In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y"−6y′+9y=18t−39−(18te3t+6e3t)y″−6y ′+9y=18t−39−(18te3t+6e3t)
with initial values y(0)=−1andy′(0)=11.
A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)
B. Write the fundamental solutions for the associated homogeneous equation.
y1= y2=
C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients.
Y=
Y′=
Y″=
D. Write the general solution. (Use c1 and c2 for c1c1 and c2c2).
y=
E. Plug in the initial values and solve for c1c1 and c2c2 to find the solution to the initial value problem.
y=

You and a friend race across a field to a fence and back. your friend has a 50-meter head start. the equations shown represent you and your friend's distances dd (in meters) from the fence tt seconds after the race begins. find the time at which you catch up to your friend. you: d=∣−5t+100∣d=∣−5t+100∣ your friend: d=∣−313t+50∣∣

An objects motion is described by the equation d= 4sin (pi t) what will the height of the object be at 1.75 seconds?

You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function. how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions