HA2 SEM1 practice 1

What is the value of [math](1+i^3)^2+(1-i^3)^2[/math]?

Consider the graph of the polynomial function [math]f(x)[/math]. Which of the following statements is true?

Consider the function [math]f(x)=\sqrt{x-1}[/math]. We compress horizontally by a factor of [math]4[/math] and then translate 3 units left. What is the new function?

Which of the following expressions is not a polynomial?

Consider the quadratic function [math]f(x)=-4x^2+24x-30[/math]. Which of the following statements is true?

Let [math]A[/math] be a matrix satisfying [math]A^2=3A-2I[/math] where [math]I[/math] is an identity matrix. Find [math]A^3[/math] in terms of [math]A[/math] ad [math]I[/math].

Use RREF to solve the linear equatino system [math]\begin{cases}x-2y+3z=4\\-5x+3y-z=-6\\3x-z=1\end{cases}[/math]

Let [math]A=\begin{bmatrix}1&3\\-2&-7\end{bmatrix}[/math] and [math]B=\begin{bmatrix}7&3\\-2&-1\end{bmatrix}[/math] be two matrix. If [math]C=3AB-2BA[/math], what is [math]c_{11}+c_{21}[/math]?

Consider two functions [math]f(x)=2x-3[/math] and [math]g(x)x^2-2x-3[/math]. Use their graphs to solve the inequality [math]f(x)\geq g(x)[/math].

The figure above shows a parabolic bridge. There is a ship tries to pass through the bridge. If the width and height of the ship are both 4 meters, can this ship pass through the bridge safely? Just answer “Yes” or “No”.

A diver is standing on a platform 24 ft above the pool. He jumps from the platform with an initial upward velocity of 8 ft/s. The track of the diver can be represented as the formula [math]h=-16t^2+vt+s[/math] where [math]h[/math] is the height above the water, [math]t[/math] is time (seconds), [math]v[/math] is his initial velocity, and [math]s[/math] is his standing height. How long, in seconds, will it take for the diver to hit the water?

(Calculator) Hannah arranges a three days trip to Korea. She plans to invite 30 people and plans to charge every person $500. If the number of people exceeds 30, she will charge $5 less for every person. How many people can maximize her revenue?

(Calculator) Daniel is a boss of a Japanese restaurant. We wants to know the relationship between the sales of tuikimi soba and sashimi, so we records 5 days. The table above shows the results

(a) If [math]x[/math] is the number of dishes of tsukimi soba and [math]y[/math] is the number of dishes of sashimi. What is the equation of line of best fit?

(b) Suppose Daniel sold 12 dishes of tsukimi soba, use (a) to predict the number of dishes of sashimi he sold. Round to the nearest integer.