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____ [38]
3 years ago
13

Without graphing, determine the domain.​

Mathematics
1 answer:
adoni [48]3 years ago
6 0

#5 - Domain - (−∞,∞),{x|x∈R}

#5 - Range - [3,∞),{y|y≥3}

#6 Domain - (−∞,9],{x|x≤9}

#6 Range - [0,∞),{y|y≥0}

Hope This Help's !!

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The function f(x) = x^2 - 2x + 8 is transformed such that g(x) = f(x-2). Find the vertex of g(x).
Serjik [45]

Answer:

Step-by-step explanation:

Since g(x) is f(x-2), every time there is a "x" in the f(x) equation, substitute "x-2". So g(x) would be (x-2)^2-2(x-2)+8. Use the method of trial and error: substitute x as 1,-1, and 3, until you found the right vertex. The answer is B (3,7).

7 0
3 years ago
Use lagrange multipliers to find the shortest distance, d, from the point (4, 0, −5 to the plane x y z = 1
Varvara68 [4.7K]
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be x+y+z=1.

You're minimizing d(x,y,z)=\sqrt{(x-4)^2+y^2+(z+5)^2} subject to the constraint f(x,y,z)=x+y+z=1. Note that d(x,y,z) and d(x,y,z)^2 attain their extrema at the same values of x,y,z, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.

The Lagrangian is

L(x,y,z,\lambda)=(x-4)^2+y^2+(z+5)^2+\lambda(x+y+z-1)

Take your partial derivatives and set them equal to 0:

\begin{cases}\dfrac{\partial L}{\partial x}=2(x-4)+\lambda=0\\\\\dfrac{\partial L}{\partial y}=2y+\lambda=0\\\\\dfrac{\partial L}{\partial z}=2(z+5)+\lambda=0\\\\\dfrac{\partial L}{\partial\lambda}=x+y+z-1=0\end{cases}\implies\begin{cases}2x+\lambda=8\\2y+\lambda=0\\2z+\lambda=-10\\x+y+z=1\end{cases}

Adding the first three equations together yields

2x+2y+2z+3\lambda=2(x+y+z)+3\lambda=2+3\lambda=-2\implies \lambda=-\dfrac43

and plugging this into the first three equations, you find a critical point at (x,y,z)=\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right).

The squared distance is then d\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right)^2=\dfrac43, which means the shortest distance must be \sqrt{\dfrac43}=\dfrac2{\sqrt3}.
7 0
3 years ago
The answer and how to do it.
Kruka [31]

let x = orginal price of the shorts

$21 = x(100%-20%) * 1.05

$21 = x(80%) * 1.05

$21 = 0.8x * 1.05

Subtract 1.05 from both sides

$19.95 = 0.8x

Divide 0.8 from both sides

$24.9375 = x

So the orginal price of the shorts are about $24.94

4 0
3 years ago
Manuel needs to make a total of 60 deliveries this week. So far he has completed 36 of them. What percentage of his total delive
Alenkasestr [34]

Answer:

60%

Step-by-step explanation:

It’s simple

He needs to do 60, he has done 36

Percentage = (36/60) * 100

= 60%

5 0
3 years ago
Favorite radio station has this hourly
IceJOKER [234]
P(n)=news time/total time 

We are told that the news is 14 minutes long during an hour so

p(n)=14/60

p(n)=7/30
7 0
3 years ago
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