The range is {-37,-25,-13,-1}. So you need to figure out what four numbers from this list of numbers (1,2,3,4,5,6,7,8), when applied to this
function, ( f(x)=-6x+11 ), equals these numbers that are in the range {-37,-25,-13,-1}.
So you apply each of these numbers (1,2,3,4,5,6,7,8) into the function (f(x)=-6x+11)
one by one.
f(1)=-6(1)+11=5
f(2)=-6(2)+11= -1
f(3)=-6(3)+11= -7
f(4)=-6(4)+11= -13
f(5)=-6(5)+11= -19
f(6)=-6(6)+11= -25
f(7)=-6(7)+11= -31
f(8)=-6(8)+11= -37
As you can see, f(2),f(4),f(6),and f(8) equal the numbers that are in the range {-37,-25,-13,-1}.
Answer:
x^2 + 25
Step-by-step explanation:
(a) Take the Laplace transform of both sides:
where the transform of 
comes from
![L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)](https://tex.z-dn.net/?f=L%5Bty%27%28t%29%5D%3D-%28L%5By%27%28t%29%5D%29%27%3D-%28sY%28s%29-y%280%29%29%27%3D-Y%28s%29-sY%27%28s%29)
This yields the linear ODE,
Divides both sides by 
:
Find the integrating factor:
Multiply both sides of the ODE by 
:
The left side condenses into the derivative of a product:
Integrate both sides and solve for 
:
(b) Taking the inverse transform of both sides gives
![y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]](https://tex.z-dn.net/?f=y%28t%29%3D%5Cdfrac%7B7t%5E2%7D2%2BC%5C%2CL%5E%7B-1%7D%5Cleft%5B%5Cdfrac%7Be%5E%7Bs%5E2%7D%7D%7Bs%5E3%7D%5Cright%5D)
I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that 
is one solution to the original ODE.
Substitute these into the ODE to see everything checks out:
Answer:
1. Both Dan and Tess are correct.
Tess:
0.15 * 24.50 = 3.675
24.5 - 3.675 = 20.825
0.1 * 20.825 = 2.0825
20.825 + 2.0825 = 22.9075
Dan:
0.85 * 24.50 = 20.825
20.825 * 1.1 = 22.9075
Both Dan and Tess used methods that provided the correct answer. Both methods follow the same path, but Dan's method simply took less steps since he used percentages that would take out the correct number, unlike Tess' percentages which would give you the number that you would then need to take out.
2. First, convert Amy's and Mike's numbers to a decimal of the whole so it is easier to compare the numbers.
13% = 0.13 of the whole
Dan has 0.14 of the whole
0.5/6 = 0.083.. of the whole
Dan used the greatest amount of milk, using 0.14 of the 6 gallon container.
3.
2p + 12 = 58 | Create an equation to show the prices relations
2p = 46 | Take out the price of the concert ticket to leave us with the passes.
p = 23 | Divide by 2 to find the cost of each pass.
4.
x ≤ (18 - 6.5 - 5.75)/1.15
18 - 6.50 = 11.5 | Take out the price of the notebook from the total.
11.5 - 5.75 = 5.75 | Take out the amount of money that she wishes to save.
5.75 / 1.15 = 5 | Divide by the price of each candy to find the max amount that she can buy.
Andrea has enough money to buy up to 5 candy bars.
x ≤ 5
