Consider the spiral given by c(t) = (e2t cos(2t), e2t sin(2t)). Show that the angle between c and c' is constant. c'(t) = Let θ be the angle between c and c'. Using the dot product rule we have the following. c(t) · c'(t) = c(t) · c'(t) cos(θ) 2e4t = cos(θ)

Which two transformations are applied to pentagon abcde to create a'b'c'd'e'? (4 points) translated according to the rule (x, y) ? (x + 8, y + 2) and reflected across the x-axis translated according to the rule (x, y) ? (x + 2, y + 8) and reflected across the y-axis translated according to the rule (x, y) ? (x + 8, y + 2) and reflected across the y-axis translated according to the rule (x, y) ? (x + 2, y + 8) and reflected across the x-axis

At a local museum, the total price for one adult and one child is $11. mrs. smith paid for herself and her three children. she spent $19. record the system of equations to be solved and then find the price of an adult and child ticket using either elimination or substitution.

Several paint mixtures are made by mixing blue paint and white paint. paint colors blue paint white paint mixture a 5 cups 12 cups mixture b 6 cups 6 cups mixture c 4 cups 12 cups mixture d 5 cups 6 cups which mixture has the highest ratio of blue paint to white paint