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Marianna [84]
3 years ago
14

The dimensions of a box are √9 by √16 by √25. Its volume is

Mathematics
2 answers:
steposvetlana [31]3 years ago
8 0
Root 9 is 3, root 16 is 4, root 25 is 5.

3 x 4 x 5 = 60
Olegator [25]3 years ago
6 0
The answer is D. (3 times 4 times 5 is 60)
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Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x+4y subject to the constraint x2+y2=9, if such values
Vesnalui [34]

The Lagrangian is

L(x,y,\lambda)=x+4y+\lambda(x^2+y^2-9)

with critical points where the partial derivatives vanish.

L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}

L_y=4+2\lambda y=0\implies y=-\dfrac2\lambda

L_\lambda=x^2+y^2-9=0

Substitute x,y into the last equation and solve for \lambda:

\left(-\dfrac1{2\lambda}\right)^2+\left(-\dfrac2\lambda\right)^2=9\implies\lambda=\pm\dfrac{\sqrt{17}}6

Then we get two critical points,

(x,y)=\left(-\dfrac3{\sqrt{17}},-\dfrac{12}{\sqrt{17}}\right)\text{ and }(x,y)=\left(\dfrac3{\sqrt{17}},\dfrac{12}{\sqrt{17}}\right)

We get an absolute maximum of 3\sqrt{17}\approx12.369 at the second point, and an absolute minimum of -3\sqrt{17}\approx-12.369 at the first point.

4 0
2 years ago
What is the slope of the line through (-1,8) and (3,-4)?
laila [671]

Hey there!!

How do we find slopes ?

Slope = \frac{y2-y1}{x2-x1}

We are given with two co-ordinates :

(-1,8) and (3,-4)  

Hence, the slope is :

\frac{-4-8}{3+1}

... \frac{-12}{4} = -3

The slope is -3.

Hope my answer helps!

4 0
2 years ago
Someone please help me thank you
german

Answer:

4

Step-by-step explanation:

7x = x² - 8

=> x² - 7x - 8 = 0

use quadratic formula:

a = 1, b = -7, c = -8

x = \frac{-(1)±\sqrt{(-7)^{2} - 4(1)(-8) } }{2(1)} <em>(pls ignore the "A" I don't know why it's showing up)</em>

=> x = \frac{-1±\sqrt{49 + 32} }{2}

=> x = \frac{-1±9 }{2}

=> x = \frac{-1 +9}{2} = 4 or \frac{-1-9}{2} = -5 <em>(the answer is only 4 since it's asking for the positive solution)</em>

6 0
2 years ago
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Which is the correct description of how to find the volume of a cylinder?
horsena [70]

Answer:

The formula for the volume of a cylinder is V=Bh  or  V=πr2h .

3 0
2 years ago
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Who ever gets this right will get a brainlest
WITCHER [35]
A. Right angle i got you!!!!!!
7 0
3 years ago
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