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]
3 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]3 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
SA = 2tr2 + 2trh
julsineya [31]

Given:

Radius of the cylinder = 5 in

Height of the cylinder = 30 in.

To find:

The surface area of the cylinder.

Solution:

The surface area of the cylinder is:

SA=2\pi r^2+2\pi rh

Where, r is the radius and h is the height of the cylinder.

Putting r=5,h=30,\pi=3.14 in the above formula, we get

SA=2(3.14)(5)^2+2(3.14)(5)(30)

SA=2(3.14)(25)+942

SA=157+942

SA=1099


Therefore, the surface area of the cylinder is 1099  square inches.

6 0
3 years ago
The box plot shows the total amount of time, in minutes, the students of a class spend reading each day
katrin2010 [14]
2. The median for the data is the correct answer
6 0
3 years ago
The back of Monique's property is a creek. Monique would like to enclose a rectangular area, using the creek as one side and fen
kondor19780726 [428]
So long as the perimeters are the same, rectangles and squares share the same area. For example, a square that is 2m by 2m across is 4m squared. A rectangle of 4m by 1m across is still 4m squared.

Therefore all we want to do here is see how big we can make our “square” perimeter using the creek. We have three sides to spread 580ft across, therefore if we divide this by 3, we get 193.3ft of fencing per side. If we then square this figure, we will then get the maximum possible area, which comes to 37,377ft squared. (That’s a huge garden).
3 0
3 years ago
Read 2 more answers
Ppppplllllllllzzzzzzz helppppppppp -7/9 - 5/10
Lyrx [107]
Simplify 5/10 to 1/2

find the LCD of both fractions and that would be 18

make the denominators the same as the LCD

Simplify, now denominators are equal

join the denominators

simplify it now (23/-18)

convert to mixed fraction 

Answer: -1 5/18.

7 0
3 years ago
Please help me asap​
puteri [66]

1. 3.875

2. .35

3. 9 3/4

3 0
3 years ago
Other questions:
  • Shawna has $750 in the bank.she deposits $37.50 each week.Ruben has $850 in the bank.He deposits his paycheck of $102.75 every M
    12·1 answer
  • Djejsiskdksjdkdkskskskskskskdkskskskskskdkxj
    9·1 answer
  • What is the value of x in the equation 8x – 2y = 48, when y = 4?
    12·1 answer
  • Find the median of this data: 18, 9, 17, 18, 15, 10, 18. If necessary, round to the nearest tenth.
    5·1 answer
  • Help pls?? got answer wrong plz assap
    8·2 answers
  • Jimmy and his friends ate pizza after the game Friday night. On Saturday, Jimmy saw there were 1 and 1/8 pizzas left. He ate 3/4
    14·1 answer
  • (3x -1) + (2x+1) (x)
    14·1 answer
  • What is the probability of rolling dice a fair four times and getting in order 1 2 3 4
    10·1 answer
  • Graph the equation.
    13·1 answer
  • Write the equation of the line that goes through the points (-1,-3) and (2,5) in POINT-SLOPE form
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!