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Arlecino [84]
3 years ago
14

7/8 = /48 A. 1 B. 6 C. 42 D. 13

Mathematics
1 answer:
Vsevolod [243]3 years ago
6 0
7/8 = x/48

Cross multiply, which is: a/b = c/d ⇒ ad = bc

After cross multiplying, we get:

8x = 7(48)

8x = 336

Divide 8 on both sides

x = 42


Your final answer is B. 42<span>.</span>
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Step-by-step explanation:

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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

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Answer:

21/10

Step-by-step explanation:

Trust Me

6 0
2 years ago
Read 2 more answers
PLEASE HELP!
Mariana [72]
-----------------------------------------------
Information Given:
-----------------------------------------------
ON = 7x - 9
LM = 6x + 4
MN = x - 7
OL = 2y - 7

-----------------------------------------------
Since it is a parallelogram:
-----------------------------------------------
ON = LM and
MN = OL

-----------------------------------------------
ON = LM:
-----------------------------------------------
7x - 9 = 6x + 4

-----------------------------------------------
Subtract 6x from both sides:
-----------------------------------------------
x - 9 = 4

-----------------------------------------------
Add 9 to both sides:
-----------------------------------------------
x = 13

-----------------------------------------------
MN = OL:
-----------------------------------------------
x - 7 = 2y - 7

-----------------------------------------------
Sub x = 13:
-----------------------------------------------
13 - 7 = 2y - 7

-----------------------------------------------
Simplify:
-----------------------------------------------
6 = 2y - 7

-----------------------------------------------
Add 7 on both sides:
-----------------------------------------------
13 = 2y

-----------------------------------------------
Divide by 2:
-----------------------------------------------
y = 13/2

-----------------------------------------------
Answer: x = 13, y = 13/2 (Answer D)
-----------------------------------------------


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3 years ago
Please help me solve 4 inequalities and show work. Will get brainiest!!
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1. y<span> ≤ 4x/3+5
2. y</span><span>< 6x/4+3</span>
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3 years ago
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