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Black_prince [1.1K]
3 years ago
11

8–8 If the derivative property of phasors is multiplication of the phasor by jω, the integral property of phasors is division of

the phasor by jω. Use phasors and these properties to find the sinusoids in each of the following: υ 2 ( t ) = 1 100 d υ 1 ( t ) d t + 20 υ 1 ( t ) and υ1(t) = 10 cos(100t + 90°) V i 2 ( t ) = 10 ∫ i 1 ( t ) d t − 3 i 1 ( t ) and i1(t) = − 4 cos(5t) A

Mathematics
1 answer:
lions [1.4K]3 years ago
8 0

Answer:

solution attached below

Step-by-step explanation:

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If alpha and beta are the zeroes of the polynomial 6x2+x-2 find the value og alpha/beta + beta/alpha
castortr0y [4]
6x^2+x-2=6x^2+4x-3x-2=2x(3x+2)-1(3x+2)\\\\=(3x+2)(2x-1)\\\\3x+2=0\to x=-\frac{2}{3}\\\\2x-1=0\to x=\frac{1}{2}\\\\\alpha=-\frac{2}{3};\ \beta=\frac{1}{2}\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{-\frac{2}{3}}{\frac{1}{2}}+\frac{\frac{1}{2}}{-\frac{2}{3}}=-\frac{2}{3}\cdot\frac{2}{1}-\frac{1}{2}\cdot\frac{3}{2}=-\frac{4}{3}-\frac{3}{4}\\\\=-\frac{16}{12}-\frac{9}{12}=-\frac{25}{12}=-2\frac{1}{12}


use\ Vieta's\ formula:\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{\alpha^2+2\alpha\beta+\beta^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2}{\alpha\beta}-2\\\\\alpha+\beta=\frac{-b}{a};\ \alpha\beta=\frac{c}{a}\\\\\frac{(\alpha+\beta)^2}{\alpha\beta}-2=\frac{\left(\frac{-b}{a}\right)^2}{\frac{c}{a}}-2=\frac{b^2}{a^2}\cdot\frac{a}{c}-2=\frac{b^2}{ac}-2

6x^2+x-2\\\\a=6;\ b=1;\ c=-2\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{1^2}{6\cdot(-2)}-2=\frac{1}{-12}-2=-2\frac{1}{12}
7 0
3 years ago
Can u pls help me with this thanks
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7 0
3 years ago
Rearrange to make x the subject of 4(x-3)/a=y
IrinaVladis [17]

Answer: x = a*y + 3

Step-by-step explanation:

To make x the subject of the equation, first, we open the bracket

4x - 12/a = y

Then cross multiply:

4x - 12 = a * y ( a*y means the product of the two variables)

Add 12 to both sides of the equation

4x = a*y + 12

Divide both sides by 4 to get the value of x

x = a * y + 12/4

x = a*y + 3

I hope this helps.

4 0
3 years ago
which of the following gives an equation of a line that passes through the point (6 over 5, -19 over 5) and is parallel to the l
victus00 [196]
One equation for this would be

y = \frac{41}{16} x-\frac{55}{8}

We start by finding the slope between the two points:

m=\frac{y_2-y_1}{x_2-x_1}=\frac{-12-\frac{-19}{5}}{-2-\frac{6}{5}}&#10;\\&#10;\\=(-12+\frac{19}{5}) \div (-2-\frac{6}{5})&#10;\\&#10;\\=(\frac{-60}{5}+\frac{19}{5}) \div (\frac{-10}{5}-\frac{6}{5})&#10;\\&#10;\\=\frac{-41}{5} \div \frac{-16}{5}=\frac{-41}{5} \times \frac{-5}{16}=\frac{41}{16}

A line parallel to this one will have the same slope.  We will use point-slope form to write our equation:

y-y_1=m(x-x_1)&#10;\\&#10;\\y-\frac{-19}{5}=\frac{41}{16}(x-\frac{6}{5})&#10;\\&#10;\\y+\frac{19}{5}=\frac{41}{16}x- \frac{41}{16} \times \frac{6}{5}&#10;\\&#10;\\y+\frac{19}{5}=\frac{41}{16}x-\frac{246}{80}&#10;\\&#10;\\y+\frac{304}{80}=\frac{41}{16}x-\frac{246}{80}&#10;\\&#10;\\y=\frac{41}{16}x-\frac{246}{80}-\frac{304}{80}&#10;\\&#10;\\y=\frac{41}{16}x-\frac{550}{80}&#10;\\&#10;\\y=\frac{41}{16}x-\frac{55}{8}
6 0
3 years ago
Elizabeth has a swimming pool at home. She wants to build a deck all the way around her rectangular swimming pool. The width of
galben [10]

Using the perimeter of a rectangle, it is found that she can make a deck of 122 ft wide.

<h3>What is the perimeter of a rectangle?</h3>

The perimeter of a rectangle of length l and width w is given by:

P = 2(l + w)

In this problem:

  • She has enough wood to build a deck that is 280ft, hence P = 280.
  • The length is of 10 feet, hence l = 10.
  • Considering that the deck's width will be added to the actual width of 8 feet, we have that w = 8 + w.

Then:

P = 2(l + w)

280 = 2(10 + 8 + w)

36 + 2w = 280

2w = 244

w = \frac{144}{2}

w = 122

She can make a deck of 122 ft wide.

You can learn more about the perimeter of a rectangle at brainly.com/question/10489198

7 0
2 years ago
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