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viktelen [127]
2 years ago
11

PLEASE HELP THIS IS A TEST

Mathematics
1 answer:
cluponka [151]2 years ago
8 0

Answer:

C, F, and maybe D are correct.

Step-by-step explanation:

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t
nataly862011 [7]

Let (<em>x</em>, <em>y</em>, <em>z</em>) be a point on the plane in the first octant. The box formed by this point has volume <em>xyz</em>, and you want to maximize this subject to the equation of the plane.

Use the method of Lagrange multipliers: the Lagrangian is

<em>L</em>(<em>x</em>, <em>y</em>, <em>z</em>) = <em>xyz</em> - <em>λ</em> (<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6)

Find its critical points:

∂<em>L</em>/∂<em>x</em> = <em>yz</em> - <em>λ</em> = 0

∂<em>L</em>/∂<em>y</em> = <em>xz</em> - 2<em>λ</em> = 0

∂<em>L</em>/∂<em>z</em> = <em>xy</em> - 3<em>λ</em> = 0

∂<em>L</em>/∂<em>λ</em> = -(<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6) = 0

Solving the first three equations for <em>λ</em> gives

<em>λ</em> = <em>yz</em> = <em>xz</em>/2 = <em>xy</em>/3

Solve these equations for <em>y</em> and <em>z</em> :

• <em>yz</em> = <em>xz</em>/2   =>   <em>y</em> = <em>x</em>/2   =>   2<em>y</em> = <em>x</em>

• <em>yz</em> = <em>xy</em>/3   =>   <em>z</em> = <em>x</em>/3   =>   3<em>z</em> = <em>x</em>

Substitute these solutions into the last equation and solve for <em>x</em>, then again for <em>y</em> and <em>z</em> :

<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6 = 3<em>x</em> - 6 = 0   =>   3<em>x</em> = 6   =>   <em>x</em> = 2, <em>y</em> = 1, <em>z</em> = 2/3

At this critical point, the maximum volume is

<em>xyz</em> = 2*1*2/3 = 4/3

4 0
3 years ago
I NEED HELP ASAP!!!! PLEASE ANSWER
dmitriy555 [2]

2nd ones your answer


6 0
2 years ago
Read 2 more answers
what is the area of the shaded sector of the circle if the radius is 14 ft? leave your answer in terms of pi
Strike441 [17]

Given:

Radius = 14 ft

θ = 45°

To find:

Area of the shaded sector

Solution:

Area of the sector formula:

$\text { area of sector }=\frac{\theta}{360^{\circ}} \times \pi r^{2}

                      $=\frac{45^\circ}{360^{\circ}} \times \pi \times 14^{2}

                      $=\frac{1}{8} \times \pi \times 196

                      =24.5\pi ft²

The area of the shaded sector of a circle is 24.5π ft².

3 0
3 years ago
WILL MARK BRAINLIEST<br> THANKS<br> FIND HEIGHT AND VOLUME
Nimfa-mama [501]

Answer:

~ 639.75 cm^3

Step-by-step explanation:

see pic

<h2>Edit: I did this with the assumption that 12 was the diameter, if it's the radius disregard this please</h2>

8 0
2 years ago
If a complementary angle measures 24 more than the other what is that angle
Lelu [443]
The definition of a complementary angle is one angle who can be added to another complementary angle to sum to 90 degrees. More simply, just an angle is complementary to another angle if they add up to 90 degrees. In this case, to find the other angle, you subtract 24 from 90 which equals 66 degrees.
5 0
3 years ago
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