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 This topic has been viewed 2562 times and has 4 replies
iposis

Phil
Joined: Oct 20, 2009
Posts: 10
Status: Offline

Ive been trying to answer these for a month now. I have modules to pass. Please help me. I will appreciate it. Thank you so much.

a) the highway roads intersect at the right angle. a car is 12 kilometers from the intersection at the same time that a truck is 5 kilometers from the same point. if the car is twice as fast as the truck, at what time will thay be 5 kilometers apart?

b) find two numbers whose sum is 38 and what product is a maximum

c) the area of an equilateral triangle is 20 sq meters. one of its sides is 10 meters long. what are the maximum dimension of the triangle.

d) the sum of two numbers is 7. if three times the squares of the first number is added to twice the square of the second number, the sum is 59. find the numbers.

e) two numbers are such that if the squares of the first number is subtrated by twice their product, the difference is -1. but twice the product added to the sum of thrice the squaresof the first number and five times that number gives 10

f) three men, Juan, pedro and jose worked together to complete a job in 13/12 days. if juan and pedro work together, it would take them 7/12 days, while pedro and jose worked together it would take them 5/6 of a day. how long would it take each of them to do the work alone?

Solve for the ff System using algebraic method:

x^2+y^2=13, 2x-3y=-5 solve for x and y

5x^2+y^2=14, 3x^2-2y^2=-15 solve for x and y

2x^2+5x-4y=3, 3x^2-3x+2y^2=2 solve for x and y
 [Oct 21, 2009 11:51:38 AM] [Link]
iposis

Phil
Joined: Oct 20, 2009
Posts: 10
Status: Offline

Even just one? pls pls pls?
 [Oct 21, 2009 11:57:02 AM] [Link]
pskinner

Joined: Apr 2, 2005
Posts: 797
Status: Offline

Consider:

b) find two numbers whose sum is 38 and what product is a maximum

Let the numbers be x and 38-x (which makes their sum 38). Then the product is:

P(x)=x*(38-x)=38x-x^2

This is a quadratic equation and since the coefficient of the quadratic term is negative (-1), the parabolic curve opens down. Consequently, the vertex is the peak.

The coordinates of the vertex are given by (-b/2a,P(-b/2a)), where a=-1 and b=38. The rest is easy to calculate.
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Principal Skinner
 [Oct 24, 2009 9:22:04 AM] [Link]
iposis

Phil
Joined: Oct 20, 2009
Posts: 10
Status: Offline

Thank you so much =)

But i dont know the formula to use for the other problems ='''''(
 [Oct 25, 2009 8:35:04 AM] [Link]
iposis

Phil
Joined: Oct 20, 2009
Posts: 10
Status: Offline