Question Graph the set of points whose polar coordinates satisfy the equation \( \theta=\frac{\pi}{3}, r \geq 0 \). Choose the graph that represents the equation \( \theta=\frac{\pi}{3}, r \geq 0 \).

15-16 Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order and explain why it's easier.> $\iint_{D} y d A, \quad D$ is bounded by $y=x-2, x=y^{2}$

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