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Sveta_85 [38]
3 years ago
13

At what point on the graph of y=1/4x^4 is the tangent line parallel to the line 24x -3y=8

Mathematics
1 answer:
Rama09 [41]3 years ago
3 0

Answer:

a) dy/dx = 4/(2y+1)^2.

(b) y = 4/9 x - 14/9

(c) d2y/dx2 = -64/243

Step-by-step explanation:

You have the following equation

  (1)

(a) You first derivative implicitly the equation (1) respect to x:

next, you solve the last result for dy/dx:

(2)

(b) The equation for the tangent line is given by:

   (3)

with yo = -2 and xo = -1

To find the slope m you use the result of the equation (2), because dy/dx evaluated in (-1,-2) is the slope at such point:

m =

Hence, by replacing in the equation (3) you obtain:

hence, the equation for the tangent line is y = 4/9 x - 14/9

(c) To find d2y/dx2 you derivative the result obtain in the equation (2):

    (4)

the second derivative for the point (-1,-2) is obtained by replacing y=-2 and dy/dx=m=4/9 in the equation (4):

hence, d2y/dx2 evaluated in (-1,-2) is -64/243

Step-by-step explanation:

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2 years ago
How to distribute this problem:<br> (x-8)^2 + 16
Usimov [2.4K]

Answer:

We conclude that:

\left(x-8\right)^2+16=x^2-16x+80

Step-by-step explanation:

Given the equation

\left(x-8\right)^2\:+\:16

First, solve (x - 8)²

Apply Perfect Square formula:    (a - b)² = a² - 2ab + b²

a=x,\:\:b=8

\left(x-8\right)^2=x^2-2x\cdot \:\:8+8^2

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so the expression becomes

\left(x-8\right)^2+16=x^2-16x+64+16

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Therefore, we conclude that:

\left(x-8\right)^2+16=x^2-16x+80

4 0
2 years ago
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Roman55 [17]

Answer:

  2.53×10^8 liters

Step-by-step explanation:

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Please help me im crying over this question
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Answer:

y = 2x - 2

Step-by-step explanation:

y= mx+b

m= slope

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Determine slope by using slope formula or by counting boxes

By counting boxes, you can see that each point is 2 units up, 1 unit right (2/1)

the slope is 2

the point where the line is touching the y-axis is (0, -2)

m = slope = 2

b  = y-intercept = -2

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