Question Question No. 5 The 50-lb wheel has a radius of gyration about its center of gravity Gof kg = 0.7 ft. If it rolls without slipping, determine its angular velocity when it has rotated clockwise 90° from the position shown. The spring AB has a stiffness k = 1.20 lb/ft and an unstretched length of 0.5 ft. The wheel is released from rest. 3 ft 0.5 ft + 0.5 ft иии, k = 1.20 lb/ft 1 ft

Q5:- Three zones A, B and C are connected by two lanes road as shown in fig below with travel time "tt car" and "tt bus" (12) Marks А B С 0 tt car= 10 tt car= 15 tt bus= 30 tt bus= 25 the total trip exchange between zones From To Person trips/day A B 1500 B. A 500 A С 800 C С A 2000 B С 500 C B 1000 If the utility function Ux = 0.85 0.08 (tt car tt bus) Determine the 2 way volume per day on the road AB if the occupancy for car 1.8 and for bus (15.5).

A 50-g weight is hung at the 20-cm mark of a meterstick and a 100-g weight is hung at the 70-cm mark. At what point must the meterstick be supported for it to be in rotational equilibrium? The weight of the meterstick is negligible. O at the 56.67-cm mark. at the 46.67 cm mark. O at the 53.33-cm mark. O at the 43.33 cm mark.

Part A The post is made of Douglas fir and has a diameter of 100 mm (Figure 1) It is subjected to the load of 20 kN and the soil provides a frictional resistance distributed around the post that is triangular along its sides that is, it varies from w=0 kN/mat y=0 m to w= 15 kN/m at y = 2 m. Neglect the weight of the post Determine the force at its bottom needed for equilibrium Express your answer to three significant figures and include appropriate units. HÅ ? Value Units Submit Request Answer Figure 1 of 1 Part B 20KN What is the displacement of the top of the post with respect to a bottom B? Express your answer to three significant figures and include appropriato unito, ? 2 m 0 = Value Units 12 kN/m Submit Request Answer

a hockey puck moving at 7.0 m/s coasts to a halt in 75m on a smooth ice surface. What is the coefficient of friction between the ice and the puck?

​​​​​​​ The bar has a cross-sectional area of \( 1900 \mathrm{~mm}^{2} \) and \( E=250 \mathrm{GPa} \). (Figure 1) Determine the displacement of its end \( A \) when it is subjected to the distributed loading. Express your answer to three significant figures and include the appropriate units. Enter negative value in the case of contraction and positive value in the case of elongation. Figure 1 of 1 X Incorrect; Try Again; 4 attempts remaining

      please solve all tasks A car rental company owns five types of cars: Small, Economy, Standard, Family, Exclusive. The prices for per day rent for each type of the cars aregiven in British pounds by the \( 1 \times 5 \) matrix \[ \mathbf{p}=\left(\begin{array}{lllll} 15 & 19 & 21 & 28 & 37 \end{array}\right) \] The care demand for five days of a week ahead is given by the matrix \[ \mathbf{A}=\left(\begin{array}{ccccc} 2 & 4 & 3 & 1 & 3 \\ 4 & 3 & 3 & 5 & 3 \\ 10 & 11 & 8 & 6 & 9 \\ 4 & 3 & 2 & 3 & 4 \\ 2 & 1 & 3 & 2 & 1 \end{array}\right) \] Calculate the total income in British pounds of the company for this week. a. 10500 b. 3420 C. 2242 d. 4520 Consider the clockwise rotation \( T \) of \( \mathbb{R}^{2} \) by the angle of \( 30^{\circ} \). Mark only correct statements. a. The matrix of \( T \) is \( \left(\begin{array}{cc}-\frac{\sqrt{3}}{2} & \frac{1}{2} \\ \frac{1}{2} & -\frac{\sqrt{3}}{2}\end{array}\right) \) b. The matrix of \( T \) is symmetric. c. The matrix of \( T \) is \( \left(\begin{array}{rr}\frac{\sqrt{3}}{2} & -\frac{1}{2} \\ \frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right) \) d. The matrix of \( T \) is \( \left(\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right) \) e. The matrix of \( T \) is \( \left(\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right) \) A company manufactures three types of perfume-refreshing \( (R) \), standard \( (S) \), and exclusive \( (E) \), in four factories in different countries \( A \), B, C, D. The distributions of costs in producing a single piece of perfume are given in the left table below. The number of pieces of perfume produced in one month at the four locations are given in the right table. a. Location A materials: \( \$ 4500 \) b. Location B: labor \( \$ 8000 \) c. Location A: labor \( \$ 14000 \) d. Location D: materials \( \$ 25000 \) e. Location C: overheads \( \$ 16000 \)