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babymother [125]

3 years ago

9

It costs $20 per hour to play pool and $3 for a cue stick rental. Write a verbal model and an algebraic expression to represent

the cost for n hours of playing pool and identify the units for the expression.

1 answer:

Scilla [17]3 years ago

3 0

Y=3+20x. X=Hours To Play Pool

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Find e^cos(2+3i) as a complex number expressed in Cartesian form.

ozzi

Answer:

The complex number $e^{\cos(2+31)} = \exp(\cos(2+3i))$ has Cartesian form

$\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2)$ .

Step-by-step explanation:

First, we need to recall the definition of $\cos z$ when $z$ is a complex number:

$\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}$ .

Then,

$\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}$ . (I)

Now, recall the definition of the complex exponential:

$e^{z}=e^{x+iy} = e^x(\cos y +i\sin y)$ .

So,

$e^{2i-3} = e^{-3}(\cos 2+i\sin 2)$

$e^{-2i+3} = e^{3}(\cos 2-i\sin 2)$ (we use that $\sin(-y)=-\sin y)$ .

Thus,

$e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)$

Now we group conveniently in the above expression:

$e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2$ .

Now, substituting this equality in (I) we get

$\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2$ .

Thus,

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)$

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right]$ .

5 0

2 years ago

DESCRIBE DOMAIN WITH ALGEBRA in my screenshot (sorry caps)

bogdanovich [222]

Answer:

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

3 0

2 years ago

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Based on the table, which function models this situation?

alexdok [17]

Answer:

F(n) =-3n+24

Step-by-step explanation:

3 0

3 years ago

How do I get this answer and what is it

Sedaia [141]

The degree is 5, so the largest exponent of the polynomial is 5. This means the answer is either A or B. Choice C is ruled out because the degree here is 7. Choice D is ruled out because the degree here is 6

For choice A, the leading coefficient is 6. This is the number to the left of the variable term of the largest exponent. So we can rule out choice A (because the leading coefficient should be 7)

Choice B is the answer. It has a degree of 5 and a leading coefficient of 7 and also a constant term of 6. The constant term is simply the term without any variables attached to it.

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3 years ago

At the end of April, Mandy told Bill that she has read 16 books this year and reads 2 books each month. Bill wants to catch up t

Dovator [93]

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant

$an=a1+d*(n-1)$

where

a1 is the first term

d is the common difference between terms

n is the number of months (in this problem)

case a) Mandy

$a1=16 books$

$d=2$

$an=16+2*(n-1)$ ------> equation $1$

in this equation the first month is April

case b) Bill

$a1=4 books$

$d=4$

$an=4+4*(n-1)$ -------> equation $2$

In this equation the first month is May

With the equation $1$ and the equation $2$

calculate the attached table

therefore

the answer is

December

8 0

2 years ago

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