Question Solve following two problems: P1. A 34 inch diameter steel rod, 100 ft long, is hanging vertically and an axial load of 8000 lb is hanging at the free end of the rod. Calculate following: a) elongation of the bar due to self weight, due to the suspended load and the total elongation b) calculate the axial stress in rod due to the applied load. Use unit weight of 490 lb/cft and E = 30x10^6 psi P2. A circular steel rod (length 7 feet, steel E = 30x10^6 psi) is to carry an axial load of 65,000 lbs. Determine the smallest diameter of the rod that can be used if these two conditions are to be met: a) axial stress should not exceed 36,000 psi b) total axial deformation should not exceed 0.085 in.

1. Suppose that A is an n x n matrix, where every entry in A is an integer. Prove that A-! also has this property (all entries are integers) if and only if det(A) = +1. Remember, the "if and only if construction means you have two things to do: Assuming A has all integer entries, and det(A) = +1, prove that all entries in A-1 are integers. Then prove that if all entries in A and all entries in A- are integers, then det(A) = +1. For this second direction, relate the determinant of A to that of A-.

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 \( \$ 16000 \)

A car rental company owns five types of cars: Small,Economy, Standard, Family, Exclusive. The prices for per day rent for eachtype of the cars are given in British pounds by the1×5matrix