Funtion ! in vertex form is given by
<span>f(x) = 4x^2 + 8x + 1</span> = 4(x^2 + 2x + 1/4) = 4(x^2 + 2x + 1 + 1/4 - 1) = 4(x + 1)^2 + 4(-3/4) = 4(x + 1)^2 - 3
Thus, the least minimun value is (-1, -3)
Also, the least minimum value of function 2 is (-1, 0)
Therefore, function 1 has the least minimum value at (-1, -3)
Answer: A 2-column table with 5 rows. Column 1 is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1. Column 2 is labeled y with entries 5, 5, 5, 5, 5.
Answer: 47
Step-by-step explanation:
simply substitute the constants with 5 and 3.
(5)^2 + 9(3) - 5 = 47
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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