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2 years ago

If sally drives to work 25% faster than she did yesterday, what would be her

Mathematics

1 answer:

dedylja [7]2 years ago

6 0

Answer:

50 percent

Step-by-step explanation:

because sally was tried yesterday and went 25 percent faster today.

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Use variation of parameters to find a general solution to the differential equation given that the functions y1 and y2 are linea

Aleks [24]

Recall that variation of parameters is used to solve second-order ODEs of the form

y''(t) + p(t) y'(t) + q(t) y(t) = f(t)

so the first thing you need to do is divide both sides of your equation by t :

y'' + (2t - 1)/t y' - 2/t y = 7t

You're looking for a solution of the form

$y=y_1u_1+y_2u_2$

where

$u_1(t)=\displaystyle-\int\frac{y_2(t)f(t)}{W(y_1,y_2)}\,\mathrm dt$

$u_2(t)=\displaystyle\int\frac{y_1(t)f(t)}{W(y_1,y_2)}\,\mathrm dt$

and W denotes the Wronskian determinant.

Compute the Wronskian:

$W(y_1,y_2) = W\left(2t-1,e^{-2t}\right) = \begin{vmatrix}2t-1&e^{-2t}\\2&-2e^{-2t}\end{vmatrix} = -4te^{-2t}$

Then

$u_1=\displaystyle-\int\frac{7te^{-2t}}{-4te^{-2t}}\,\mathrm dt=\frac74\int\mathrm dt = \frac74t$

$u_2=\displaystyle\int\frac{7t(2t-1)}{-4te^{-2t}}\,\mathrm dt=-\frac74\int(2t-1)e^{2t}\,\mathrm dt=-\frac74(t-1)e^{2t}$

The general solution to the ODE is

$y = C_1(2t-1) + C_2e^{-2t} + \dfrac74t(2t-1) - \dfrac74(t-1)e^{2t}e^{-2t}$

which simplifies somewhat to

$\boxed{y = C_1(2t-1) + C_2e^{-2t} + \dfrac74(2t^2-2t+1)}$

4 0

2 years ago

the perimeter of a rectangle is 132 m. the length is 2 meters more than 3 times the width. find the dimensions of the rectangle

Anon25 [30]

2l + 2w = 132
l = 3w + 2

2(3w+2)+2w=132
6w + 4 + 2w = 132
8w + 4 = 132
8w = 128
w = 16

l = 3(16) + 2
l = 48 + 2
l = 50

2(50) + 2(16) __ 132
100 + 32 = 132

7 0

2 years ago

I need help I’m in math class! Help please

AVprozaik [17]

Answer:

1350π $cm^3$ should be your answer

Step-by-step explanation:

15 x 15 x π = 225π

225π x 6 = 1350π

7 0

3 years ago

!!!!!!!!!!!!!!!100100100100100pts!!!!!!!!!!!!!!!!!!!!!!!!!!

Alex_Xolod [135]

Answers

1. B) 31
2. B) 4
3. A) 15
4. D) 24
5. A) 3

MARK BRAINLEIST PLS THIS TOOK A LOT OF TIME

7 0

2 years ago

Please Help!

vovikov84 [41]

Answer:

Step-by-step explanation:

We can use triangle inequality, let AC = x:

x+4 > 5

x+5 > 4

9 > x

Simplifying:

x>1

x>-1

9>x

Thus: 9>x>1

So the Largest whole number is 8

3 0

3 years ago