Find the value of the expression -1/3-(-5/12).

Use the procedures developed to find the general solution of the differential equation. (Let x be the independent variable.)

makkiz [27]

Solution :

Given :

2y''' + 15y'' + 24y' + 11y= 0

Let x = independent variable

$(a_0D^n + a_1D^{n-1}+a_2D^{n-2} + ....+ a_n) y) = Q(x)$ is a differential equation.

If $Q(x) \neq 0$

It is non homogeneous then,

The general solution = complementary solution + particular integral

If Q(x) = 0

It is called the homogeneous then the general solution = complementary solution.

2y''' + 15y'' + 24y' + 11y= 0

$(2D^3+15D^2+24D+11)y=0$

Auxiliary equation,

$2m^3+15m^2+24m +11 = 0$

-1 | 2 15 24 11

2 13 11 0

∴ $2m^2+13m+11=0$

The roots are

$=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{-13\pm \sqrt{13^2-4(11)(2)}}{2(2)}$

$=\frac{-13\pm9}{4}$

$=-5.5, -1$

So, $m_1, m_2, m_3 = -1, -1, -5.5$

Then the general solution is :

$= (c_1+c_2 x)e^{-x} + c_3 \ e^{-5.5x}$

8 0

3 years ago

Polygon F has an area of 36 square units. Aimar drew a scaled version of Polygon F and labeled it Polygon G. Polygon G has an ar

mariarad [96]

Area is a squared number. We know that from the label we use when we solve problems involving area. Perimeter is a single unit label. This single unit label can also be used to find scale factor, since single unit labels are one-to-one. If the area of polygon F is 36, that means that the single unit measure was a number that was squared to get to the area. Same goes for polygon G. That means that in order to find the single unit measure of each of those we have to take the square root of the area. The square root of 36 is 6, and the square root of 4 is 2. 6:2 is the scale factor, but that can be reduced to 3:1, larger to smaller.

6 0

3 years ago

Read 2 more answers

A candy manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock. He decides

Ilia_Sergeevich [38]

Answer:

He should prepare 260 pounds of first mixture and 0 pounds of second mixture

Step-by-step explanation:

Let x be the total quantity ( in pounds ) of cherries and mints in the first mixture and y be the total quantity in second mixture,

Since, first mixture will contain half cherries and half mints by weight,

That is, in first mixture,

Cherries = $\frac{x}{2}$

Mints = $\frac{x}{2}$ ,

While, second mixture will contain one-third cherries and two-thirds mints by weight,

That is, in second mixture,

Cherries = $\frac{y}{3}$

Mints = $\frac{2y}{3}$

According to the question,

The manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock,

That is,

$\frac{x}{2}+\frac{y}{3} \leq 130$

$\frac{x}{2}+\frac{2y}{3}\leq 170$

Also, pounds can not be negative,

x ≥ 0, y ≥ 0,

Since, the first and second mixture must be sell at the rate of $2.00 per pound and $1.25 per pound respectively,

Hence, the total revenue,

Z = 2.00x + 1.25y

Which is the function that have to maximise,

By plotting the above inequalities,

Vertex of feasible regions are,

(0,255), (180, 120) and (260, 0),

Also, at (260, 0), Z is maximum,

Hence, he should prepare 260 pounds of first mixture and 0 pounds of second mixture in order to maximize his sales revenue.

7 0

3 years ago

In physics, if a moving object has a starting position at s 0, an initial velocity of v 0, and a constant acceleration a, then t

stiks02 [169]

Actually the position function with respect to time under constant acceleration is:

a=g

v=⌠g dt

v=gt+vi

s=⌠v

s=gt^2/2+vit+si

So if vi and si are zero then you just have:

s=gt^2/2

Notice that it is not gt^2 but (g/2) t^2

So the first term in any quadratic is half of the acceleration times time squared because of how the integration works out...

Anyway....

sf=(a/2)t^2+vit+si

(sf-si)-vit=a(t^2)/2

2(sf-si)-2vit=at^2

a=(2(sf-si)-2vit)/t^2 and if si and vi equal zero

a=(2s)/t^2

8 0

3 years ago

Read 2 more answers

Vector component of ū and w are as

Helen [10]

Answer:

r = ( -14.4 , 6.47 )

Step-by-step explanation:

in the photo you will find all the steps

7 0

2 years ago