Answer:
Step-by-step explanation:
<u>Given</u>
- m∠ABC = x°
- m∠BCD = 25°
- m∠CDE = 55°
- m∠DEF = 3x°
Add two more parallel lines passing through points C and D.
Consider alternate interior angles formed by the four parallel lines.
<u>The angles between the two middle lines are equal to:</u>
- m∠BCD - m∠ABC = m∠CDE - m∠DEF
<u>Substitute values and solve for x:</u>
- 25 - x = 55 - 3x
- 3x - x = 55 - 25
- 2x = 30
- x = 15
m∠ABC = 15°
Answer:
Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)
Step-by-step explanation:
Center at (-5,-1) because of the plus 5 added to the x and the plus 1 added to the y.
a(squared)=36 which means a=6 and a=distance from center to vertices so add and subtract 6 from the x coordinate since this is a horizontal hyperbola, which is (1,-1), (-11,-1). From there you dont need to find the focus since there is only one option for this;
Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)
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:
Step-by-step explanation:
