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patriot [66]
3 years ago
7

Dominic runs a farm stand that sells peaches and grapes yesterday Dominic sold 34 pounds of peaches and 45 lb of grapes for a to

tal venue of $192.25 today he sold 47 pounds of peaches in 16 lb of grapes for a total revenue of $208 write a system of equations that could be used to determine the price of each pound A peaches and the price of each pound of grapes and Define the variables that use to write the system ​
Mathematics
1 answer:
iren2701 [21]3 years ago
3 0

Answer:34p+16g=208

47p+16g=208

Step-by-step explanation:

Let p=the price of each pound of peaches.

Let g=the price of each pound of grapes.

Each pound of peaches sells for $p, so 34 pounds of peaches will bring in 34p dollars. Each pound of grapes will bring in 45g dollars. Therefore, the total amount 34p+45g=192.25

Likewise, if 47 pounds of peaches and 16 pounds of grapes brought in $208 then

47p+16g=208

34p+45g=192.25

47+16g=208

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Answer:

True, True, False

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Let s(t) = 36 − t. find the equation of the tangent line to s(t) when t = 0.
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When t = 0 the point on the graph is (0,36). Your equation is just a line and always has the same tangent line so your equation is the same s = 36 - t.
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A line includes the points (8,-2) and (-8,-4). What is the slope intercept
VladimirAG [237]

Answer:

The equation of the line would be y = 1/8x - 3

Step-by-step explanation:

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Read 2 more answers
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

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