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2 answers:
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Answer:
Linear second-order differential equation F(x, y, y′, y″) = 0
y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given differential equation
y = c₁x + c₂x⁴ ...(i)
Differentiating equation (i) with respective to 'x', we get
y¹ = c₁(1) + c₂ ( 4 x³ ) ...(ii)
Differentiating equation (ii) with respective to 'x', we get
y¹¹ = c₂ ( 12 x² )
...(a)
<u><em>Step(ii)</em></u>:-
Substitute (a) in equation (ii)
...(b)
<u><em>Step(iii):</em></u>-
12 x² y = (y¹12 x³ - 4 x⁴ y¹¹) + x⁴ y¹¹
x⁴ y¹¹ - 4 x⁴ y¹¹ + y¹12 x³ - 12 x² y= 0
y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0
The options are not clear enough, so i have attached it.
Answer:
A: The independent variable (x) is the amount of time Rosetta shoots photos. The dependent variable (y) is the amount, in dollars, Rosetta earns for a wedding.
Rosetta charges a one-time fee of $100 (this is when x = 0), so the y-intercept is 100. Rosetta earns $50 for each hour she works, so the slope is 50
Step-by-step explanation:
We are given the equation of total amount of money Rosetta earns per wedding as;
y = 50x + 100
Where x is number of hours.
Now, the independent variable will be x because it doesn't depend on any other variable whereas the dependent variable will be y because it depends on how many hours which is x.
Now, the y-intercept occurs when x = 0.
Thus;
y = 50(0) + 100
y = 100
Thus,she charges a one time fee of $100, so the y-intercept = $100 at x = 0.
From slope intercept equation which is;
y = mx + c and comparing with y = 50x + 100, where m is the slope, we can see that m = 50.
Thus, since she earns $50 per hour, the slope is 50.
The correct option is Option A.
