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slava [35]
3 years ago
11

Showing statements are true of the graph of the function F(x)= (x+5) (x-3)

Mathematics
1 answer:
Elan Coil [88]3 years ago
5 0

x intercepts are -5 and 3

the y intercept is -15  

it opens up, which means it looks like ∪


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Answer:

-7x-56

Step-by-step explanation:

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Find a compound proposition involving the propositional variables p, q, and r that is true when exactly two of p, q, and r are t
VLD [36.1K]

Answer:

Consider the proposition C=(p∧q∧¬r)∨(p∧¬q∧r)∨(¬p∧q∧r)

Step-by-step explanation:

This compound proposition C uses the outer disjunction (∨) then the proposition is true if and only if one of the three propositions (p∧q∧¬r),(p∧¬q∧r),(¬p∧q∧r) is true.

First, it is impossible that two or three of these propositions are simultaneously true. For example, if (p∧q∧¬r) and (p∧¬q∧r) are both true, then ¬r is true (from the first conjuntion) and r is true (from the second one), a contradiction. All the other possibilities can be discarded reasoning in the same way.

Since these propositions are mutually excluyent, C is true if and only if exactly one of the three propositions is true (and false otherwise). This can only happen if exactly two of p,q, and r are true and the other one is false. For example, (p∧q∧¬r) is true when p and q are true, and r is false.

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3 years ago
What is the area of the figure?
Andreyy89

Answer:

88 \:  {in}^{2}

Step-by-step explanation:

Area of the figure = Area of rectangle with dimensions 16 in and 4 in + Area of two right triangles with base (7 - 4 = 3) 3 in and height 8 in

= 16 \times 4 + 2 \times  \frac{1}{2}  \times 3 \times 8 \\  \\  = 64 + 24 \\  \\  = 88 \:  {in}^{2}

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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
2 years ago
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