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tatyana61 [14]
3 years ago
11

Which unit of measurement would be the most appropriate to measure a bottle of nail polish

Mathematics
1 answer:
lys-0071 [83]3 years ago
7 0

Answer:

milliliter

Step-by-step explanation:

Most of nail polish have their measurement in ml

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Which fraction is equivalent to 0.3636?
deff fn [24]
The answer is0.4/1.0.good luck
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3 years ago
Polynomial in standard form.
nataly862011 [7]

Answer:

-2x² - 8x - 15

Step-by-step explanation:

-(2x² + 4x + 11) + (-4)

-2x² - 8x - 11 - 4

-2x² - 8x - 15

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3 years ago
HURRY! What is the value of x in the diagram? Please leave an explanation fr the answer
melomori [17]
X = -15 because first u move the ax’s to one side so it would be 3x-5x=25+5 then u calculate each side 3x-5x= -2x and 25+5=30 so -2x=30 and then u divide both sides by -2 and -2/-2 cancels out and 30/-2 equals -15 (I hope his helps) :))
6 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}.
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The constant of proportionality is $1.5 per jar of sauce. Hope it help!
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