Express in terms of the unit step function, the piecewise continuous causal functions () = { 2 2 , 0 ≤ < 3 + 4, 3 ≤ < 5 9, ≥ 5 [3 marks] ii. Use Laplace transforms to solve the initial value problem ) ′′ + 16 = 43 + ( − ⁄3) where (0) = 0 and ′(0) = 0.

Use the function value to find the indicated trigonometric value in the specified quadrant. function value quadrant trigonometric valuecsc(θ) = −4 iv cot(θ)cot(θ)=?

An assembly consists of two mechanical components. suppose that the probabilities that the first and second components meet specifications are 0.87 and 0.84. assume that the components are independent. determine the probability mass function of the number of components in the assembly that meet specifications. x

Solve this system of equations. 12x − 18y = 27 4x − 6y = 10