1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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
You might be interested in
How do i solve the square root problems?
Gwar [14]
You may want to elaborate on what you mean by "square root problems"
6 0
3 years ago
Convert 23° 12' to decimal form
Lina20 [59]

Answer:

15813.64 rounded to nearest hundredth

3 0
2 years ago
Cindy has $25 saved and earns $12 per week for walking dogs. Mindy has $55 saved and earns $7 per week for watering plants. Cind
Rufina [12.5K]

Answer:

c : they will have both saved 97

Step-by-step explanation:

7*6 = 42 + 55(base) = 97

12*6 = 71 = 25(base) =97

7 0
2 years ago
PLZ CAN SOMEONE ANSWER THIS !!
Cerrena [4.2K]

Answer:

(-4,2)

Step-by-step explanation:

First we have to find a common multiple to use to add and find the system of equations. We need to eliminate one of the variables in order to solve.

Since 5 * 3 = 15, and 3 * -5 = 15, -15x and 15x will cancel each other out. Therefore x will be eliminated.

Before:

5x + 2y = -16

3x + 7y = 2

After:

15x + 6y = -48   <----------Now we solve for y

-15x + -35y = -10

+----------------------

-29y = -58

-29      -29

y = 2

Now what we do is we choose and equation and solve for x, since it is still unknown. Any equation is fine but I will choose the second one since it has easy numbers.

3x + 7y = 2

3x + 7(2) = 2

3x + 14 = 2

   -14     -14

----------------------

3x = -12

3        3

x = -4

Therefore our final answer is (-4,2)

5 0
3 years ago
How do you find the bearing and speed of a ship?
Usimov [2.4K]
Finding the Bearing<span> of a </span>Ship<span> 
Example : A </span>ship<span> leaves the port of Miami with a </span>bearing<span> of S80◦E and a </span>speed<span> of. 15 knots. After 1 hour, the </span>ship<span> turns 90◦ toward the south.</span>
3 0
3 years ago
Other questions:
  • When using the metric system conversations which required division get be made by moving the decimal to the ____
    11·1 answer
  • How do you simplify 15.5 in fraction form
    11·1 answer
  • −1.5(4−n)+2.8−1.5(4−n)+2.8 simplified is
    5·1 answer
  • Emily is 62 years old. Colin is 3 years older than Emily. Dan is 8 years younger than Emily. What is the total of their combined
    14·2 answers
  • Consider the polynomial P(x)=x³+kx²+x+6.Find the value of k so that x+1 is a factor of P.
    11·1 answer
  • Comparison of Ani and Ina 3 money: 5. The amount of their money is Rp.400,000.00. The difference in money is both
    7·1 answer
  • The temperature increased from (-3) degrees to (+12) degrees on Friday what was the temperature change over the course of the da
    7·1 answer
  • 5.
    5·1 answer
  • Can someone answer this really fast?
    5·2 answers
  • Help with Another Pre Calculus Question
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!