Solve the equation for the problem above

Find the second partial derivatives of the following functions

artcher [175]

(a) z = 3x ² - 4xy + 15y ²

has first-order partial derivatives

∂z/∂x = 6x - 4y

∂z/∂y = -4x + 30y

and thus second-order partial derivatives

∂²z/∂x ² = 6

∂²z/∂x∂y = -4

∂²z/∂y∂x = -4

∂²z/∂y ² = 30

where ∂²z/∂x∂y = ∂/∂x [∂z/∂y] and ∂²z/∂y∂x = ∂/∂y [∂z/∂x].

(b) z = 4x eʸ

∂z/∂x = 4eʸ

∂z/∂y = 4x eʸ

∂²z/∂x ² = 0

∂²z/∂x∂y = 4eʸ

∂²z/∂y∂x = 4eʸ

∂²z/∂y ² = 4x eʸ

(c) z = 6x ln(y)

∂z/∂x = 6 ln(y)

∂z/∂y = 6x/y

∂²z/∂x ² = 0

∂²z/∂x∂y = 6/y

∂²z/∂y∂x = 6/y

∂²z/∂y ² = -6x/y ²

6 0

2 years ago

The club's total number of members will grow exponentially each month. She uses the given expression to model the number of club

mihalych1998 [28]

Answer:

1.8 represents the initial number of the club members in hundreds.

Step-by-step explanation:

* Lets revise the exponential grows

- If a quantity grows by a fixed percent at regular intervals,

the pattern can be depicted by this function.

- The function of the exponential growth is:

y = a(1 + r)^x

# a = initial value (the amount before measuring growth)

# r = growth rate (most often represented as a percentage and

expressed as a decimal)

# x = number of time intervals that have passed

* Now Lets study the problem to solve it

- The club's total number of members will grow exponentially

each month

- The expression to model the number of club members, in

hundreds, after advertising for t months is

1.8(1.02)^12t

* Lets compare between this model and the function above

# a = 1.8 ⇒ initial number of members in hundreds

# r = 1.02 - 1 = 0.02 ⇒ growth rate

# x = 12t ⇒ number of time intervals

* 1.8 represents the initial number of the club members in hundreds.

6 0

3 years ago

Solve for x: 5/x^2-4+2/x=2/x-2

IRINA_888 [86]

$\dfrac{5}{x^2 - 4} + \dfrac{2}{x} = \dfrac{2}{x - 2}$

$\dfrac{5}{(x + 2)(x - 2)} + \dfrac{2}{x} = \dfrac{2}{x - 2}$

$\dfrac{5}{(x + 2)(x - 2)} \times x(x + 2)(x - 2) + \dfrac{2}{x} \times x(x + 2)(x - 2) = \dfrac{2}{x - 2} \times x(x + 2)(x - 2)$

$5x + 2(x + 2)(x - 2) = 2x(x + 2)$

$5x + 2(x^2 - 4) = 2x^2 + 4x$

$5x + 2x^2 - 8 = 2x^2 + 4x$

$5x - 8 = 4x$

$x - 8 = 0$

$x = 8$

Now we look at the common denominator.

It is x(x + 2)(x - 2).

x cannot be zero, -2 or 2 because that would cause a zero in the denominator.

Since we get x = 8, and x = 8 does not have to be excluded from the domain, the answer is x = 8.

Answer: x = 8

6 0

3 years ago

The number and frequency of Atlantic hurricanes annually from 1940 through 2007 is shown here:

klio [65]

Answer:

The probability table is shown below.

A Poisson distribution can be used to approximate the model of the number of hurricanes each season.

Step-by-step explanation:

(a)

The formula to compute the probability of an event E is:

$P(E)=\frac{Favorable\ no.\ of\ frequencies}{Total\ NO.\ of\ frequencies}$

Use this formula to compute the probabilities of 0 - 8 hurricanes each season.

The table for the probabilities is shown below.

(b)

Compute the mean number of hurricanes per season as follows:

$E(X)=\frac{\sum x f_{x}}{\sum f_{x}}=\frac{176}{68}= 2.5882\approx2.59$

If the variable X follows a Poisson distribution with parameter λ = 7.56 then the probability function is:

$P(X=x)=\frac{e^{-2.59}(2.59)^{x}}{x!} ;\ x=0, 1, 2,...$

Compute the probability of X = 0 as follows:

$P(X=0)=\frac{e^{-2.59}(2.59)^{0}}{0!} =\frac{0.075\times1}{1}=0.075$

Compute the probability of X = 1 as follows:

$\neq P(X=1)=\frac{e^{-2.59}(2.59)^{1}}{1!} =\frac{0.075\times7.56}{1}=0.1943$

Compute the probabilities for the rest of the values of X in the similar way.

The probabilities are shown in the table.

On comparing the two probability tables, it can be seen that the Poisson distribution can be used to approximate the distribution of the number of hurricanes each season. This is because for every value of X the Poisson probability is approximately equal to the empirical probability.

5 0

3 years ago

I NEED HELP !!!!!!!!!!! THIS DUE TODAY!!!!!!!!!!!! IT IS URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

rusak2 [61]

Answer:

they only had one pair of trunks

Step-by-step explanation: i hope that helps you

4 0

3 years ago