All categories

2 years ago

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

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

Step 3: Find d²y/dx²

Quotient Rule: y'' = [y(-1) - y'(-x)] / y²
Substitute y': y" = [-y - (-x/y)(-x)] / y²
Simplify: y" = [-y - x²/y] / y²
Multiply top/bottom by y: y" = (-y² - x²) / y³
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

A circular mirror is surrounded by a square metal frame the radius of the mirror is 2X the side length of the metal frame is 6X

vovangra [49]

Answer:

Area of the metal frame is $23.43x^2$ .

Step-by-step explanation:

Given:

Radius of circular mirror = $2x$

Side length of the metal frame = $6x$

We need to find the area of the metal frame.

Solution:

First we will find the area of the whole thing.

area of the whole thing is in square shape we can say that;

area of the whole thing is equal to square of the length of the metal frame.

framing in equation form we get;

area of the whole thing = $(6x)^2 = 36x^2$

Now we will find the area of the circular mirror.

Since mirror is in circular form we will use area of the circle.

So area of circular mirror is equal to π times square of the radius.

framing in equation form we get;

area of the circular mirror = $\pi r^2 = \pi(2x)^2 = \pi 4x^2 = 12.57x^2$

Now to find the area of the metal frame surrounded my the mirror we will subtract area of the circular mirror from area of the whole thing.

framing in equation form we get;

area of the metal frame = $36x^2-12.57x^2 = 23.43x^2$

Hence Area of the metal frame is $23.43x^2$ .

6 0

2 years ago

Read 2 more answers

4. What are the coefficients in the polynomial 7x² - 4x + 6? (1 poin

skad [1K]

Answer:

D.) 7 and -4

Step-by-step explanation:

Coefficients are numbers placed directly before a variable.

(7) is a coefficient because it is placed before x².

(-4) is a coefficient because it is placed before x. The negative is included.

(6) is not a coefficient because it is not altering any variable through multiplication/division.

5 0

1 year ago

In a group of 60 students, 20%are girls. How many are boys?

Firlakuza [10]

Answer: About 12 of those 60 students are boys.

To find the percent, you'll convert 20% to a decimal.

20 / 100 = 0.2

Then, multiply 60 by 0.2

0.2 × 20 = 12

That's one way, another way is:

Convert 20% to a fraction.

20% = 1/5

Then multiply 60 by 1/5.

60 × 1/5 = 60/5

Lastly, divide 60 by 5

60 / 5 = 12.

Hence, 12 is the answer.

<em>Any questions? Comment down.</em>

4 0

2 years ago

Very large or very small numbers are best input with exponential notation. For instance, the number 8,000,000 (eight million) is

Lerok [7]

Answer:

$9*10^{12}km$

Step-by-step explanation:

$9,460,730,472,580.8 km$

First, we can work out 5% of our number, by multiplying it by 0.05

$9,460,730,472,580.8 * 0.05 = 473,036,523,629$

Now, if we add and subtract our 5% calculated from our original number, we can work out the minimum and maximum value that our final answer can be in the range of.

$9,460,730,472,580.8 + 473,036,523,629 = 9.933767*10^{12}\\9,460,730,472,580.8 - 473,036,523,629 =8.98769395*10^{12}$

We can see that $9*10^{12}$ is in the range of valid answers, as:

$8.9*10^{12} \leq 9*10^{12} \leq 9.9 * 10^{12}$

So, our final answer is:

$9*10^{12}km$

5 0

2 years ago

Read 2 more answers

There were 230 shoppers at an electronics store on opening day. The specials that day allowed 21% of shoppers to receive a free

anastassius [24]

Answer:

a) About 48 of the shoppers, that is $230\frac{21}{100}$ of the shoppers, received a free set of earbuds.

b) About 58 shoppers, that is $\frac{230}{4}$ received $5 off their first purchase.

Step-by-step explanation:

a. About how many shoppers received a free set of earbuds?

21% out of 230. So

$230\frac{21}{100} = 2.3(21) = 48.3$

About 48 of the shoppers, that is $230\frac{21}{100}$ of the shoppers, received a free set of earbuds.

b. About how many shoppers received $5 off their first purchase?

25% out of 230, so:

$230\frac{25}{100} = 230\frac{1}{4} = \frac{230}{4} = 57.5$

About 58 shoppers, that is $\frac{230}{4}$ received $5 off their first purchase.

5 0

2 years ago

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

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