Answer:
So any time you are multiplying something, you are making "groups of"
so 3 groups of 2 = 6, 4 groups of 3 = 12
But with decimals or fractions, because they are a value less than zero, the numbers become increasingly small instead of bigger, like standard multiplication.
So for example, 1 group of 1/2 = 1/2
2 groups of 1/4 = 1/2
and so on
hope this helps!
It means for example instead of writing 2 2/5 You would write 12/5
You can find out an improper fraction by simply multiplying the denominator by the front number and adding the answer to you numerator
So, 2x5= 10. 10+2= 12. So 12/5
Let car b be travelling at x mph. as they are travelling towards each other their speed of approach is (x + x + 15 ) mph. So we have the equation
speed = distance / time
2x + 15 = 250 / 2
2x = 125 - 15 = 110
x = 55 mph
Car b travels at 55 mph and car a travels at 70 mph Answer
The only 'small number' that I know that would affect the answer is an exponent that looks like ³ so the problem would be x³+x
remember that x³=x times x times x
if x=3 then
3³+3=27+3=30
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
