A flywheel with a diameter of 20 is rotating at \( 15 \frac{\text { radians }}{\text { second }} \). What is the speed of a point on the rim of the fywheel measured in fu/min?

1. Sea la matriz \( \mathrm{A}=\left(\begin{array}{ccc}-1 & 2 & \mathrm{k} \\ 2 & -3 & -3 \\ 3 & -5 & 0\end{array}\right) \) Hallar los valores de k para los cuales la matriz A es inversible. 2. En una economia de tres rubros independientes I, II y II: Para producir \( 1 \$ \) de I se necesitan \( \$ 0,6 \) de I y \( \$ 0,1 \) de II. Para producir \( 1 \$ \) de II se necesitan \( \$ 0,4 \) de I, \( \$ 0,5 \) de II y \( \$ 0,1 \) de III. Para producir \( 1 \$ \) de III se necesitan \( \$ 0,2 \) de II \( \$ 0,7 \) de III. ¿Qué demanda externa de cada rubro es posible satisfacer con una producción de \( \$ 240 \) de I . \( \$ 120 \) de II y \( \$ 100 \) de III?

1.2: Real Life Geometry 1.1.The pleture below is of bridge made out of steel. Each section of the bridge is triangle, 3 metres wide, 4 metres high and a slant height of 5 m . How much steel is needed to create each section of the bridge? What do we call a triangle with these measurements? How many triangles are found in the design of one complete side panel? Calculate the amount of steel that is needed for one side panel of the bridge? (2)

Apply Newton's method to \( f(x)=x^{\frac{1}{3}} \) with \( x_{0}=1 \) and calculate \( x_{1}, x_{2}, x_{3} \), and \( x_{4} \). Find a formula for \( \left|x_{n}\right| \). What happens to \( \left|x_{n}\right| \) as \( n \rightarrow \infty \) ? Draw a picture that shows what is going on. \( x_{2}=\square \) (Simplify your answer.)

Find the zeros, if any, of the quadratic function using the quadratic formula. What are the \( x \)-intercepts, if any, of the graph of the function? \( g(x)=5 x^{2}+9 x+4 \) Select the correct choice below and, if necessary, fill in the answer box to complete your cholce. (Simplity your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) A. The zeros and the x-intercepts are the same. They are \( \square \). The zeros and the xintercepts are different. The zeros are \( \square \), the x-intercepts are B. There is no real zero solution and no x-intercept.

Solve the initial value problem. \[ \frac{d^{2} y}{d x^{2}}=12-30 x, y^{\prime}(0)=7 \text {, and } y(0)=7 \] \( y(x)= \)