Answer:
- 3x² + 5x + 1 = 0 simplified
- x = (-5 ±
)/6 roots
Step-by-step explanation:
<u>Given quadratic formula</u>
<u>Standard form</u>
<u>Simplifying</u>
- 3x² + 5x - 5 + 6 = 0
- 3x² + 5x + 1 = 0
<u>Solving</u>
- x = (-5 ±
)/(2*3) - x = (-5 ± )/6
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)
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Answer:
The balance after 1 year is;
$1,014.05
Step-by-step explanation:
To do this, we use the compound interest formula
That will be ;
A =P (1 + r/n)^nt
A is the amount generated which we want to calculate
r is the rate = 1.4% = 0.014
P is the amount deposited = $1,000
n is the number of times it is compounded annually which is 2 (semi-annually means 2 times in a year)
this the number of years which is 1
we have this as:
A = 1,000( 1 + 0.014/2)^(2*1)
A = 1,000(1 + 0.007)^2
A = 1,000(1.007)^2
A = $1,014.05
