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Karo-lina-s [1.5K]
3 years ago
8

2 v What is the equation of a line that is parallel to y = -4x – 3 and shifted down 3 units?

Mathematics
1 answer:
Ugo [173]3 years ago
3 0

Answer: y=-4x-6

Step-by-step explanation:

Given

The equation of line is y=-4x-3

The line which is parallel to the given line is y=-4x+c

and shifted by 3 units down i.e. its y-intercept is 3 units below the given line

\therefore y=-4x-3-3\\\Rightarrow y=-4x-6

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xenn [34]

It sounds like <em>R</em> is the region (in polar coordinates)

<em>R</em> = {(<em>r</em>, <em>θ</em>) : 2 ≤ <em>r</em> ≤ 3 and 0 ≤ <em>θ</em> ≤ <em>π</em>/2}

Then the integral is

\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}

5 0
3 years ago
What is the definition of “i”? What do we use it for? Demonstrate with an example of your own.
lyudmila [28]

Answer:

The letter "i" is used to signify that a number is an imaginary number.

Step-by-step explanation:

An imaginary number is one that gives a negative result when squared. This differs from when you square real numbers where you always get a positive result. For example:

i = √-1

Imaginary numbers can be especially useful when trying to find the square root of a real negative number such as -16. Normally we cannot find the square root of -16 but through the use of imaginary numbers we can:

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~Hope this helps!~

6 0
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Step-by-step explanation:

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maria [59]

Answer:

3x-21

Step-by-step explanation:

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5 0
4 years ago
Read 2 more answers
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