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2 years ago

Which of these represents the side lengths of a right triangle?

Mathematics

1 answer:

ki77a [65]2 years ago

8 0

15, 20, 25 is the correct answer

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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

A baseball card that originally cost $24 has been decreasing in value

dimaraw [331]

Answer:

I believe it is four dollars

6 0

2 years ago

Consider the function f(x)=-2/3x +5 what is f(-6) enter your answer in the box f(-6)=

GaryK [48]

Answer:

f(- 6) = 9

Step-by-step explanation:

to evaluate f(- 6), substitute x = - 6 into f(x)

f(- 6) = - $\frac{2}{3}$ × - 6 + 5

= - $\frac{2(-6)}{3}$ + 5 = 4 + 5 = 9

4 0

3 years ago

Jose's school has 426 students. His principal has promised the Student Council that their idea will be carried out if they can

evablogger [386]

Answer:

they need 25 more signatures to get their idea carried out

Step-by-step explanation: 25% of 426 is 107 and 107 minus 82 is 25

3 0

2 years ago

Read 2 more answers

Be confident and be paitent to help people tahnky ou

Aleksandr [31]

12!!!! Hope this helped and good encouragement

4 0

2 years ago