Consider the function f(x) = (ax + b) eax+b, with a, a > 0. answer the following in terms of a, b, a, and b: (i) what are the critical numbers of f? critical numbers: x = (ii) where is f increasing? f is increasing on (intervals) (iii) where is f decreasing? f is decreasing on (intervals) (iv) at which x does f achieve its local maxima? f achieves local maxima at x = (v) at which x does f achieve its local minima? f achieves local minima at x = (vi) where is f concave up? f is concave up on (intervals) (vii) where is f concave down? f is concave down on

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.

The dipole moment of the water molecule (h2o) is 6.17x10^-30 c.m. consider a water molecule located at the origin whose dipole moment p points in the +x-direction. a chlorine ion ( of charge-1.60x10^-19c , is located at x=3.00x10^-9m . assume that is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis can be used. a) find the magnitude of the electric force that the water molecule exerts on the chlorine ion. b) what is the direction of the electric force. -x-direction or +x-direction c) is this force attractive or repulsive?

What is the speed vfinal of the electron when it is 10.0 cm from charge 1?