X - 5 = x^2
i) 0 - 5 = -5^2 = 25
ii) 4 - 5 = -1^2 = 1
iii) -4 - 5 = -9^2 = 81
Format: y = mx + b
m = slope, b = y intercept
Solution: slope: -2, y intercept: 0
Answer:
(b) The number of pounds of berries each person would receive is 
pounds.
Step-by-step explanation:
The amount of berries in first basket = 3 3/8 pounds
Now, 
So, the amount of berries in first basket = 3.375 pounds
The amount of berries in second basket = 2 7/8 pounds
Now, 
So, the amount of berries in second basket = 2.875 pounds
Now, the total berries = Berries in ( First + Second) basket
= 3.375 pounds + 2.875 pounds
= 6.25 pounds
So, the number of pounds each person would have = 
Now, 
So, the number of pounds of berries each person would receive is pounds.
Answer:
S₁₅ = 645
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
= 
[ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Using the nth term formula 
= 5n + 3 , then
a₁ = 5(1) + 3 = 5 + 3 = 8
a₂ = 5(2) + 3 = 10 + 3 = 13 , then
d = a₂ - a₁ = 13 - 8 = 5
Thus
S₁₅ = 
[ (2 × 8) + (14 × 5) ]
= 7.5( 16 + 70)
= 7.5 × 86
= 645
The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
For more information about differential equation, visit
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