Math Answers

A 50 gallons tank initially contains 10 gal of fresh water. At t = 0, a brine solution

containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gal/min, while the

well-stirred mixture leaves the tank at the rate of 2 gal/min. Find

a. the amount of time required for overflow to occur

b. the amount of salt in the tank at the moment of overflow

A metal bar at a temperature of 100 deg. fahrenheit is placed in a room at a constant temperature of 0 deg. fahrenheit. If after 20 minutes the temperature of the bar is 50 deg. Fahrenheit, find: a) the time it will take the bar to reach a temperature of 25 deg. Fahrenheit? b) the temperature of the bar after 10 minutes?

There are 5 different roads from city A to city B and 3 different roads from city B to city C. In how many ways can someone go from city A to city C passing by city B?

A car manufacturing company was able to release 1,860 units at the end of January. Based on records, they were able to increase their sales by 46 units per month thereafter. In what month did their car sales reach 2, 320 units?

Suppose a recurrence relation

an=7an−1−12an−2

where a1=16 and a2=52

can be represented in explicit formula, either as:

Formula 1:

an=pxn+qnxn

                      or  

Formula 2:

an=pxn+qyn

where 

x

and

y

are roots of the characteristic equation.

**If the explicit formula is in the form of Formula 2, consider p < q.

Determine

p and q

f four marbles are to be picked at random, in how many ways could we pick

One marble for each color.

All the green marbles

3 of the green marbles

B , C and D vying for for the position.

List all the possible combinations of applicants to be hired.

Use the formula for combination to solve for the number of possible of

filling the vacant positions.

ways could we arrange so that marbles of the same color are together? In

how many ways could we pick 3 marbles so that one marble of each color

are picked ?

a spherical balloon is inflated at a rate of 36pi cm³/sec. How fast is the radius of the balloon increasing when radius is 7cm?

Evaluate

d^2r/dt^2 at t=0 when

r=(t3+2t)i−3e−2tj+2sin5tk