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3 years ago

Use this equation to find dy/dx. 4y cos(x) = x2 + y2

1 answer:

7 0

Let's differentiate implicitly,
don't worry about solving for y explicitly before differentiating.

(4y)cosx = x^2 + y^2

Apply product rule on the left,
and power rule on the right-hand terms,

(4y)'cosx + 4y(cosx)' = (x^2)' + (y^2)'
4y'cosx + 4y(-sinx) = 2x + 2yy'
4y'cosx - 4ysinx = 2x + 2yy'

Let's get both y' terms on the left side,
and everything else on the right,

4y'cosx -2yy' = 2x + 4ysinx

Factor y' out of each term,

y'(4cosx - 2y) = 2x + 4ysinx

Solve for y' (which is dy/dx) by dividing by the stuff,

y' = (2x + 4ysinx) / (4cosx - 2y)

You can divide a 2 out of everything to simplify it down a little bit.

y' = (x + 2ysinx) / (2cosx - y)

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3x+4y=-23 2y-x=-19 What is the solution (x,y) to the systems of equations above?

Shkiper50 [21]

If we multiply the bottom equation by 2 and move x to the right, it becomes:

4y = 2x-38

Now we can substitute it for the 4y in the top equation:

3x + (2x-38) = -23 => 5x = -23+38 => 5x = 15 => x=3

Then 4y = 2*3-38 => y = -8

So the solution is (3,-8)

3 0

4 years ago

Is the relation a function? Why or why not?

tatuchka [14]

Answer: it is c

Step-by-step explanation:

It has two of the same domain

7 0

3 years ago

Find the area of the composite figure

kompoz [17]

Answer:

196 ft

Step-by-step explanation:

Bc im guessing

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5 0

3 years ago

In a study, 42% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people

kobusy [5.1K]

Answer:

The probability that when 11 adults are randomly selected, 3 or fewer are in excellent health is 0.6483.

Step-by-step explanation:

The random variable X can be defined as the number of adults questioned reported that their health was excellent.

A random sample of n = 11 adults are selected randomly selected from an area a nuclear power plant.

Of these 11 adults X = 3 reported that their health was excellent.

The proportion of adults who reported that their health was excellent is:

$p=\frac{X}{n}=\frac{3}{11}$

An adult's health condition is not affected by others, i.e. they are independent.

The random variable X follows a Binomial distribution with parameters n = 11 and p = $\frac{3}{11}$ .

The probability mass function of X is:

$P(X=x)={11\choose x}(\frac{3}{11})^{x}(1-\frac{3}{11})^{11-x};\ x=0,1,2,3...$

Compute the probability that when 11 adults are randomly selected, 3 or fewer are in excellent health as follows:

P (X ≤ 3) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)

$=\sum\limits^{3}_{x=0}{{11\choose x}(\frac{3}{11})^{x}(1-\frac{3}{11})^{11-x}}\\=0.02998+0.12385+0.23254+0.26197\\=0.64834\\\approx 0.6483$

Thus, the probability that when 11 adults are randomly selected, 3 or fewer are in excellent health is 0.6483.

5 0

3 years ago

Please help me asap

Bezzdna [24]

Answer:

Step-by-step explanation:

cannot be a or c cause it has a negative sign in front of it causing it to reflect over y axis. Cannot be B cause it doesn't have two coefficients with X. I also graphed it.

5 0

3 years ago