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KATRIN_1 [288]
3 years ago
14

Simplify the following expression: |2+4i|

Mathematics
2 answers:
Damm [24]3 years ago
8 0

Answer:

\sqrt{20}

Step-by-step explanation:

This is a complex number expression, and you are asked to find the absolute value.

in a complex number, there are two parts, the real and the imaginary part.

in the question ; 2 = real part,   4 = imaginary part

based on the diagram, we will use Pythagoras theorem to solve for the hypotenuse which gives the absolute value of the complex number.

|2+4i|^{2} = 2^{2} + 4^{2}

                              = 4 + 16

                              = 20

  ;                |2+4i|   = \sqrt{20}

Eva8 [605]3 years ago
4 0
Use distance formula (Pythagorean theorem) to find the complex number's distance from zero. There is an imaginary axis and a real axis, and these behave very much like the regular x and y axes. √(2² + 4²) = √20 
The absolute value of 2 + 4i is √20
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Which functions domain consists of all real numbers except -2?
Eddi Din [679]

Answer:

option (a) f(x)= 1/x+2

Step-by-step explanation:

(a) f(x) = 1/ x+2

To find the restriction for domain , we set the denominator =0  and solve for x

x+2 =0, so x=-2

When x=-2  then denominator becomes 0 that is undefined.

So, domain is all real numbers except -2

(b) f(x)= 2x

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

(c) f(x) = 2x-2

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

f(x) = 1/ sqrt(x+2)

if we have square root in the denominator then we set the denominator >0 and solve for x. because square root of negative values are undefined

x+2>0, x>-2

Hence domain is all real numbers that are greater than -2

8 0
3 years ago
Land in downtown Columbia is valued at $10 a square foot. What is the value of a triangular lot with sides of lengths 119, 147,
stiks02 [169]

Answer:

$87,461

Step-by-step explanation:

Given that the dimensions or sides of lengths of the triangle are 119, 147, and 190 ft

where S is the semi perimeter of the triangle, that is, s = (a + b + c)/2.

S = (119 + 147 + 190) / 2 = 456/ 2 = 228

Using Heron's formula which gives the area in terms of the three sides of the triangle

= √s(s – a)(s – b)(s – c)

Therefore we have = √228 (228 - 119)(228 - 147)(228 - 190)

=> √228 (109)(81)(38)

= √228(335502)

=√76494456

= 8746.1109071 * $10

= 87461.109071

≈$87,461

Hence, the value of a triangular lot with sides of lengths 119, 147, and 190 ft is $87,461.

6 0
3 years ago
If the weight of a package is multiplied by 5/7 the result is 40.5 pounds. Find the weight of the package.
ololo11 [35]
Well, it would become 5/7x=40.5. Divide both sides by 5/7, so it is 40.5 * by the reciprocal of 5/7 (7/5). The answer is 56.7 pounds.
6 0
3 years ago
Each side of a square is increasing at a rate of 5 cm/s. At what rate (in cm2/s) is the area of the square increasing when the a
nikklg [1K]

Answer:

knkkl

Step-by-step explanation:

bjkjjjkhjhjhjkhjhj

4 0
2 years ago
Read 2 more answers
Gabe made a rectangular sandbox for his brother to play in. Gabe wants to paint only the sides of the sandbox. A prism has a len
alukav5142 [94]

Answer: The surface area of the sides of the sandbox that Gabe wants to paint is 47ft2

Step-by-step explanation:

Hi to answer this we have to apply the formula:

Surface Area of a rectangular prism = 2lw + 2wh + 2lh

Where:

l= length

w= width

h= height

Since the sandbox is open , it has one less surface (length x width), we have to add only one lw term.

Surface Area of the sandbox = lw + 2wh + 2lh

A = (4x5) + 2( 5x1.5) + 2( 4x1.5)

A = 20+15+12

A= 47 ft2

4 0
3 years ago
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