MATHalino

Problem
Solve for x from the following equations:

Problem
A germ population has a growth curve $Ae^{0.4t}$. At what value of $t$ does its original value doubled?

Problem
The sum and product of three distinct positive integers are 15 and 45, respectively. What is the smallest integer?

Problem
A contractor can buy a dump trucks for P800,000 each (surplus) or rent them for P1,189 per truck per day. The truck has salvage value of P100,000 at the end of its useful life of 5 years. Annual cost of maintenance is P20,000. If money is worth 14% per annum, determine the number of days per year that a truck must be used to warrant the purchase of the truck.

Problem
Mar wants to make a box with no lid from a rectangular sheet of cardboard that is 18 inches by 24 inches. The box is to be made by cutting a square of side x from each corner of the sheet and folding up the sides. Find the value of x that maximizes the volume of the box.

Situation
An investment of P250,000 is made at the end of each year with interest of 2.5% compounded annually.

1. Determine the equal-payment-series compound-amount factor after 10 years.
   

   A.   11.203	C.   9.632
   B.   10.578	D.   8.736

2. Determine the total amount of the investment after 10 years.
   

   A.   P2,800,000.00	C.   P2,400,000.00
   B.   P2,600,000.00	D.   P2,200,000.00

3. How long (in years) will it take for the investment to amount to P10,000,000.00?
   

   A.   25	C.   15
   B.   18	D.   28

Problem
A train is moving at the rate of 8 mi/h along a piece of circular track of radius 2500 ft. Through what angle does it turn in 1 min?

Problem
Find the Cartesian equation of the curve represented by $x = 4t + 3$ and $y = 16t^2 - 9$, -∞ < t < +∞.

Problem
Find the equation of a sphere of radius 3 and tangent to all three coordinate planes if the center is on the first octant.