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aalyn [17]
3 years ago
11

The tables represent the functions f(x) and g(x).

Mathematics
1 answer:
alexgriva [62]3 years ago
3 0

Answer:

rtyujn

Step-by-step explanation:

er456y7ujm

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PLEASE HELP WITH THESE 4 QUESTIONS IF CORRECT ILL MARK BRAINLIEST
Serjik [45]

Answer:

the first box maybe

Step-by-step explanation:

6 0
3 years ago
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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 speed of the current in a creek is 5 mph. A person clan kayak 3 mi upstream in the same time that it takes him to kayak 13 m
Brut [27]

Answer:

8

Step-by-step explanation:

0) the basic formula is: L=v*t, where L - distance, v - speed/velocity; t - time;

1) if the person's speed in still water is 'v' and the speed of water is 5 (according to the condition), then the upstream speed is 'v-5' and the downstream speed is 'v+5';

2) according to the condition the upstream time and the downstream time are the same, it means t₁=t₂=t, where t₁=upstream time and t₂=downstream time;

3) according to the items above it is possible to make up the equation of the upstream travel: t(v-5)=3; ⇒ t=3/(v-5);

4) according to the items above it is possible to make up the equation of the downstream travel: t(v+5)=13; ⇒ t=13/(v+5);

5) if t=3/(v-5) and t=13/(v+5), then

\frac{3}{v-5} =\frac{13}{v+5}; \ => \ v=8.

8 0
2 years ago
Frank had 42 rocks that he wanted to share with his friends. If he gave each friend the same number of rocks(and kept the same n
shutvik [7]

Answer:6. 42 split 7 ways is 6

Step-by-step explanation:

7 0
2 years ago
How do you write -x+3y=6 in slope intercept form?
Afina-wow [57]

Commenter jdoe said it right: solve for y and leave the rest on the other side.

-x + 3y = 6

3y = 6 + x add x on both sides

3y = x + 6 rearrange to get the x first

y = (x + 6) /3 divide both sides by 3

y = x/3 + 6/3 split the numerator (caution - never split denominators)

y = x/3 + 2 simplify 6/3


Thus the line in slope intercept form of y = mx + b is y = y = \frac{1}{3} x + 2


8 0
3 years ago
Read 2 more answers
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