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3 years ago

Factor the expression over the complex numbers. x2+20

Mathematics

2 answers:

vovangra [49]3 years ago

6 0

X²+20=0
x=±√(-80)/2
x=±4i√5/2=2i√5

factorised it is then
(x+2i√5)*(x-2i√5)

Blababa [14]3 years ago

4 0

Answer:

$x^2+20=(x-2\sqrt{5}i)(x+2\sqrt{5}i)$

Step-by-step explanation:

Given : Expression $x^2+20$

To find : Factor the expression over the complex numbers ?

Solution :

To factor we equate the expression to zero.

$x^2+20=0$

Subtract 20 both side,

$x^2+20-20=-20$

$x^2=-20$

Taking root both side,

$x=\sqrt{-20}$

$x=\pm 2\sqrt{5}i$

The factor of the expression is $x^2+20=(x-2\sqrt{5}i)(x+2\sqrt{5}i)$

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What is the other endpoint if one endpoint is (10,12) and the midpoint is (6,9).?

Lubov Fominskaja [6]

Answer:

$(2,\, 6)$ .

Step-by-step explanation:

Let $(x_{0},\, y_{0})$ and $(x_{1},\, y_{1})$ denote the two endpoints.

The formula for the midpoint of these two points would be:

$\displaystyle \left(\frac{x_{0} + x_{1}}{2},\, \frac{y_{0} + y_{1}}{2}\right)$ .

(Similar to taking the average of each coordinate.)

In this question, it is given that $x_{0} = 10$ whereas $y_{0} = 12$ . Substitute these two values into the expression for the coordinate of the midpoint:

$x$ -coordinate of the midpoint: $\displaystyle \frac{10 + x_{1}}{2} = 6$ .
$y$ -coordinate of the midpoint: $\displaystyle \frac{12 + y_{1}}{2} = 9$ .

Solve these two equations for $x_{1}$ and $y_{1}$ : $x_{1} = 2$ whereas $y_{1} = 6$ .

Hence, the coordinate of the other point would be $(2,\, 6)$ .

4 0

2 years ago

What kind of question will ask us to use this type of format to evaluate the integral instead of doing the regular integral eval

ANEK [815]

Answer:

Great work!

Step-by-step explanation:

These kind of questions are calculated through Riemann Sum. You can evaluate any definite integral using the Riemann Sum. It should be in the following form:

f(x)dx on the interval [a, b], or

$\int _a^b\:f\left(x\right)dx$

Now f(x) is simply y. Therefore in this example y = x^3 - 6x. We just need the sufficient amount of data to apply the Riemann Sum, including the interval [a, b] that bounds the area, and the the number of rectangles 'n' that we need to use.

Consider an easier approach to this question: (First attachment)

Graph: (Second Attachment)