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Ann [662]
2 years ago
5

PLEASE HELP ASAP!!!!!! i’ll mark brainlest

Mathematics
2 answers:
Doss [256]2 years ago
7 0

Answer: A) 5 x 1/2

Step-by-step explanation: 5 x 1/2 yields 2.5, which is also the answer to 5 / 2.

tatuchka [14]2 years ago
7 0

Answer: A. 5 x 1/2

5 divided by 2 is 2.5, and 5 x 1/2 is also 2.5

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Find the absolute maximum and absolute minimum of the function f(x,y)=2x3+y4f(x,y)=2x3+y4 on the region {(x,y)|x2+y2≤64}{(x,y)|x
ddd [48]

Check where the first-order partial derivatives vanish to find any critical points within the given region:

f(x,y)=2x^3+y^4\implies\begin{cases}f_x=6x^2=0\\f_y=4y^3=0\end{cases}\implies(x,y)=(0,0)

The Hessian for this function is

\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}12x&0\\0&12y^2\end{bmatrix}

with \det\mathbf H(0,0)=0, so unfortunately the second partial derivative test fails. However, if we take x=0 we see that f(x,y)>0 for different values of y; if we take y=0 we see f(x,y) takes on both positive and negative values. This indicates (0, 0) is neither the site of an extremum nor a saddle point.

Now check for points along the boundary. We can parameterize the boundary by

(x,y)=(8\cos t,8\sin t)

with 0\le t\le2\pi. This turns f(x,y) into a univariate function F(t):

F(t)=f(8\cos t,8\sin t)=2^{10}\cos^3t+2^{12}\sin^4t

\implies F'(t)=3\cdot2^{10}\cos^2t(-\sin t)+2^{14}\sin^3t\cos t=2^{10}\sin t\cos t(16\sin^2t-3\cos t)

F'(t)=0\implies\begin{matrix}\sin t=0\implies t=0,\,t=\pi\\\\\cos t=0\implies t=\dfrac\pi2,\,t=\dfrac{3\pi}2\\\\16\sin^2t-3\cos t=0\implies t=2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3},\,t=2\pi-2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3}\end{matrix}

At these critical points, we get

F(0)=1024

F\left(2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3}\right)\approx893

F\left(\dfrac\pi2\right)=4096

F(\pi)=-1024

F\left(\dfrac{3\pi}2\right)=4096

F\left(2\pi-2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3}\right)\approx893

We only care about 3 of these results.

t=\dfrac\pi2\implies(x,y)=(0,8)

t=\pi\implies(x,y)=(-8,0)

t=\dfrac{3\pi}2\implies(x,y)=(0,-8)

So to recap, we found that f(x,y) attains

  • a maximum value of 4096 at the points (0, 8) and (0, -8), and
  • a minimum value of -1024 at the point (-8, 0).
6 0
3 years ago
Help I need answers!! please
Aleksandr [31]
Whats the question here
6 0
3 years ago
Please answer it now in two minutes
just olya [345]

Answer:

no

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Farmer frank is planting corn in a three-acre field.He will plant a total of 347 rows with 270 corn plants in each row.How many
iren [92.7K]
This is simple long multiplication. 347 x 270 is 93,690. Then you divide this number by the amount of acres, in this case, 3. So 93,690/3 is 31,230. Hope this helped
3 0
3 years ago
Read 2 more answers
Rectangle OPEN has diagonals intersecting at S. If m∠ENP=42 find m∠ EON, m∠ONP, m∠OSP, and m∠PSE
poizon [28]

Answer:

m∠EON = 48°

m∠ONP = 48°

m∠PSE = 90°

4 0
3 years ago
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