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pav-90 [236]
3 years ago
11

If 3x^2 + y^2 = 7 then evaluate d^2y/dx^2 when x = 1 and y = 2. Round your answer to 2 decimal places. Use the hyphen symbol, -,

for negative values.
Mathematics
1 answer:
S_A_V [24]3 years ago
3 0
Taking y=y(x) and differentiating both sides with respect to x yields

\dfrac{\mathrm d}{\mathrm dx}\bigg[3x^2+y^2\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[7\bigg]\implies 6x+2y\dfrac{\mathrm dy}{\mathrm dx}=0

Solving for the first derivative, we have

\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x}y

Differentiating again gives

\dfrac{\mathrm d}{\mathrm dx}\bigg[6x+2y\dfrac{\mathrm dy}{\mathrm dx}\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[0\bigg]\implies 6+2\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2+2y\dfrac{\mathrm d^2y}{\mathrm dx^2}=0

Solving for the second derivative, we have

\dfrac{\mathrm d^2y}{\mathrm dx^2}=-\dfrac{3+\left(\frac{\mathrm dy}{\mathrm dx}\right)^2}y=-\dfrac{3+\frac{9x^2}{y^2}}y=-\dfrac{3y^2+9x^2}{y^3}

Now, when x=1 and y=2, we have

\dfrac{\mathrm d^2y}{\mathrm dx^2}\bigg|_{x=1,y=2}=-\dfrac{3\cdot2^2+9\cdot1^2}{2^3}=\dfrac{21}8\approx2.63
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A rectangular poster is 3 times as long as it is wide. A rectangular banner is 5 times as it is wide. Both the banner and the po
Svetradugi [14.3K]

The length and width of poster are 9 inches and 3 inches respectively and length and width of banner are 10 inches and 2 inches respectively

<u> Solution:</u>

Given, A rectangular poster is 3 times as long as it is wide.  

Rectangular banner is 5 times as long as it is wide.  

Both the banner and the poster have perimeters of 24 inches

Let, the width of poster be p, then its length will be 3p

And, the width of banner be b, then its length will be 5b

Now, according to given information,

Perimeter of poster = 24 inches and perimeter of banner = 24 inches

2(length of poster + width of poster) = 24

2(3p + p) = 24

2(4p) = 24

8p = 24

p = 3

And 2(length of banner + width of banner) = 24

2(5b + b) = 24

2(6b) = 24

12b = 24

b = 2

So, width of poster is 3 inches, then length of poster is 3p = 3 x 3 = 9 inches

And, width of banner is 2 inches, then length of banner is 5b = 5 x 2 = 10 inches

8 0
3 years ago
Which is the correct graph of y=2/x^2-4 ?
Elis [28]
The correct graph would be the first one

6 0
2 years ago
Is this graph Proportioal or Not Proportional?
Over [174]

Answer:

Proportioal

Step-by-step explanation:

?

3 0
3 years ago
(9/89)x490+324<br> Please help
Likurg_2 [28]

Answer:

  1. (9/89)×490+324=
  2. 9/89×490=
  3. 4410/89+324=?
6 0
3 years ago
Read 2 more answers
Points A, B, and C are collinear. Find the value of x given AB = 3x, BC = 5x + 10. and AC = 74.​
Mars2501 [29]

Answer:

x = 8

Step-by-step explanation:

since it's a collinerar

or, AB+BC=AC

or, 3x+5x+10 = 74

or, 8x = 74-10

or, 8x = 64

or, x = 64/8

x = 8

6 0
3 years ago
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