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vekshin1
3 years ago
14

Verify that the indicated function y = ϕ(x) is an explicit solution of the given first-order differential equation. (y − x)y' =

y − x + 8; y = x + 4 x + 3
Mathematics
1 answer:
JulijaS [17]3 years ago
4 0

Answer:

The function y = x + 4x - 3 is not a solution of the given differential equation.

Step-by-step explanation:

Verify that a function f (x) is a solution to a differential equation, consists in finding the derivatives of the function and entering them into the equation. If the given function, indeed, is the solution, equality must be checked.

y = x + 4x +3 = 5x+3\\\\y' = 5\\\\\left(y - x\right)y' = y - x + 8\\\\\left(5x + 3 - x\right)\left(5\right) = 5x + 3 - x + 8\\\\\left(4x + 3\right)\left(5\right) = 4x + 11\\\\20x + 15 = 4x + 11\\\\

The function y = 5x - 3 is not a solution of the given differential equation

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A function f is defined by f(x) = 2x - 3. By writing the full working, write the values of (a) f(0) (b) f(-2) (c) f(3) (d) f(-1)
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3 years ago
Luis is going to an amusement park. The price of admission into the park is $20, and once he is inside the park, he will have to
Marysya12 [62]

Using a linear function, it is found that the costs are given as follows:

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<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

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Considering the price of admission and the price per ride, the y-intercept is of 20 and the slope is of 4, the cost for r rides is given by:

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Hence, for 6 rides, the cost is given by:

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More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

6 0
1 year ago
For $360, a rock-climbing gym offers yearly membership where members can climb as many days as they want and pay $4 per day for
IRISSAK [1]
So, we have the two equations $4x+$360, and $10x+$6x. x represents how much members pay each day. The total number of visits when the cost for a member and nonmember is the same means we will have to set both equations equal to one another. 
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<span>To check your work, plug in what x equals or 30 in the original equation. If you come up with a true statement, then you know your answer has to be correct. </span>
<span>4x+360=16x </span>
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<span>480=480 </span>
<span>Because this is a true statement, you can be certain that the total number of visits when the cost of a member and a nonmember will be the same is 30 visits. Hope I helped! Brainliest too please.</span>
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