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mezya [45]
2 years ago
9

I really need help with this thanks a lot

Mathematics
1 answer:
aleksandrvk [35]2 years ago
8 0

Answer:

  • Graph B

Step-by-step explanation:

<u>According to data in the table we see pairs of points:</u>

  • (3, 75), (5, 125)

<u>This gives us the rate of change:</u>

  • (125 - 75)/(5 - 3) = 50/2 = 25

<u>The y - intercept is zero:</u>

  • 75 = 3*25 + b
  • 75 = 75 + b
  • b = 0

<u>The line is:</u>

  • y = 3x

This is the line on the graph B

<u>Note.</u> <em>Its not clear what is needed regarding the table on the bottom</em>

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Answer:

Step-by-step explanation:

Given that,

g(x, y) = 5 - (x - 3)² - (y + 2)²

Let find the grad of the function,

The grad of a function is defined as

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∇g = gx•i + gy•j + gz•k

gx = -2(x-3) = -2x+6

gy = -2(y+2) = -2y -4

∇g = (-2x+6) •i + (-2y-4)•j

We have a maximum or a minimum If g conservative, then, ∇g = 0i +0j

Then comparing this to the grad of the function

(-2x+6) •i + (-2y-4)•j = 0i +0j

Then, -2x+6 = 0

2x=6

x = 3

Also, -2y-4=0

-2y=4

y = -2

Then, g(x, y) = 5 - (x - 3)² - (y + 2)²

g(x, y) = 5 - (3 - 3)² - (-2 + 2)²

g(x, y) = 5

So the critical point is (3, -2, 5)

gx =-2x+6

Second derivative of gx with respect to x

gxx=-2

gy=-2y-4

Second derivative of gy with respect to y

gyy=-2

Second derivative of gx with respect to y

gxy =0

d =gxxgyy - (gxy)²

Then, gyy=gxx

d = -2×-2 -0²

d = 4-0=4

Since d>0

Since d is greater than 0, then, it is not a chair points.

Then, since gxx=-2<0, gyy=-2<0

Cause the second derivative in x (or in y) is less than zero, then the point is relatively maximum

So the maximum point is (3, -2, 5).

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Answer:

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2. 19 1/4

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To change into an improper fraction:

((2 times 4)+3)/4

=11/4

To calculate total distance:

(11/4) times 7

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3 years ago
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zhuklara [117]

Let

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C. 4x2 + 16x - 4.25 = 0

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3 years ago
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