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Quiz 3 - Math 1A, section 106
1. Prove that
limx→2(x2 + x - 6/x - 2) = 5
using the ε, δ definition of a limit.
When using the substitution method, how can you tell if a system of linear equations has no solution?
Cole's student loans totaled $31,000. One of his loans was at 2.8% simple interest and the other at 4.5%. After one year, Cole owed $1024.40 in interest. What was the amount of each loan.
A rancher has 288 feet of fencing to enclose two adjacent rectangular corrals. What dimensions will produce the largest total area.
The Flamey-Wamey Company (FWC) produces extinguishers and heat detectors. Each extinguisher takes three hours of labor from the materials department and four hours of labor from the contruction department.
Find the gradient of the straight line joining the points P(2, 3) and Q(8, 6). Also calculate the the equation of the line through P perpendicular to the line PQ.
Vectors as linear combinations of the vectors
Find the score that marks the top 5 percent
Fit a linear regression model as in Q5, and plot your estimates for β0 and β1 as N increases, together with a line indicating their true values.
At the beginning of an experiment, a scientist has 272 grams of radioactive goo. After 180 minutes, her sample has decayed to 17 grams.
The height, h(x), of a punted rugby ball is given by where x is the horizontal distance in feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point?
A polynomial f of x is irreducible over Q if and only if (x+alpha) is irreducible over Q for some alpha belong to q Q is a rational.
An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 1..
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