Answer: A=113.1cm
Step-by-step explanation:
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:
1.) The correct answer is A.
2.) The correct answer is C.
3.) The correct answer is B.
4.) The correct answer is A.
5.) The correct answer is B.
Step-by-step explanation:
Answer:
The approximate volume of the tank is 
Step-by-step explanation:
we know that
The volume of a hemisphere (water storage tank) is equal to
we have
assume
substitute
I'm pretty sure the answer is no. A function looks like this: f(x) = mx + c. Let's add another function, f(y) = ny + d. If the x-intercept is the same, we can subtract c and d from their respective equations. f(x) = mx, f(y) = ny. If the domains are the same, then x and y can have the same value, so we divide it out. f(x) = m, f(y) = n. Finally, if the ranges are the same, the value of f(x) = f(y). So by the substitution property, m=n. Since all the variables equal each other, both functions are equal to f(x) = mx+c! Therefore, they can only be the same function.
Answer: No
