This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x).
<span>Multiplying both sides of the equation by the integrating factor: </span>
<span>(y')e^(6x) + 6ye^(6x) = e^(12x) </span>
<span>The left side is the derivative of ye^(6x), hence </span>
<span>d/dx[ye^(6x)] = e^(12x) </span>
<span>Integrating </span>
<span>ye^(6x) = (1/12)e^(12x) + c where c is a constant </span>
<span>y = (1/12)e^(6x) + ce^(-6x) </span>
<span>Use the initial condition y(0)=-8 to find c: </span>
<span>-8 = (1/12) + c </span>
<span>c=-97/12 </span>
<span>Hence </span>
<span>y = (1/12)e^(6x) - (97/12)e^(-6x)</span>
- The information to complete the table is given below:
- Equation that shows the relationship between the cost per night C and the number of people staying in the chalet n: C= 4000-100(n-1)
<h3>What is Equation?</h3>
An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in math when you do not know the exact number in a calculation.
Given that:
Pules Rs 4000 per night but will decrease the amount by R100 per person occupying the chalet.
Number of People Cost per night
1 4000
2 3900
3 3800
4 3700
5 3600
6 3500
7 3400
8 3300
9 3200
10 3100
let C be cost per night and n be the number of people of staying in chalet.
equation: C= 4000-100(n-1)
for n=1: C= 4000- 0=4000
n=2, C= 4000-100(1)= 3900
The graph is attached below:
Learn more about equation here:
brainly.com/question/10413253
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Whats the question?
Sorry but can't answer if theres no question
I would say that the correct answer is D. because y is always the numerator while x is the denominator for the equation y2 - y1/x2 - x1 which means if there is two y's or two x's on the same line you subtract the second one from the first one. If there is only one y and/or x and the other is 0 on the same line, it stays at y or x without subtracting y2 - y1 or x2 - x1.
Since b is on the y coordinate and -a is on the x coordinate, you would make it b/a while -a is gonna be a positive since the lines are going up and to the right. Now, since c is the y coordinate and d is the x coordinate, make C the numerator and d the denominator since y is always the numerator and x is the denominator for these parallel line figures on the graph and the equation will be equaled to the fraction to the other fraction for parallel lines.
So, your answer would be D. b/a = c/d
Hope this helps, and is correct!
<em>~ ShadowXReaper069</em>
