Our Kalman filter tries to track both the position and velocity of a car in 1 −D. The state vector is Px
Vx

and
the initial guess is

Px = 12m
Vx = 4m
s

The motion model is constant acceleration with a = 2m
s2 . The initial position uncertainty is 1.4m and the
initial velocity uncertainty is 0.5m
s . the time constant of the system (Δt) equals 2s.
A. Write the F, B, U, P matrices.
B. What is the predicted state after Δt?
We also have a position sensor. The noise model of the sensor is normally distributed with μ = 0, σ = 2m.
At t = 2 we get the following measurement from the sensor: z = 19.5m
C. Write H, R matrices
D. Compute the posterior system state after the measurement.
2

Find the volume of the solid generated when the region bounded by y= x and y= 4√x is revolved about the x-axis the volume of the solid is: (type an exact answer cubic units)

Use addition and subtraction to simplify the following polynomials. a. add polynomials: (3 – 4x + 8x^2) + (–6 + 2x – 5x^2) step 1: rewrite the polynomials without the parentheses. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial. b. subtract polynomials: (3x – 5 – 7x^2) – (–2 + 6x^2 – 5x) step 1: rewrite the polynomials without the parentheses. remember to multiply each term in the second parentheses by –1. show your work. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial.

The focus of parabola is (-4, -5), and its directrix is y= -1. fill in the missing terms and signs in parabolas equation in standard form