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4 years ago

The modulus of (3 - 4i)^4 is _____. 5 20 81 625

Mathematics

1 answer:

Ierofanga [76]4 years ago

5 0

Answer:

625

Step-by-step explanation:

The modulus of 3 - 4i is

$\sqrt{3^2+(-4)^2}$ = $\sqrt{9+16}$ = $\sqrt{25}$ = 5, thus

| $(3-4i)^{4}$ |

= $5^{4}$

= 625

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D x= -9
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3 years ago

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Using the diagram on the right, find the length of GT and TA.

Art [367]

Answer:

$GT=10\ units$ and $TA=6\ units$

Step-by-step explanation:

we know that

In the diagram

Triangles GRT and GEA are similar by AA Similarity Postulate

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional

$\frac{GR}{GE}=\frac{GT}{GA}$

we have

$GR=5\ units$

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$GT=16-x\ units$

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therefore

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3 years ago

What compound inequality describes this graph

nadezda [96]

Answer:

0≥x<4

Step-by-step explanation:

first, let's look at this number line.

there is a closed circle at 0 and an open circle at 4. this means that 0 is included (≤ or ≥) and that 4 is not included (< or >).

these are the endpoints, meaning that in this compound inequality, the numbers next to the symbols are 0 and 4.

x is in the middle of this compound inequality.

0 x 4

now, we have to figure out the symbols in between. i wrote out our choices above for each number. the highlighted portion is greater than or equal to 0 and less than 4, so we can write this compound inequality as the following:

0≥x<4

x is greater than or equal to 0, but less than 4

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3 years ago

One of the parking lot lights at a hospital has a motion detector on it, and the equation (x+10)2+(y−8)2=16 describes the bounda

Pani-rosa [81]

We are given an equation:
$(x+10)^{2} + (y-8)^{2} = 16$

This is an equation of a circle. General form of a circle equation is:
$(x-a)^{2} + (y-b)^{2} = r^{2}$
Where:
a = x coordinate of a center
b = y coordinate of a center
r = radius of a circle

Motion detector can detect person anywhere within a boundary. The greatest distance at which detector can detect is at the edge of a circle. That distance, between detector and edge of circle, is equal to radius.

From the equation we have:
$r^{2} =16 \\ r=4$
The greatest distance at which person can be detected is 4ft.

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3 years ago

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a person travels 8 miles due north, 3 miles due west, 7 miles due north and 11 miles due east. how far so the person from the st

PilotLPTM [1.2K]

Answer:

The correct answer would be 7. Explaination below

Step-by-step explanation:

8 + 7 = 15

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18 - 11 = 7

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3 years ago