In this exercise, we consider finding the first five coefficients in the series solution of the first-order linear initial value
problem (x²+2)y′′ − 6y = 0 subject to the initial condition y(0) = 1, y′(0) = 2. Since the equation has an ordinary point at x=0 and it has a power series solution in the form y = Lim(n=0→[infinity])Σ cₙxⁿ.(1) Insert the formal power series into the differential equation and derive the recurrence relation: cn= __________cₙ₋₂ for n=2,3,⋯ The solution to this initial value problem can be written in the form y(x)= c₀y₁(x)+c₁y₂(x) where c₀ and c₁ are determined from the initial conditions. The function y₁(x) is an even function and y₂(x) is an odd function. For this example, from the initial conditions, we have c₀ = ______ and c₁ = ______. The function y₁(x) is an infinite series y₁(x) = 1+ Lim(n=1→[infinity])Σ aₙx²ⁿNote that the constant c₀ has been factored out. (2) Use the recurrence relation to find the first few coefficients of the infinite series: a₂ = _______, a₄ = _______, a₆ = _______, a₈ = _______.Note that the constant c₀ has been factored out. Finally the polynomial y₂(x)= _______NOTE: The function y₂(x) is an odd degree polynomial with first term x. In other words, note that the constant c₁ has been factored out.
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Answer:
$284.99 should go to Mr. Aceves’ class, $174.41 should go to Mrs. Baca’s class, and $140.60 should go to Mr. Canyon’s class.
Step-by-step explanation:
Firstly, to calculate the portions each class should have, we should find the proportion each class takes up.
Hence, let's say A represents Mr. Aceves' class, B represents Mrs. Baca's class, and C represents Mr. Canyon's class.
The total number of box tops collected would be 3760 + 2301 + 1855 = 7916 box tops.
Therefore, the total proportions would be:
A =
B =
C =
Hence, we can finally multiply these proportions with the total prize to find the appropriate division:
Mr. Aceves' class gets .
Mrs. Baca's class gets .
And Mr. Canyon's class gets .
Finally, $284.99 should go to Mr. Aceves’ class, $174.41 should go to Mrs. Baca’s class, and $140.60 should go to Mr. Canyon’s class.
Hope this helped!
The scale factor is: 1/5.
The missing sides of figure B are: 2.4, 3.6, and 4.
<h3>How to find Scale Factor?</h3>Scale factor = dimension of new figure / dimension of original figure
The polygons given are shown in the diagram attached below.
Figure A is the original figure
Figure B is the new figure.
x, y, and z has been used to mark the missing sides of figure B.
One dimension of original figure = 15
Corresponding dimension of the new figure = 3
Scale factor = new/original = 3/15
Scale factor = 1/5
To find the missing sides of figure B, multiply each corresponding side lengths of Figure A by the scale factor:
x = 12 × 1/5 = 2.4
y = 18 × 1/5 = 3.6
z = 20 × 1/5 = 4
In summary:
The scale factor is: 1/5.
The missing sides of figure B are: 2.4, 3.6, and 4.
Learn more about scale factor on:
