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Ganezh [65]
3 years ago
14

Jake, Sara, and Cole are selling tickets for the school drama show. Sara sells half as many tickets as Jake. Cole sells 6 more t

han twice as many as Jake. They sold a total of 538 tickets together. Write an equation to represent the situation.
Mathematics
1 answer:
borishaifa [10]3 years ago
4 0
Let x be Jake's number of sold tickets. Sara's number is half as Jake's, so x/2 while, Cole's number is twice as Jake's, 2x. The equation that represents the problem is just the summation of their sold tickets. Therefore, 538= x+ x/2 + 2x, further simplifying the equation, it becomes, 538= 7/2 x. Solving for Jake's number of tickets, Sara and Cole's number of tickets can be determined.
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Consider the differential equation x2y′′ − 9xy′ + 24y = 0; x4, x6, (0, [infinity]). Verify that the given functions form a funda
pantera1 [17]

Answer:

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

y= c_1x^4+c_2x^6

Step-by-step explanation:

Given equation is

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This Euler Cauchy type differential equation.

So, we can let

y=x^m

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Again differentiate with respect to x

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Putting the value of y, y' and y'' in the differential equation

x^2m(m-1) x^{m-2} - 9 x m x^{m-1}+24x^m=0

\Rightarrow m(m-1)x^m-9mx^m+24x^m=0

\Rightarrow m^2-m-9m+24=0

⇒m²-10m +24=0

⇒m²-6m -4m+24=0

⇒m(m-6)-4(m-6)=0

⇒(m-6)(m-4)=0

⇒m = 6,4

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The general solution of this equation is

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and

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         =x⁴×6x⁵- x⁶×4x³    

        =6x⁹-4x⁹

        =2x⁹

       ≠0

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

y= c_1x^4+c_2x^6

5 0
3 years ago
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Answer:

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Step-by-step explanation:

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We need to find b, therefore we'll eliminate f

<u>To do so we'll double the first equation and subtract the second one:</u>

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Answer:

Step-by-step explanation:

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4 0
3 years ago
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