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2 years ago

Which problems result in a positive number? Choose all answers that are correct. A. –4.6 • 1.6 B. –10 • (–5.2) C. 8.4 ÷ 2 D.

1 answer:

8 0

Well you can automatically eliminate, A, because when you multiply one number that's positive and another number that's negative the result is always going to be negative.
However, when you multiply two negatives the result is always positive!

So, the only ones up there that would result in a positive number is B and C

***D. was not posted so I cannot determine that one!

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Assume z = x + iy, then find a complex number z satisfying the given equation. d. 2z8 – 2z4 + 1 = 0

kodGreya [7K]

Answer: complex equations has n number of solutions, been n the equation degree. In this case:

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i11,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i101,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i191,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i281,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i78,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i168,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i258,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i348,75°}$

Step-by-step explanation:

I start with a variable substitution:

$Z^{4} = X$

Then:

$2X^{2}-2X+1=0$

Solving the quadratic equation:

$X_{1} =\frac{2+\sqrt{4-4*2*1} }{2*2} \\X_{2} =\frac{2-\sqrt{4-4*2*1} }{2*2}$

$X=\left \{ {{0,5+0,5i} \atop {0,5-0,5i}} \right.$

Replacing for the original variable:

$Z=\sqrt[4]{0,5+0,5i}$

or $Z=\sqrt[4]{0,5-0,5i}$

Remembering that complex numbers can be written as:

$Z=a+ib=|Z|e^{ic}$

Using this:

$Z=\left \{ {{{\frac{\sqrt{2}}{2} e^{i45°} } \atop {{\frac{\sqrt{2}}{2} e^{i-45°} }} \right.$

Solving for the modulus and the angle:

$Z=\left \{ {{\sqrt[4]{\frac{\sqrt{2}}{2} e^{i45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i45}} } \atop {\sqrt[4]{\frac{\sqrt{2}}{2} e^{i-45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i-45}} }} \right.$

The possible angle respond to:

$RAng_{12...n} =\frac{Ang +360*(i-1)}{n}$

Been "RAng" the resultant angle, "Ang" the original angle, "n" the degree of the root and "i" a value between 1 and "n"

In this case n=4 with 2 different angles: Ang = 45º and Ang = 315º

Obtaining 8 different angles, therefore 8 different solutions.

3 0

3 years ago

The measure of an angle is 8 degrees less than three times the measure another angle. If the two angels are supplementary, what

GalinKa [24]

Answer:

133°

Step-by-step explanation:

Let the measure of one angle be x, then the measure of the other angle is

3x - 8

Supplementary angles sum to 180°

Sum the 2 angles and equate to 180

x + 3x - 8 = 180

4x - 8 = 180 ( add 8 to both sides )

4x = 188 ( divide both sides by 4 )

x = 47

The larger angle = 3x - 8 = (3 × 47) - 8 = 141 - 8 = 133°

6 0

3 years ago

Read 2 more answers

A truck driver can travel 560 miles on 28 gallons of gas. How far can he travel on 35 gallons of gas?

Shtirlitz [24]

560 / 28 = 20....so the driver travels 20 miles per gallon

on 35 gallons......35 * 20 = 700 miles <==

or u can also do it this way...

560/28 = x / 35....560 miles to 28 gal = x miles to 35 gal
cross multiply because this is a proportion
(28)(x) = (560)(35)
28x = 19600
x = 19600/28
x = 700 miles <==

so u can either do it by finding the unit rate or by making a proportion. either way will result in the same answer.

8 0

3 years ago

The quotient of 9 3/4 and 5/8

rewona [7]

Answer:

15.6

Step-by-step explanation:

The answer is 15.6 because if you divide 9 3/4 by 5/8, you get 78/5, or 15.6 in decimal form. Hope it helps!

8 0

3 years ago

Read 2 more answers

Sara owns an exotic pet store. She wants to make sure she has more than a pound of food for every 15 lizards she has in the stor