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2 years ago

9

There are 32 players on the football team in total. If 75% of the students are in seventh grade, how many seventh graders are on

the football team?

1 answer:

Mars2501 [29]2 years ago

8 0

Answer:

There's 24 seventh graders

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Consider the following equation. f(x, y) = e−(x − a)2 − (y − b)2 (a) Find the critical points. (x, y) = a,b (b) Find a and b suc

murzikaleks [220]

a.

$f(x,y)=e^{-(x-a)^2-(y-b)^2}\implies\begin{cases}f_x=-2(x-a)e^{-(x-a)^2-(y-b)^2}\\f_y=-2(y-b)e^{-(x-a)^2-(y-b)^2}\end{cases}$

Critical points occur where $f_x=f_y=0$ . The exponential factor is always positive, so we have

$\begin{cases}-2(x-a)=0\\-2(y-b)=0\end{cases}\implies(x,y)=\boxed{(a,b)}$

b. As the previous answer established, the critical point occurs at (-3, 8) if $\boxed{a=-3}$ and $\boxed{b=8}$ .

c. Check the determinant of the Hessian matrix of $f(x,y)$ :

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

The second-order derivatives are

$f_{xx}=(-2+4(x-a)^2)e^{-(x-a)^2-(y-b)^2}$

$f_{xy}=4(x-a)(y-b)e^{-(x-a)^2-(y-b)^2}$

$f_{yx}=4(x-a)(y-b)e^{-(x-a)^2-(y-b)^2}$

$f_{yy}=(-2+4(y-b)^2)e^{-(x-a)^2-(y-b)^2}$

so that the determinant of the Hessian is

$\det\mathbf H(x,y)=f_{xx}f_{yy}-{f_{xy}}^2=\left((4(x-a)^2-2)(4(y-b)^2-2)-16(x-a)^2(y-b)^2\right)e^{-2(x-a)^2-2(y-b)^2}$

$\det\mathbf H(x,y)=(16(x-a)^2(y-b)^2-8(x-a)^2-8(y-b)^2)+4)e^{-2(x-a)^2-2(y-b)^2}$

The sign of the determinant is unchanged by the exponential term so we can ignore it. For $a=x=-3$ and $b=y=8$ , the remaining factor in the determinant has a value of 4, which is positive. At this point we also have

$f_{xx}(-3,8;a=-3,b=8)=-2$

which is negative, and this indicates that (-3, 8) is a local maximum.

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3 years ago

What is 2.5 repeating as a mixed number

wel

$2.55555...=2\frac{5}{10^1-1}=2\frac{5}{9}$

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2 years ago

Can someone please help me with #1 through #14 of the geometry angle pairs #6 assignment?

leonid [27]

1) adjacent

2) linear pair

3) complementary

4) vertical

5) linear pair

6) linear pair

7) complementary

8) vertical

9) adjacent

10) adjacent

11) vertical

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13) adjacent

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1 year ago

Please help. I need to find the Slope and identify the type of Slope. I already know the type. (Number 11)

elena-14-01-66 [18.8K]

The slope =0. Horizontal lines have a slope of 0

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2 years ago

Solve the equation. 33 = p – 6.71<br> A. –39.71 <br> B. –26.29 <br> C. 39.71 <br> D. 26.29

jeka57 [31]

<u>Answer</u>

C. 39.71

<u>Explanation</u>

33 = p - 6.71

The first step is to make the like terms to be on the same side.

Add 6.71 on both sides of the eqution

33 + 6.71 = p - 6.71 + 6.71

39.71 = p

∴ p = 39.71

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2 years ago