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Gelneren [198K]
3 years ago
11

What is the value of Y?

Mathematics
1 answer:
lord [1]3 years ago
8 0
92° i believe im bad at math lol
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Use lagrange multipliers to find the maximum volume of a rectangular box that is inscribed in a sphere of radius r
vesna_86 [32]

For the derivative tests method, assume that the sphere is centered at the origin, and consider the circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined

1

by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner by

x2+y2+z2=r2 =⇒z= r2−(x2+y2). Then the volume of a box with this coordinate for the corner is given by

V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),

and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the boundary of this domain, so we need only consider critical points contained inside the domain in order to carry this optimization out.

For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint x2 + y2 + z2 = r2<span>. </span>

7 0
3 years ago
Can any one solve this?<br> -23x + 345t - 234t + 34x
Lyrx [107]

Answer:

111 t  +  11 x

Step-by-step explanation:

8 0
3 years ago
The recursive rule for a sequence is an=an-1+7, where a1=15.What is the explict rule for this sequence
posledela

well, the recursive rule of aₙ = aₙ₊₁ + 7, where a₁ = 15, is simply saying that

we start of at 15, and the next term is obtained by simply adding 7, and so on.

well, that's the recursive rule.

so then let's use that common difference and first term for the explicit rule.

\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=15\\ d=7 \end{cases} \\\\\\ a_n=15+(n-1)7\implies a_n=15+7n-7\implies a_n=7n+8

5 0
3 years ago
WHO IS CORRECT? LIAM or TEHYA?
horsena [70]

Answer: Both Liam and Tehya

Step-by-step explanation:

5 0
3 years ago
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What is the midpoint of the segment with endpoints (-1,6) and (0,7)
polet [3.4K]

Answer:

( -0.5 , 6.5 )

Step-by-step explanation:

4 0
3 years ago
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