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3 years ago

Find an equation of variation in which y varies directly as x and y = 12 when x = 6

1 answer:

8 0

Direct variation:-

y = kx where k is a constant

y=12 when x=6 so we have:-

12 = k*6

k = 12/6 = 2

so our equation of variation is y = 2x Answer

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Does the set {t, t Int} form a fundamental set of solutions for t^2y" -- ty' +y = 0?

Ivanshal [37]

Answer:

yes

Step-by-step explanation:

We are given that a Cauchy Euler's equation

$t^2y''-ty'+y=0$ where t is not equal to zero

We are given that two solutions of given Cauchy Euler's equation are t,t ln t

We have to find the solutions are independent or dependent.

To find the solutions are independent or dependent we use wronskain

$w(x)=\begin{vmatrix}y_1&y_2\\y'_1&y'_2\end{vmatrix}$

If wrosnkian is not equal to zero then solutions are dependent and if wronskian is zero then the set of solution is independent.

Let $y_1=t,y_2=t ln t$

$y'_1=1,y'_2=lnt+1$

$w(x)=\begin{vmatrix}t&t lnt\\1&lnt+1\end{vmatrix}$

$w(x)=t(lnt+1)-tlnt=tlnt+t-tlnt=t$ where t is not equal to zero.

Hence,the wronskian is not equal to zero .Therefore, the set of solutions is independent.

Hence, the set {t , tln t} form a fundamental set of solutions for given equation.

6 0

3 years ago

If 40% of a number is 56 what was the original number

svp [43]

Percent is pars out of 100
40%=40/100=4/10=0.4
'of' means multiply
0.4 times something=56
divide both sides by 0.4
something=140

th enumber is 140

5 0

3 years ago

Please help ASAP. I really need this it is almost due. Please give me the right answer.

IceJOKER [234]

A and D
Put 3 in the equations and solve

5 0

3 years ago

Heather brought $7.14 to school. She then spent $1.08 to buy lunch. How much money does she have left?

Wewaii [24]

Answer:

6.06

Step-by-step explanation:

Simple subtraction.

5 0

3 years ago

Read 2 more answers

The new playground equipment for the park was delivered in the box shown.

Maurinko [17]

5*4*12=240

Hope it helps :D

3 0

3 years ago