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vesna_86 [32]
3 years ago
10

Can someone help me please ?

Mathematics
2 answers:
mario62 [17]3 years ago
5 0

x - y = 3

We rewrite it in a more functional form:

y = x - 3

I'll make a vertical table, easier to type. For each x we subtract 3 to get y.

x y

0 -3

1 -2

2 -1

3 0

Amanda [17]3 years ago
5 0

For this question, we have an equation in two unknowns. This means that, if we're given the value of one, we can (in this example) easily solve for the other. Let's pick values for x, then, and see what those force y to be.

When x = 3:

3 - y = 3

The only number that would work for y here is 0, so our ordered pair for x = 3 is (3, 0).

When x = 4:

4 - y = 3

and y = 1, giving us (4, 1)

When x = 5, 5 - y = 3 and y = 2, giving us (5, 2)

And when x = 6, 6 - y = 3 and y = 3, giving us (6, 3)

Four ordered pairs that make this equation true then are (3, 0), (4, 1), (5, 2), and (6, 3)

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Help me this is really hard
nirvana33 [79]
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6 0
3 years ago
What is (2-2i√3)4 equivalent to?
maxonik [38]

a. (2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

b. (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

To answer the question, we need to know what complex numbers are

<h3>What are complex numbers?</h3>

Complex numbers are numbers of the form z = x + iy

<h3>a. Complex numbers in polar form</h3>

Complex numbers in polar form z = r(cosθ + isinθ) where

  • r = √(x² + y²) and
  • θ = tan⁻¹(y/x)

Given that z = (2 - 2i√3)⁴ =

So,

  • x = 2 and
  • y = -2√3

So, converting to polar form

r = √(x² + y²)

= √[2² + (-2√3)²]

= √[4 + 4(3)]

= √[4 + 12]

= √16

= 4

θ = tan⁻¹(y/x)

θ = tan⁻¹(-2√3/2)

θ = tan⁻¹(-√3)

θ = -π/3

So, z = r(cosθ + isinθ)

= 4(cos(-π/3) + isin(-π/3))

<h3>Powers of complex numbers</h3>

A complex number z raised to power n is zⁿ = rⁿ(cosnθ + isin(nθ)]

z⁴ = (2 - 2i√3)⁴

= r⁴(cos4θ + isin4θ)

= 4⁴(cos(4 × -π/3) + isin(4 × -π/3))

= 256(cos(-4π/3) + isin(-4π/3))

= 256cis(-4π/3)

(2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

<h3>b. Complex numbers in rectangular form</h3>

The complex number z =  r(cosθ + isinθ) in rectangular form is z = x + iy where

  • x =  rcosθ and
  • y =  rsinθ

Given that z⁴ = 256(cos(-4π/3) + isin(-4π/3)) in rectangular form,

x = rcosθ

= 256(cos(-4π/3)

= 256cos(-4 × 60°)

= 256cos(-240)

= 256cos(240)

= 256 × -1/2

= -128

y =  rsinθ

= 256sin(-4π/3)

= 256sin(-4 × 60°)

= 256sin(-240)

= -256sin240

= -256 × -√3/2

= 128√3

So, z⁴ = x + iy

= -128 + 128√3

So, (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

Learn more about complex numbers in polar form here:

brainly.com/question/9678010

#SPJ1

7 0
1 year ago
A number line contains points Q, R, S, and T. Point Q is on the coordinate 4, R is on the coordinate 8, S is on the coordinate 9
blagie [28]
Length of ST / length of QT

3/8
7 0
3 years ago
Read 2 more answers
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