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djverab [1.8K]
3 years ago
9

Solve the Equations

Mathematics
1 answer:
kkurt [141]3 years ago
3 0

Answer and Step-by-step explanation:

1) - 6.5 r = - 58.5

- r = - 58.5/6.5

- r = - 9

<h2>r = 9 </h2>

2) c - 5.5 = 2.3

c = 2.3 + 5.5

<h2>c = 7.8</h2>

3) 56 = - 5.6s

56/5.6 = - s

10 = - s

- 10 = s

<h2>s = - 10</h2>

4) d/4 = 4.7

d = 4.7 / 1/4

d = 4.7 * 4

<h2>d = 18.8</h2>

5) - 9 = 6.9 + x

- 9 - 6.9 = x

- 15.9 = x

<h2>x = - 15.9</h2>

6) 23.5 = 4.7z

23.5/4.7 = z

5 = z

<h2>z = 5</h2>

7) - 2.7 = v + 4.9

- 2.7 - 4.9 = v

- 7.6 = v

<h2>v = - 7.6</h2>

8) 2.6 = k/3

k/3 = 2.6

k = 2.6 / 1/3

k = 2.6 * 3

<h2>k = 7.8</h2>

9) - 5.6f = 44.8

- f = 44.8/5.6

- f = 8

<h2>f = - 8</h2><h2 />

hope it helps, my friend

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(a)5%)Let fx, y) = x^4 + y^4 - 4xy + 1. and classify each critical point Find all critical points of fx,y) as a local minimum, l
lara31 [8.8K]

f(x,y)=x^4+y^4-4xy+1

has critical points wherever the partial derivatives vanish:

f_x=4x^3-4y=0\implies x^3=y

f_y=4y^3-4x=0\implies y^3=x

Then

x^3=y\implies x^9=x\implies x(x^8-1)=0\implies x=0\text{ or }x=\pm1

  • If x=0, then y=0; critical point at (0, 0)
  • If x=1, then y=1; critical point at (1, 1)
  • If x=-1, then y=-1; critical point at (-1, -1)

f(x,y) has Hessian matrix

H(x,y)=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}

with determinant

\det H(x,y)=144x^2y^2-16

  • At (0, 0), the Hessian determinant is -16, which indicates a saddle point.
  • At (1, 1), the determinant is 128, and f_{xx}(1,1)=12, which indicates a local minimum.
  • At (-1, -1), the determinant is again 128, and f_{xx}(-1,-1)=12, which indicates another local minimum.
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3 years ago
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dusya [7]

Answer:

sorry i dont understand

Step-by-step explanation:

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Answer:

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How many solutions does the following equation have?<br><br> 3x + 6 = 3(x + 2)
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3 years ago
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Whitepunk [10]

Answer:

A dilation (similarity transformation) is a transformation that changes the size of a figure. It requires a center point and a scale factor , k . The value of k determines whether the dilation is an enlargement or a reduction.

In simple words, it's stretching, when you dilate with scale factor of x, means you multiply the previous value with x, say co-ordinates area -2,4, so you do (-2x,4x) to find the co-ordinates after dialation,

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Answered by GAUTHMATH

5 0
3 years ago
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