Issebelles car holds 16 gallons of gas the fuel gauge shows that the tank is 3/4 full how many gallons of gas are in the tank

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

A jug of juice has 6 cups of pineapple juice and 5 cups of orange juice. Write the ratio of the number of cups of pineapple juic

REY [17]

Answer:

number of cups of pineapple to total number of cups...

6:11 or 6/11 or 6 to 11

Step-by-step explanation:

6 0

3 years ago

If the fuel tank in Jim's car holds 14 gallons of fuel, define a formula to determine the number of gallons of fuel in Jim's fue

salantis [7]

Considering that the car does 50 miles per gallon, the linear function for the number of gallons of fuel in Jim's fuel tank, n, in terms of the number of miles x that Jim has driven since filling his tank is given by:

$y = -0.02x + 14$

<h3>What is a linear function?</h3>

A linear function is modeled by:

$y = mx + b$

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0.

In this problem:

Jim's car holds 14 gallons of fuel, hence $b = 14$ .

Considering it does 50 miles per gallon, and the amount in the tank will decrease, the slope is $m = -\frac{1}{50} = -0.02$ .

Hence, the function is:

$y = -0.02x + 14$

You can learn more about linear functions at brainly.com/question/25898120

5 0

3 years ago

A new DVD is available for sale in a store one week after its release. The cumulative revenue, $R, from sales of the DVD in this

AnnyKZ [126]

Solution :

It is given that :

$f'(t) = (350 \ln t)'$

$=350(\ln t)'$

$=\frac{350}{t}$

So, $f(5)=350 \ln (5) \approx 563$

$f'(5) = \frac{350}{5}$

$=70$

The relative change is then,

$\frac{f'(5)}{f(5)}=\frac{70}{350\ \ln(5)}$

$=\frac{1}{5\ \ln(5)}$

$\approx 0.12$

$=12\%$

This means that after 5 weeks, the revenue from the DVD sales in $563 with a rate of change of $70 per week and the increasing at a continuous rate of 12% per week.

3 0

3 years ago

Plzzzzzzzzzzzzzzzz help meeeeeeeeeeeeeeeeeeeeee if u do ill give u a dollar

myrzilka [38]

Answer:

B

x is the price of the sweater so 3x and add $15 for the skirt which would add up to $90

6 0

3 years ago

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