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2 years ago

Can you guys please help me with these problems?

Mathematics

1 answer:

Andrews [41]2 years ago

7 0

Answer:

Step-by-step explanation:

$2x^-3\\2*(\frac{1}{x^3} )\\\\\frac{2}{x^3} \\\\b)$

$x^3*2x^0\\x^3*2\\2x^3\\$

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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

2 years ago

Earl invested 6,000 in a money market account that pays 5% interest quarterly. How much money will he have in his account after

Sedbober [7]

Answer:

The amount becomes $6964.53 after 3 years .

Step-by-step explanation:

Formula

$Amount = P (1+\frac{r}{4})^{4t}$

Where P is the principle , r is the rate of interest in the decimal form and t is the time in the years .

As given

Earl invested 6,000 in a money market account that pays 5% interest quarterly for 3 years .

P = $6000

5% is written in the decimal form.

$= \frac{5}{100}$

= 0.05

r = 0.05

t = 3 years

Putting all the values in the formula

$Amount = 6000(1+\frac{0.05}{4})^{4\times 3}$

$Amount = 6000(1+0.0125)^{12}$

$Amount = 6000\times 1.16075452$

$Amount =\$ 6964.53\ (Approx)$

Therefore the amount becomes $6964.53 after 3 years .

3 0

2 years ago

Explain how to write and evaluate an algebraic expression that represents the situation. The blueberries were divided equally in

ser-zykov [4K]

The variable is the number of blueberries, the operation is division, and the constant is 6. Write the division expression as the fraction, b/6 . To evaluate, substitute 210 in for the variable, b, and simplify. 210 divided by 6 is 35. So each bowl has 35 blueberries.

4 0

2 years ago

Read 2 more answers

Pls help this is due in soon!!

Rasek [7]

Answer:

Step-by-step explanation:

6 0

2 years ago

Pls help me

mylen [45]

1.x+16
2.x-8
3.12/x
these are the algebraic expressions