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Digiron [165]
2 years ago
11

Refer to the equation x - 5y = 20.

Mathematics
1 answer:
Rainbow [258]2 years ago
5 0

Answer:

Kindly check explanation

Step-by-step explanation:

Given the equation :

X - 5y = 20

x - 20 = 5y

(x - 20) / 5 = y

x = - 5

y = (-5 - 20) / 5 = -5

x = 0

y = (0 - 20) / 5 = - 4

x = 5

y = (5 - 20) / 5 = - 3

x = 10

y = (10 - 20) / 5 = - 2

X : _____ - 5 ___ 0 ____ 5 ____10

y : _____ - 5 ___- 4 ___ - 3 ___ - 2

Kindly make use of a graph for better clarity and accuracy

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Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).
I am Lyosha [343]
Take the homogeneous part and find the roots to the characteristic equation:

y''+4y=0\implies r^2+4=0\implies r=\pm2i

This means the characteristic solution is y_c=C_1\cos2x+C_2\sin2x.

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form y_p=ax\cos2x+bx\sin2x. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With y_1=\cos2x and y_2=\sin2x, you're looking for a particular solution of the form y_p=u_1y_1+u_2y_2. The functions u_i satisfy

u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx
u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx

where W(y_1,y_2) is the Wronskian determinant of the two characteristic solutions.

W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2

So you have

u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx
u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x

u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx
u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x

So you end up with a solution

u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x

but since \cos2x is already accounted for in the characteristic solution, the particular solution is then

y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x

so that the general solution is

y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x
7 0
3 years ago
Find the exact volume of the cylinder.
Verizon [17]

Answer:

\boxed {\boxed {\sf C. \ 200 \pi \ ft^3}}

Step-by-step explanation:

We are asked to find the volume of the cylinder. The formula for calculating a cylinder's volume is:

v= \pi r^2 h

We know the height of the cylinder is 8 feet. We are given the diameter, the distance from edge to edge through the center. We want to find the radius, the distance from the edge to the center.

The radius is half the diameter.

  • r = d/2
  • r= 10 ft/2
  • r=5 ft

We know both variables (h= 8ft and r=5 ft) and can substitute them into the formula.

v= \pi (5 \ ft)^2 * (8 \ ft)

Solve the exponent.

  • 5 ft * 5ft = 25 ft²

v= \pi (25 \ ft^2)(8 \ft)

Multiply the numbers in parentheses.

v= \pi (200 \ ft^3)

v= 200 \pi \ ft^3

The volume of the cylinder is <u>200π cubic feet and choice C is correct.</u>

5 0
2 years ago
Answer choices 6 cubic units8 cubic units 10.6 cubic units 18 cubic units
antiseptic1488 [7]

Given,

Cylinder A has a volume of 6 cubic units

and height =3 units

The radius of cylinder A,

\begin{gathered} r=\sqrt[]{\frac{V}{\pi h}} \\ =\sqrt[]{\frac{6}{3\pi}} \\ =0.8 \end{gathered}

To find the volume of a cylinder B

\begin{gathered} V=\pi r^2h \\ =(3.14)\times(0.8)^2\times(3) \\ =6.03 \end{gathered}

Thus the volume of cylinder B is 6.03

7 0
1 year ago
The freshmen class is going on a field trip. There are 316 people going.
marishachu [46]
The equation would be 6x+5y=316. X represents the car travelers and the y represents the bus travelers
3 0
3 years ago
A number N divided by -9 is -16
lianna [129]

Answer: no

Step-by-step explanation:

algebraic expression for "a number , n, divided by 4 is 4. I

3 0
3 years ago
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