First find the common denominator. It would be 24. For 8 to get to 24 you have to multiply it by 3. So 8*3=24 and 5*3=15. For 6 to get to 24 you have to multiply it by 4. So 6*4=24 and 1*4=4. Our fractions are now at 15/24 and 4/24. 15+4 is 19 and 15-4 is 11. Your answers are 19/24 and 11/24.
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:
307.5
Step-by-step explanation:
He drove 123 miles in 2 hours. If you go 100 miles in 2 hours that means you went 50 miles in one hour right? Using the same logic we can convert 123 miles in 2 hours to 61.5 miles per hour and then multiply it by 5.
Hello There!
The first statement is incorrect as congruent angles have the same measure but it doesn't have to 45°. It can be any value.
The second one is also incorrect. Congruent angles have the same measure but don't always total to 180° (which is what supplementary means). It would only be true if they are congruent right angles.
The third one is also incorrect as they don't always total to 90° either (Which is what complementary means).
The fourth one is correct, this is because congruent angles are simply angles with the same measure.
In short, you're answer is 4. Congruent angles always have the same measure.
Hope This Helps You!
Good Luck :)
Answer:
B.
Step-by-step explanation:
The absolute value of 0 is 0 so 0 = 0 is true.
