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
bogdanovich [222]
2 years ago
14

If 5-y^2=x^2 then find d^2y/dx^2 at the point (2, 1) in simplest form. ​

Mathematics
1 answer:
ratelena [41]2 years ago
3 0

Answer:

y"(2, 1) = -5

Step-by-step explanation:

Step 1: Define implicit differentiation

5 - y² = x²

Step 2: Find dy/dx

  1. Take implicit differentiation: -2yy' = 2x
  2. Isolate y': y' = 2x/-2y
  3. Isolate y': y' = -x/y

Step 3: Find d²y/dx²

  1. Quotient Rule: y'' = [y(-1) - y'(-x)] / y²
  2. Substitute y': y" = [-y - (-x/y)(-x)] / y²
  3. Simplify: y" = [-y - x²/y] / y²
  4. Multiply top/bottom by y: y" = (-y² - x²) / y³
  5. Factor negative: y" = -(y² + x²) / y³

Step 4: Substitute and Evaluate

y"(2, 1) = -(1² + 2²) / 1³

y"(2, 1) = -(1 + 4) / 1

y"(2, 1) = -5/1

y"(2, 1) = -5

You might be interested in
The altitudes of a triangle _______ go through the vertices?
Masteriza [31]
Never because I had this question and saw it on khan
7 0
2 years ago
Read 2 more answers
Someone Please Help Quickly! Its an Easy Question
Paul [167]

Answer:

y=\frac{2}{3}x-6

Step-by-step explanation:

Use the slope-intercept form:

y=mx+b

m is the slope and b is the y-intercept. Looking at the graph, you can find the y-intercept. The y-intercept is the point where x equals 0:

b=-6

y-intercept=(0,-6)

To find the slope, take any two points from the line:

(6,-2)(3,-4)

Use the slope formula for when you have two points:

\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}

The rise over run is the change in the y-axis over the change of the x-axis. Insert the appropriate values:

(6(x_{1}),-2(y_{1})\\(3(x_{2}),-4(y_{2})

\frac{-4-(-2)}{3-6}

Simplify parentheses (two negatives makes a positive):

\frac{-4+2}{3-6}

\frac{-2}{-3}

Simplify (two negatives make a positive):

m=\frac{2}{3}

The slope is \frac{2}{3} and the y-intercept is -6. Insert these into the equation:

y=\frac{2}{3}x-6

Finito.

7 0
2 years ago
1. Look for a pattern in the first three equations. Then, fill in the missing numbers in the rest of the
Alla [95]

Answer:

1=1 times 2/2 1 + 2=2 times 3/2 1 +2+3=3 times 4/2 1+2+3+4=4 times 5/2 1+2+3+4+5=5 times 6/2

4 0
2 years ago
What is the solution of the equation sqrt 2 x+4-sqrt x=2
ivann1987 [24]
There are 2 answers to this 

x=0 
x=16
3 0
3 years ago
A local gym offers a trial membership for 3 months. It discounts the regular monthly fee x by $25. If the total cost of the tria
kati45 [8]
3(x - 25) < $100.  We're not req'd to solve this.


8 0
2 years ago
Other questions:
  • Please help with this problem
    9·1 answer
  • Please help and explain good luck
    15·1 answer
  • Toby skated from his house to the beach at a constant speed of 8 88 kilometers per hour, and then skated from the beach to the p
    7·1 answer
  • 50 POINTS PLEASE HELP ME!! PLEASE HURRY ASAP!!!!!<br> Solve for x
    13·1 answer
  • Pls helpppppppppp ....
    15·1 answer
  • In the United States, federal tax rates are based on the amount of income an individual or family earns. What do you think happe
    10·1 answer
  • 3/4 of the class are girls. 1/6 of the girls have long hair. What fraction of the class with long hair? Place your answer in sim
    14·1 answer
  • F(x) is the same thing as ___________(fill in the blank), if we are dealing with points in
    15·1 answer
  • The dimensions of the right triangle shown below are given in feet. What is the length of the hypotenuse of the triangle, in fee
    10·1 answer
  • Are 0.2 and<br> 1 /5 equivalent? Explain your answer in complete sentences.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!