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Svetach [21]
3 years ago
15

Soshi’s rhombus has a base of 12 in and a height of 10 in. Jack’s rhombus has base and height measures that are double those of

Soshi’s rhombus. Compare the area of Jack’s rhombus to the area of Soshi’s rhombus. Explain.
Mathematics
1 answer:
Roman55 [17]3 years ago
3 0

Answer:

360

Step-by-step explanation:

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Find the vertex of the graph y=x^2+6x-2
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Answer:

The vertex for this graph is going to be point (-3,-11)

Step-by-step explanation:

If you graph your graph given, you should get (-3,-11) as your vertex. Remember your vertex is going to the highest or lowest point in your graph.

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475 round to the nearest ten
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Masja [62]

Step-by-step explanation:

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3 years ago
The equations that must be solved for maximum or minimum values of a differentiable function w=​f(x,y,z) subject to two constrai
sammy [17]

The Lagrangian is

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

with partial derivatives (set equal to 0)

L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0

L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0

L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0

L_\lambda=4x^2+4y^2-z^2=0

L_\mu=2x+4z-2=0\implies x+2z=1

Case 1: If y=0, then

4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|

Then

x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23

\implies x=\dfrac15\text{ or }x=-\dfrac13

So we have two critical points, \left(\dfrac15,0,\dfrac25\right) and \left(-\dfrac13,0,\dfrac23\right)

Case 2: If \lambda=-\dfrac14, then in the first equation we get

x(1+4\lambda)+\mu=\mu=0

and from the third equation,

z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0

Then

x+2z=1\implies x=1

4x^2+4y^2-z^2=0\implies1+y^2=0

but there are no real solutions for y, so this case yields no additional critical points.

So at the two critical points we've found, we get extreme values of

f\left(\dfrac15,0,\dfrac25\right)=\dfrac15 (min)

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Please help me with 9&10
Andrew [12]
This is problem #9. I'm not sure how to solve #10, although the solution may be found in a similar way.

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