 8 feet? Use 3.14 for ON d=80 O A. 25.12 ft B. 12.56 ft C. 50.24 ft D. 1

Andrew [12]

Answer:

25.12

Step-by-step explanation:

Formula: 2πr, r = d/2

Given: π = 3.14, d = 8

Sub: r = 8/2

Simplify: r = 4

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2 years ago

Help!! 50 points and brainliest!

Viktor [21]

Answer:

Second choice:

$x=2t$

$y=4t^2+4t-3$

Fifth choice:

$x=t+1$

$y=t^2+4t$

Step-by-step explanation:

Let's look at choice 1.

$x=t+1$

$y=t^2+2t$

I'm going to subtract 1 on both sides for the first equation giving me $x-1=t$ . I will replace the $t$ in the second equation with this substitution from equation 1.

$y=(x-1)^2+2(x-1)$

Expand using the distributive property and the identity $(u+v)^2=u^2+2uv+v^2$ :

$y=(x^2-2x+1)+(2x-2)$

$y=x^2+(-2x+2x)+(1-2)$

$y=x^2+0+-1$

$y=x^2$

So this not the desired result.

Let's look at choice 2.

$x=2t$

$y=4t^2+4t-3$

Solve the first equation for $t$ by dividing both sides by 2:

$t=\frac{x}{2}$ .

Let's plug this into equation 2:

$y=4(\frac{x}{2})^2+4(\frac{x}{2})-3$

$y=4(\frac{x^2}{4})+2x-3$

$y=x^2+2x-3$

This is the desired result.

Choice 3:

$x=t-3$

$y=t^2+2t$

Solve the first equation for $t$ by adding 3 on both sides:

$x+3=t$ .

Plug into second equation:

$y=(x+3)^2+2(x+3)$

Expanding using the distributive property and the earlier identity mentioned to expand the binomial square:

$y=(x^2+6x+9)+(2x+6)$

$y=(x^2)+(6x+2x)+(9+6)$

$y=x^2+8x+15$

Not the desired result.

Choice 4:

$x=t^2$

$y=2t-3$

I'm going to solve the bottom equation for $t$ since I don't want to deal with square roots.

Add 3 on both sides:

$y+3=2t$

Divide both sides by 2:

$\frac{y+3}{2}=t$

Plug into equation 1:

$x=(\frac{y+3}{2})^2$

This is not the desired result because the $y$ variable will be squared now instead of the $x$ variable.

Choice 5:

$x=t+1$

$y=t^2+4t$

Solve the first equation for $t$ by subtracting 1 on both sides:

$x-1=t$ .

Plug into equation 2:

$y=(x-1)^2+4(x-1)$

Distribute and use the binomial square identity used earlier:

$y=(x^2-2x+1)+(4x-4)$

$y=(x^2)+(-2x+4x)+(1-4)$

$y=x^2+2x+-3$

$y=x^2+2x-3$ .

This is the desired result.

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3 years ago

Read 2 more answers

consider a dianmeter of 8 feet and height of h feet.which equation can be used to find v,the volumeof the cylinder in cubic feet

yarga [219]

Answer:

diameter times height times x = volume

Step-by-step explanation:

using the length times width times height equation for volume.

good luck :)

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3 years ago