Exercise 1.4: Round the following numbers to the nearest tenth. 1. 1.3556 = 2. 21.4333 = Round the following numbers to the nearest hundredth (two decimal places). 3. 3.546 = 4. 24.9312= Round the following numbers to the nearest whole number. 5. 24.589 = 6. 12.158 =
Suppose we have a mechanical system with the following model: \bar{v}+6 \dot{v}+13 v=13 n where y is the output of the system and u is the input of the system. Initial conditions are y(0)and y(0). ) Based on the given model, generate the transfer function Y(s)/U(s). (b) What are the poles and zeros of the transfer function? (c) If the input u(t) is a unit step, find the output y(t) when y(0) = 0 and ý(0) = 0. (d) Write down an expression for the free response with initial conditions y(0) =1 and ÿ(0)=0 (e) Is this system stable? Please explain.
*12-108. The baseball player A hits the baseball a A = 40 ft/s and 0 = 60° from the horizontal. When the ball is directly overhead of player B he begins to run under it. Determine the constant speed at which B must run and the distance d in order to make the catch at the same elevation at which the ball was hit.
4. (10 pts) Prove the following statement:Let l be a line and let A and B be points on opposite sides of l. Then there is a unique point O E l with A * O * B.
1. Consider an interpretation where "points" are the numbers 1,2,3 and 4, "lines" are the sets {1,2}, {1,3}, {1,4}, and {2,3, 4}, and “lies on" means "is contained in." (b) (6 pts) Which (if any) parallel postulate does this interpretation satisfy? Prove your answer. (a) (8 pts) Is this a model for incidence geometry? Prove your answer. (c) (4 pts) Is this a model for neutral geometry? Prove your answer.
12-79. The particle travels along the path defined by the parabola y = 0.5x². If the component of velocity along the x axis is v, = (5t) ft/s, where t is in seconds, determine the particle's distance from the origin O and the magnitude= 0.of its acceleration when t = 1 s. When t0, x 0, y =
6. Are there any Datum Feature Targets on this drawing (Yes or No)? If yes, describe where
7. Referring to the conventional tolerances on the drawing, what method of tolerancing is shown?
5. (8 pts) Prove the following statement:Let A, B, and C be non-collinear points, and let D be a point on the same side of AB as C. If M<BAC > m<BAD, then D is in the interior of <BAC.
12-94. A golf ball is struck with a velocity of 80 ft/s as shown. Determine the speed at which it strikes the ground at B and the time of flight from A to B.