This angle is "29 degrees 6 minutes 6 seconds".
-- There are 60 minutes in 1 degree.
So 1 minute = 1/60 degree.
-- There are 60 seconds in 1 minute.
So 1 second = 1/60 minute = 1/3600 degree.
29 6' 6" = (29)° + (6/60)° + (6/3600)°
= (29)° + (0.1)° + (0.001666...)°
= 29.101666...°
Rounded to the nearest thousandth of a degree: 29.102°
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:
f(x) = - 8
Explanation:
The given function is
f(x) =2x^2 -4x -6
The first step is to find the derivative of the function. Recall, if
y = ax^b
y' = abx^(b - 1)
Thus,
f'(x) = 4x - 4
We would equate f'(x) to zero and solve for x. We have
4x - 4 = 0
4x = 4
x = 4/4
x = 1
We would substitute x = 1 into the original function and solve for f(x) or y. It becomes
f(1) =2(1)^2 -4(1) - 6 = 2 - 4 - 6
f(1) = - 8
Thus, the minimum value is f(x) = - 8
Answer:
$780.50
Step-by-step explanation:
I will update this if I figure how it's solved as well.
Answer:
The airplane would starts its descent from an altitude 500 feet lower.
Step-by-step explanation:
The x-axis is horizontal and the y-axis is vertical (altitude). It would be 500 feet lower because they took 500 away from the 30,000.
