The resquest of the y'+6y=e^4t, y(0)=2

Answers

Answer 1

Answer: This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x).
Multiplying both sides of the equation by the integrating factor:

(y')e^(6x) + 6ye^(6x) = e^(12x)

The left side is the derivative of ye^(6x), hence

d/dx[ye^(6x)] = e^(12x)

Integrating

ye^(6x) = (1/12)e^(12x) + c where c is a constant

y = (1/12)e^(6x) + ce^(-6x)

Use the initial condition y(0)=-8 to find c:

-8 = (1/12) + c
c=-97/12

Hence

y = (1/12)e^(6x) - (97/12)e^(-6x)

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For which system of equations is (2, 2) a solution? A.–3x + 3y = 0
x + 6y = 10B.–2x + 5y = –6
4x – 2y = 4C.5x – 2y = –6
3x – 4y = 2D.2x + 3y = 10
4x + 5y = 18

Answers

$A.)\n\n-3x + 3y = 0\nx + 6y = 10 \ / *3\n\n-3x + 3y = 0\n3x + 18y = 30\n+------\n21y =30 \ / :21\n \ny=(30)/(21)=(10)/(7)\n\nnot \ true$

$B.)\n\n-2x + 5y = -6 \ / \cdot 2\n4x - 2y = 4\n \n-4x + 10y = -12 \n4x - 2y = 4 \n+-------- \n8y=-8\ /:8\n \ny=-1\n \n not \ true$

$C.\n\n5x - 2y = -6 \ / \cdot 2\n3x - 4y = 2 \n \n 10x - 4y = -12 \n 3x- 4y = 2\n+------\n13x=-11 \ / :13\n \nx=-(11)/(13)\n\n not \ true$

$D.)\n\n2x + 3y = 10\ / \cdot (-2)\n4x + 5y = 18\n\n-4x -6y =-20\n4x + 5y = 18\n+-------\n-y = -2 \ / \cdot (-1)\n \ny=2$

$2x + 3*2 = 10\n \n2x=10-6 \n \n2x=4 \ / :2 \n \n x=2 \n \n true$

$x=2\ \ \ and\ \ \ y=2\n\nA.\ \ \ \ \ \ x + 6y = 2+6\cdot2=2+12=14 \neq 10\n\nB.\ \ \ \ \ -2x + 5y =-2\cdot2+5\cdot2=-4+10=6 \neq -6\n\nC.\ \ \ \ \ \ \ 5x-2y =5\cdot2-2\cdot2=10-4=6 \neq -6\n\nD.\ \ \ \ \ \ \ 2x + 3y =2\cdot2+3\cdot2=4+3= 10\nand\ \ \ \ \ \ 4x + 5y = 4\cdot2+5\cdot2=8+10=18\n\nAns.\ (2,\ 2)\ is\ a\ solution\ for\ system \ D$

Find the sum of the arithmetic sequence.

-10, -7, -4, -1, 2, 5, 8

Answers

Answer:

+3 every time or the total?

Or is it 18? U specify which

Help real quick! !!!!! click here! !

Answers

varies directly means
if y varies directly as x that means
y=kx where k is a constant

so
y=kx
y=2 and 2/3 when y=1/4 then find k
convert 2 and 2/3 to imporoper fraction for ease
2 and 2/3=6/3+2/3=8/3

8/3=k(1/4)
multiply both sides by 4/1 to clear fraction
32/3=k

so now we have
y=(32/3)x

when x=1 and 1/8
find y
convert 1 and 1/8 to imporopor=9/8

y=(32/3)(9/8)
y=(288)/(24)
y=12

SOMEONE PLEASE HELP ME
IT'S TIMED

Answers

Answer:

H = 8 cm

Step-by-step explanation:

The formula of a volume of a cylinder:

$V=\pi r^2H$

We have

$r=6cm,\ V=904.78\ cm^3$

Substitute:

$\pi(6^2)H=904.78\n\n36\pi H=904.78\qquad\text{use}\ \pi\approx3.14\n\n(36)(3.14)H=904.78\n\n113.04H=904.78\qquad\text{divide both sides by}\ 113.04\n\nH\approx8\ cm$

What two numbers add up to 20 but multiply to 75?

Answers

First you find all the numbers that multiply to get 75.

75 x 1
25 x 3
15 x 5

Then find out which two add together to get 20.

75 + 1 = 76
25 + 3 = 28
15 + 5 = 20

So the answer would be 15 and 5.

15 and 5 because 15 times 5 is 75 and 15 plus 5 is 20

One fourth of a number is 1 more than one fifth of the same number

Answers

The most important part of this question is understanding the words of the problem. The trick lies in the words of the problem. Once the web of words is simplified, the problem becomes very easy. The main thing is converting the words into numbers.
Let us assume the unknown number = x
Then from the question we get
(x/4) = (x/5) + 1
(x/4) - (x/5) = 1
(5x - 4x)/20 = 1
x/20 = 1
x = 20
So the unknown number is 20

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