Algebra Answers

The sum of the squares of two consecutive integers is 85. What are the integers?

Assumptions:
1. All cars are approximately the same length (average = 4.2m).
In dense, uniform traffic flow, all cars maintain the same “safe distance” apart.
This “safe distance” is the stopping distance required for a car travelling at V km/h. This distance is composed of two parts –
Reaction Distance, the distance the car travels as the driver reacts to the situation and applies the brake, and Braking Distance, the distance the car travels once the brake has been applied.
The “safe distance” can be reliably obtained from the table given on the next page based on the Ministry of Transportation Code used in England.
Number of cars/second=(m/second)/(m/car)
Show how the formula for traffic flow was developed. Include in your response any assumptions and their associated effects.
Velocity (Km/h) RD m BD m
10 1.905 0.600
20 3.810 2.400
30 5.715 5.400
40 7.620 9.600
50 9.525 15.000
60 11.430 21.600
70 13.335 29.400
80 15.240 38.400
90 17.145 48.600
100 19.050 60.000

Solve the exponential equation. Express the solution in exact form (ie. no calculator) then express the solution in
approximate form to two decimal places. 1) 2x + 8= 5

1000 people entered a math contest to see how many questions out of 20 they could answer correctly in 5 minutes. 15% of them answered 12 correct, 3/5 answered 15 correct and the rest answered 18 correct. What was the percentage correct everyone earned?

pedro needs to call his glassmates to give them final instructions about their class project. he thinks he will need about 2 minutes to talk to each one of them. if hiscellular phone has a current load worth Php 425 and a call would cost him Php 6.15 per minute, how many of his classmates will he be able to talk to?

In order to widen a section of the Pacific Highway from three lanes to four lanes in preparation for the holidays, a construction company will have to close one of the existing lanes for a period of one week.

The Department of Transport would like to have the traffic move as quickly as possible along the one available lane, but does not want a lot of rear-end collisions. They need to consider what speed limit should be set in order to maximise the flow of traffic and still ensure safe travel.

The Department of Transport Engineers have produced the following formula for traffic flow,
F=(0.27 ̅V)/(4.2+0.1905V+0.006V^2 )

where F is the number of cars per second passing a given point, and V is the common speed in km/h at which all cars travel to provide uniform traffic flow.

By using differentiation, determine the speed limit that should be posted on the road to maximise the traffic flow. State any assumptions that affect your results.
Assuming that the cars stick to the advised speed.

You want to mass produce your boxes from Question 2 to sell. You can make your boxes out of different quality paper (q). The higher the quality the paper the less you will sell but the more you can charge. You have done your market research have come up with the following equations.

n=(100-3q)where n is number of sales,q is quality of paper from 1 to 10.
total sale=$0.5qn
total cost=$0.3qn

Identify the maximum number of relative extrema g(x)=2/x^2+3

Find the X value for the vertex : (show all work)
1. f(x)=x^2+4x+6
2.f(x)=2(x-4)^2+5
3.f(x)=-2(x+4)^2+3
4.f(x)=-12x^2+12x+3

A laboratory technician has made up a stock mixture of two chemicals, X and Y, ready for use by all of the groups in Year 9 at a High School. He has mixed 6.0 kg which is 1/4 of X and 3/4 of Y. He realises that he has used the wrong mix and, rather than waste the chemicals he has used so far, he is going to add some more of chemical X so that the mix consists of 40% of X and 60% of Y.
What mass of chemical X must he add?