8x + 1/3 = 2/3 what is the answer?

Answer:

33333

Step-by-step explanation:

1. The given equation is probably supposed to read

y'' - 2y' - 3y = 64x exp(-x)

First consider the homogeneous equation,

y'' - 2y' - 3y = 0

which has characteristic equation

r² - 2r - 3 = (r - 3) (r + 1) = 0

with roots r = 3 and r = -1. Then the characteristic solution is

[tex]y = C_1 e^{3x} + C_2 e^{-x}[/tex]

and we let y₁ = exp(3x) and y₂ = exp(-x), our fundamental solutions.

Now we use variation of parameters, which gives a particular solution of the form

[tex]y_p = u_1y_1 + u_2y_2[/tex]

where

[tex]\displaystyle u_1 = -\int \frac{64xe^{-x}y_2}{W(y_1,y_2)} \, dx[/tex]

[tex]\displaystyle u_2 = \int \frac{64xe^{-x}y_1}{W(y_1,y_2)} \, dx[/tex]

and W(y₁, y₂) is the Wronskian determinant of the two fundamental solutions. This is

[tex]W(y_1,y_2) = \begin{vmatrix}e^{3x} & e^{-x} \\ (e^{3x})' & (e^{-x})'\end{vmatrix} = \begin{vmatrix}e^{3x} & e^{-x} \\ 3e^{3x} & -e^{-x}\end{vmatrix} = -e^{2x} - 3e^{2x} = -4e^{2x}[/tex]

Then we find

[tex]\displaystyle u_1 = -\int \frac{64xe^{-x} \cdot e^{-x}}{-4e^{2x}} \, dx = 16 \int xe^{-4x} \, dx = -(4x + 1) e^{-4x}[/tex]

[tex]\displaystyle u_2 = \int \frac{64xe^{-x} \cdot e^{3x}}{-4e^{2x}} \, dx = -16 \int x \, dx = -8x^2[/tex]

so it follows that the particular solution is

[tex]y_p = -(4x+1)e^{-4x} \cdot e^{3x} - 8x^2\cdot e^{-x} = -(8x^2+4x+1)e^{-x}[/tex]

and so the general solution is

[tex]\boxed{y(x) = C_1 e^{3x} + C_2e^{-x} - (8x^2+4x+1) e^{-x}}[/tex]

2. I'll again assume there's typo in the equation, and that it should read

y''' - 6y'' + 11y' - 6y = 2x exp(-x)

Again, we consider the homogeneous equation,

y''' - 6y'' + 11y' - 6y = 0

and observe that the characteristic polynomial,

r³ - 6r² + 11r - 6

has coefficients that sum to 1 - 6 + 11 - 6 = 0, which immediately tells us that r = 1 is a root. Polynomial division and subsequent factoring yields

r³ - 6r² + 11r - 6 = (r - 1) (r² - 5r + 6) = (r - 1) (r - 2) (r - 3)

and from this we see the characteristic solution is

[tex]y_c = C_1 e^x + C_2 e^{2x} + C_3 e^{3x}[/tex]

For the particular solution, I'll use undetermined coefficients. We look for a solution of the form

[tex]y_p = (ax+b)e^{-x}[/tex]

whose first three derivatives are

[tex]{y_p}' = ae^{-x} - (ax+b)e^{-x} = (-ax+a-b)e^{-x}[/tex]

[tex]{y_p}'' = -ae^{-x} - (-ax+a-b)e^{-x} = (ax-2a+b)e^{-x}[/tex]

[tex]{y_p}''' = ae^{-x} - (ax-2a+b)e^{-x} = (-ax+3a-b)e^{-x}[/tex]

Substituting these into the equation gives

[tex](-ax+3a-b)e^{-x} - 6(ax-2a+b)e^{-x} + 11(-ax+a-b)e^{-x} - 6(ax+b)e^{-x} = 2xe^{-x}[/tex]

[tex](-ax+3a-b) - 6(ax-2a+b) + 11(-ax+a-b) - 6(ax+b) = 2x[/tex]

[tex]-24ax+26a-24b = 2x[/tex]

It follows that -24a = 2 and 26a - 24b = 0, so that a = -1/12 = -12/144 and b = -13/144, so the particular solution is

[tex]y_p = -\dfrac{12x+13}{144}e^{-x}[/tex]

and the general solution is

[tex]\boxed{y = C_1 e^x + C_2 e^{2x} + C_3 e^{3x} - \dfrac{12x+13}{144} e^{-x}}[/tex]

Answer:

250

Step-by-step explanation:

You can take the explicit formula and simply substitute the n value with 64:

-2 + 4 * (64 - 1)

-2 + 4 * (63)

-2 + 252

250

Answer:

it is D

Step-by-step explanation:

I have to show you, but if I do it don't on the paper

Answer:

This is indeed a function

Answer:

2.25

Step-by-step explanation:

m = 9 / 4 = 2.25

points belong to an increasing, linear function.

Equation: y = 2.25x + 2.75.

BRAINLIEST?

Answer:

15.625

Step-by-step explanation:

Answer:

[tex] (\frac{2}{5} ) {}^{ - 3} \\ = (\frac{a}{b} ) {}^{ - x} = (\frac{b}{a} ) {}^{x} \\ so \: \: \: \: \: \: (\frac{2}{5} ) {}^{ - 3} \\ = (\frac{5}{2} ) {}^{3} \\ = \frac{5 {}^{3} }{2 {}^{3} } \\ \: = \: \frac{125}{8} [/tex]

Answer:

95% of 80 is 76 and 85% of 60 is 51.

Step-by-step explanation:

Answer:

a. 76,  b. 60.

Step-by-step explanation:

a)  80 * 0.95 = 76.

b)   0.85 x = 51

x = 51/0.85 = 60.

Answer:

A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)

Step-by-step explanation:

A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)

Answer:

Step-by-step explanation:

x² + (x + 17)² = 25²

x² + x² + 34x + 289 = 625

2x² + 34x - 336 = 0

x² + 17x - 168 = 0

x = (-17 ±√(17² - 4(1)(-168))) / (2(1))

x = 7 or - 24   the negative distance makes no sense, but if we plug our good answer of 7 ft in for the base length, the height comes out to be + 24 ft

base = 7 ft

height = 24 ft

Answer:

That would be negative 45 or - 45

Please correct me if im wrong

Answer:

Fertilizer puts nitrogen into the soil, so using fertilizer puts more nitrogen into the carbon cycle.

When you use fertilizer, its because a certain plant you are planting uses all the nitrogen in the soil, so it won't grow next time. Too much fertilizer, though, would burn up your plant (not literally). Some plants put their own nitrogen into the soil. I can't think of one off the top of my head, but I believe potatoes do. Anyways, this is where crop rotation came into play.

Things like corn take a lot of nitrogen, so the next time you had to plant whatever plant potatoes, which again may be wrong, in order to get nitrogen for the corn to grow next season. Today we have fertilizer, so we can give them nitrogen while they grow, instead of putting in other plants, taking more time.

So really, it doesn't do much, because your plant takes all the nitrogen that the Fertilizer adds.

Answer:

People have been converting atmospheric nitrogen into nitrogen fertilizers and then applying the fertilizers to plants in to grow more crops. This has previously been quite effective, allowing individuals to farm on previously unproductive lands, and provide adequate food for expanding populations of people. Unfortunately, fertilizers are frequently overused, which can lead to issues.

Nitrogen from fertilizers excretes into soils, typically promoting the growth of weeds rather than native vegetation. Nitrogen then washes into streams, resulting in a nutrient overload, a phenomenon known as eutrophication.

Eutrophication causes aquatic weeds to proliferate excessively in freshwater lakes. These aquatic weeds  occasionally occupy entire lakes, streams, or rivers. Green algae cloud the water, and gooey algal slime covers the shallow rocks. 

When nitrogen-rich waters flow down into the ocean, they worsen the situation. High nitrogen concentrations in the Mississippi River Delta have generated a 'dead zone' where the water flows into the Gulf of Mexico. This has occurred every summer for over 30 years. In 2001, this dead zone, where oxygen levels are too low for species to thrive, encompassed over 8000 square miles of water. It occurs when nitrogen in the water enables algae to quickly grow out of control.

Step-by-step explanation:

Great article to look at for more information -

https://www.nytimes.com/2017/07/27/climate/nitrogen-fertilizers-climate-change-pollution-waterways-global-warming.html

Answer:

Yes, because (-1,2) is a solution to both inequalities

Step-by-step explanation:

2>-1 so the first inequality is correct

-1+2>0 so the second inequality is correct

Answer:

x > 2 or 2 < x

Step-by-step explanation:

x-3 < 3x-7

-3 < 2x-7

4 < 2x

2 < x

x > 2

Answer:

4 better inbox

Step-by-step explanation:

Answer: annualcreditreport.com

Step-by-step explanation: The only authorized website for free credit reports, or call 1-877-322-8228

Answer:

A.

Step-by-step explanation:

All choices show the first original equation.

Each choice shows a different second equation.

Take the second original equation:

6x + 5y = 30

Multiply both sides by -5.

-30x - 25y = -150

Answer: A.

Answer:

35

Step-by-step explanation:

since i couldn't answer before

Answer:

Possible errors: Triangle classification and definition.

Step-by-step explanation:

An isoceles triangle has at least two congruent sides of the same length.  

Given the triangle that has two equal angles, and that you'll have to prove that the triangle also has two equal sides.  

Using the Converse of Isoceles Triangle Theorem, where it states that if a triangle has two congruent angles < PQR ≅ < PRQ, for which opposite sides of those angles are congruent:  

Additionally, connecting point P to point X along the line QR such that PX ⊥ QR, divides △PQR into two symmetrical sections, where points Q and R are equidistant from point X.      

Answer:

Possible errors: Triangle classification and definition.

Answer:

81 - a

Step-by-step explanation:

Decreased

means to subtract

81 –

by an unknown number

means a variable such as a or x

therefor

81 – a

Answer:

1 11/12 cups of water

Answer:

ok you to !!!!!!!!! good night!!

Step-by-step explanation:

Answer:

Uuuuh thats kind of suspicious, maybe you could post your question without  a link? But links are usually scams, so dont do that :)

Answer:

d because your taking away 6 from the 275

Step-by-step explanation:

Answer:8x-40

Step-by-step explanation:

Because when we simply 4(x-5)/2

We multiply both sides by 2 because the inverse operations of division is multiplication. 2*4(x-5)*2/2 we cancel two by two then it leave us 4*2(x-5).

Next four times two is eight. So 8(x-5) we distribe eight that means eight times x and 5, 8x-40thos is the answer. Hope this help

Answer:

Just go to the 6 on the bottom line, and add a point

Answer:

see below

Step-by-step explanation:

(6,0)

 The first coordinate is the x coordinate.  Since it is positive we go to the right 6 units.  The second coordinate is the y coordinate.  We go up zero units