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Step2247 [10]
3 years ago
14

3. A rectangular sheet of paper is folded diagonally from A to C. What is the length of side BD?

Mathematics
1 answer:
Kipish [7]3 years ago
7 0
If AD is a diagonal and the length is 24 BD is given by Pythagoras √26²-24²=√676-576=√100=10 answer A.
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Find the local maximum and minimum values and saddle point(s) of the function.
iogann1982 [59]
f(x,y)=9e^y(y^2-x^2)
\nabla f=\left\langle-18xe^y,9ye^y(2+y)\right\rangle

Critical points occur where the gradient is zero. This is guaranteed whenever x=0 and either y=0 or y=-2.

The Hessian matrix for this function looks like

H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}-18e^y&-18xe^y\\-18xe^y&9e^y(2-x^2+4y+y^2)\end{bmatrix}

and has determinant

|H(x,y)|=-162e^{2y}(2+x^2+4y+y^2)

Maxima occur whenever the determinant is positive and f_{xx}. Minima occur whenever both the determinant and f_{xx} are positive. Saddle points occur whenever the determinant is negative.

At (0,0), you have a saddle point since the determinant reduces to -324, so (0,0,0) is the saddle point.

At (0,-2), the determinant is \dfrac{324}{e^4}>0 and f_{xx}(0,-2)=-\dfrac{18}{e^2}, so \left(0,-2,\dfrac{36}{e^2}\right) is a local maximum.

No other critical points remain, so you're done.
4 0
3 years ago
Jaylyn rode her bike Ina a bike thon. she rode 33.48 miles in 2.7 hours. of she rode at the same speed, what was her speed in mi
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3 years ago
What are the possible answers for the equation 9x?- 16 = 0 ? A. 1-13, 13) 4 4 } 3 3 C. 14, VA) D. 3, 3) 16 E.​
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Answer:

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Step-by-step explanation:

because I did the math and I learned this today it's simple

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2 years ago
2n +9+5n=30 need help on this
Rus_ich [418]
2n+9+5n=30  combine like terms on left side

7n+9=30  subtract 9 from both sides

7n=21  divide both sides by 7

n=3
8 0
3 years ago
Read 2 more answers
4x - 6 + x + 3<br><br> ASAP BRAINLIEST
Pachacha [2.7K]

Answer:

5x - 3

Step-by-step explanation:

Add like terms: (4x + x) + (-6 + 3) = 5x - 3

3 0
3 years ago
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