Ask question

Ask question

All categories

4 years ago

14

You have a box with a square bottom and top. you are to construct this box so it has a volume of 600 cubic inches. find the dime

nsions of the box that will minimize the surface area of the box. then find the minimum surface area.

1 answer:

natta225 [31]4 years ago

4 0

We need to get two equations. One equation will be the value at the curve. The other will contain derivative. For the first equation, find the value on the curve. -k = m

You might be interested in

What is the factored form of x^2-x-2

lisov135 [29]

Answer:

(x-2),(x+1)

Step-by-step explanation:

5 0

3 years ago

Find the mass of the lamina that occupies the region D = {(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1} with the density function ρ(x, y) = xye

Alona [7]

Answer:

The mass of the lamina is 1

Step-by-step explanation:

Let $\rho(x,y)$ be a continuous density function of a lamina in the plane region D,then the mass of the lamina is given by:

$m=\int\limits \int\limits_D \rho(x,y) \, dA$ .

From the question, the given density function is $\rho (x,y)=xye^{x+y}$ .

Again, the lamina occupies a rectangular region: D={(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}.

The mass of the lamina can be found by evaluating the double integral:

$I=\int\limits^1_0\int\limits^1_0xye^{x+y}dydx$ .

Since D is a rectangular region, we can apply Fubini's Theorem to get:

$I=\int\limits^1_0(\int\limits^1_0xye^{x+y}dy)dx$ .

Let the inner integral be: $I_0=\int\limits^1_0xye^{x+y}dy$ , then

$I=\int\limits^1_0(I_0)dx$ .

The inner integral is evaluated using integration by parts.

Let $u=xy$ , the partial derivative of u wrt y is

$\implies du=xdy$

and

$dv=\int\limits e^{x+y} dy$ , integrating wrt y, we obtain

$v=\int\limits e^{x+y}$

Recall the integration by parts formula: $\int\limits udv=uv- \int\limits vdu$

This implies that:

$\int\limits xye^{x+y}dy=xye^{x+y}-\int\limits e^{x+y}\cdot xdy$

$\int\limits xye^{x+y}dy=xye^{x+y}-xe^{x+y}$

$I_0=\int\limits^1_0 xye^{x+y}dy$

We substitute the limits of integration and evaluate to get:

$I_0=xe^x$

This implies that:

$I=\int\limits^1_0(xe^x)dx$ .

Or

$I=\int\limits^1_0xe^xdx$ .

We again apply integration by parts formula to get:

$\int\limits xe^xdx=e^x(x-1)$ .

$I=\int\limits^1_0xe^xdx=e^1(1-1)-e^0(0-1)$ .

$I=\int\limits^1_0xe^xdx=0-1(0-1)$ .

$I=\int\limits^1_0xe^xdx=0-1(-1)=1$ .

No unit is given, therefore the mass of the lamina is 1.

3 0

3 years ago

Please help!!! How many coefficients does this polynomial have in its complete form, including any missing terms?

frez [133]

-5x^3 + 2x^2 + 1

a coefficient is the number that is multiplied by the variable.For instance, the coefficient of 2x is 2....because 2 (the number) is multiplied by the variable x.

so in ur problem....there are 2 coefficients..-5 and 2.

** the number 1 is not a coefficient, it is a constant...a " loner " with no variables (letters) attached.

** and if u have just the letter...such as n, the coefficient to that is 1 but the one is just not written...it is actually 1n.

okay...I am gonna shut up now :)

7 0

3 years ago

I'm very confused on how to solve this problem, can anyone please help? Thanks!

Pepsi [2]

Answer:

.

Step-by-step explanation:

DC = 16 and

DB = 30 so

CB = 14

DB = 30 and

EB = 49 so

EB = 19

5 0

3 years ago

Please help me lol aaaaa

miss Akunina [59]

Answer:

−0.125 or - 1/8

Step-by-step explanation:

8 0

3 years ago