For 0 < t < 2, v(t) = t + 1. For 2 < t < 4, v(t) = -t/2 +4, sketch a graph of x(t) assuming x(0) = -1

Vector A→, which is directed along an x axis, is to be added to vector B→, which has a magnitude of 9.30 m. The sum is a third vector that is directed along the y axis, with a magnitude that is 5.10 times that of A→. What is the magnitude of A→?

The force P of magnitude 50 KN is acting at 215° from the x-axis. Find the components of P in u 157° from x, and v negative 69°from x. (Draw the Figure)

Two vectors A→ and  B→ are at right angles to each other. The magnitude of  A→ is 1.00. What should be the length of  B→ so that the magnitude of their vector sum is 2.00?

Given the pair of vectors, A = (9.00î − 5.00ĵ ) and B =(−3.00î + 9.00ĵ ),use the definition of a scalar product to determine the following.   (a) the scalar product (b) the angle between the vectors (Enter an answer between 0 and 180 degrees.)                      ° (c) the angle ? between the vector A and the +x axis (Enter an answer between 0 and 180 degrees.)                      ° (d) the angle ? between the vector B and the +y axis (Enter an answer between 0 and 180 degrees.)                      °

A vector is given by: i = (-2.11) + ( -4.28) ĵ+ ( 2.8 ) k. Determine the component of the unit vector û .

Part (a)  Do this for the range r > R.  E = _____ Part (b)  Do this for the range r < R.  E = _____

Here's how gym membership works for a potential customer: If the customer decides to join the gym, she will pay J on day 0. Then, she can use the gym starting the next day for 5 days (1; 2; 3; 4; 5), paying an additional F on each day she visits. If she goes to the gym on any given day, it costs her (10+ F) that day, but beneÖts her 30 the next day. In other words, her "costs" are a sum of her psychic costs (10) and actual Onancial costs (F). Assume that, when indi§erent, the individual will go to the gym. (a) Suppose the potential customer is a standard exponential discounter with a discount factor of = 12. If gym membership was free (i.e. J = 0 and F = 0) would she join the gym? If so, how many days would she actually go? (b) Suppose the gym did not charge a joining fee. How high could it set the usage fee? What would its revenues from this customer be? (c) Suppose instead the gym decided not to charge a usage fee. How high could it set the joining fee? [Hint: To Ögure out the…

(6%) Problem 5: Consider the following vectors: A = 4.6i + 1.4j+ 3.4k В = -6. 5i + 7.1j + 10.2k 25% Part (a) What is the x-component of the vector V = 3(A × 2B)? Vx= sin() cos() tan() 7 8 9 НOME cotan() asin() acos() E 4 5 atan() acotan() sinh() 1 cosh() tanh() cotanh() + END Degrees Radians Vd BACKSPACE DEL CLEAR Feedback Submit Hint I I give up! Hints: 2 for a 0% deduction. Hints remaining: 0 Feedback: 3% deduction per feedback. -This is a cross-product, so the answer will be a vector. In this part, we just want the x-component of the vector. Keep in mind that scalars like "2" and "3" distribute 3.

Item 12 (Figure 1)A neutral conducting sphere contains a spherical cavity. A point charge q is placed at the center of the cavity. Part A What is the total surface charge dint on the interior surface of the conductor? ► View Available Hint(s) VE ΑΣΦ gint = Submit ?