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
PLEASE HELP!!! WILL REWARD BRAINLIEST!!!
jonny [76]

Answer:

The approximate monthly rate of growth is 1.24%

Step-by-step explanation:

we have the future value formula

F=P(1+r)^t

we have

r=16\%=16/100=0.16 ----> annual interest rate

so

F=P(1+0.16)^t

F=P(1.16)^t

Find the approximate monthly rate of growth

Remember that

1\ year=12\ months

so

Divide the number of periods t by 12

F=P(1.16)^{\frac{t}{12}}

Applying power rules property

F=P(1.16^\frac{1}{12})^t

F=P(1.0124)^t}

1.0124-1=0.0124

Convert to percentage

0.0124*100=1.24\%

therefore

The approximate monthly rate of growth is 1.24%

6 0
3 years ago
A boat travelling upstream goes 36 kilometers in 6 hours. If the return trip takes only 3 hours, what is the speed (in kilometer
mr_godi [17]
11 kilometer per hour
8 0
3 years ago
Manchu has drawn a
timama [110]

Answer:

Height of each triangle: 14cm

Area of each triangle: 168cm²

Step-by-step explanation:

So we know that the base of the area is 24. Lets find the height.

336 ÷ 24 = 14

If he makes two triangles out of the rectangle that just means he cuts it in half.

To find the area of one triangle lets do:

336 ÷ 2 = 168

Let's double check our answer:

(14 × 24) ÷ 2 = 168

Seems great!

6 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7D%20%3D%20%5Cfrac%7Bx%20-%204%7D%7B3%7D" id="TexFormula1" title="\frac{5}{
valentina_108 [34]

Step-by-step explanation:

\frac{5}{2}  =  \frac{x - 4}{3}

3 \times \frac{5}{2}  =  \frac{x - 4}{3}

\frac{3}{1}  \times  \frac{5}{2}  =  \frac{x - 4}{3}

cross multiplication

\frac{6 \times 5}{2}  =  \frac{x - 4}{3}

15 =  \frac{x - 4}{3}

15 \times 3 = x - 4

45 + 4 = x

49 = x

4 0
3 years ago
Read 2 more answers
Transformation of quadratic functions
Kitty [74]

Answer:

g(x) = a(x − h)2 + k, where a ≠ 0.

Step-by-step explanation:

The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.

6 0
2 years ago
Other questions:
  • If H is the set of vectors    2a ab 3b    in R 3 for all real a and b, then H is closed under scalar multiplication. True
    5·1 answer
  • Sofia places 26 tiles representing each letter of the alphabet into a bag. Five of the tiles represent the vowels A, E, I, O, an
    14·1 answer
  • What is the central tendencies- mean, median, and mode of this data set?
    10·1 answer
  • Please solve this with working asap much appreciated!!
    10·1 answer
  • Given each scenario, identify an appropriate type of chart or plot that you would use to determine the answer. (e.g. pie chart,
    10·1 answer
  • What’s the percent of 4.3% of 1200
    13·2 answers
  • Which matrix represents the system of equations shown below?5x - y = 82x - 3y = 12
    9·1 answer
  • Express 145 feet below sea level as an integer
    7·1 answer
  • Please help me solve -2(-3-3n)+1
    8·2 answers
  • Write the ratio in simplest form.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!