Answer:
Step-by-step explanation:
step a system of two equations c = child ticket a = adult ticket
eq 1) 2c + 1a = 8.2 multiply by 2
eq 2) 3c + 2a = 14.1
I will multiply eq 1 times TWO and subtract eq 2 from eq 1a)
eq 1a) 4c + 2a = 16.4
eq 2) 3c + 2a = 14.1
subtract (4c - 3c) + (2a -2a) = 16.4 - 14.1
c + 0 = 2.3 euros for one child ticket
Now find the adult ticket price, plug 2.3 for c into eq 1)
eq 1) 2c + 1a = 8.2
eq 1) 2(2.3) + 1a = 8.2 solve for a
4.6 + a = 8.2 substract 4.6 from both sides
a = 8.2 - 4.6
= 3.6 euros for one adult ticket
double check using eq 2) we know c and a values
eq 2) 3c + 2a = 14.1
eq 2) 3(2.3) + 2(3.6) = 14.1
6.9 + 7.2 = 14.1
14.1 = 14.1
Answer:
yp = -x/8
Step-by-step explanation:
Given the differential equation: y′′−8y′=7x+1,
The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)
First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;
y′′−8y′=0
The auxiliary equation will give us;
m²-8m = 0
m(m-8) = 0
m = 0 and m-8 = 0
m1 = 0 and m2 = 8
Since the value of the roots are real and different, the complementary solution (yc) will give us
yc = Ae^m1x + Be^m2x
yc = Ae^0+Be^8x
yc = A+Be^8x
To get yp we will differentiate yc twice and substitute the answers into the original DE
yp = Ax+B (using the method of undetermined coefficients
y'p = A
y"p = 0
Substituting the differentials into the general DE to get the constants we have;
0-8A = 7x+1
Comparing coefficients
-8A = 1
A = -1/8
B = 0
yp = -1/8x+0
yp = -x/8 (particular integral)
y = yc+yp
y = A+Be^8x-x/8
Answer:
What is the average rate of change from x = −4 to x = 1? x= -4 x + 5
Im not sure but maybe 1 adult and one child but im not sure if this is a trick question
