 |
|
|
|
|
|
|
|
|
Integrating e^x sin(x) |
2003-05-03 |
|
From Lech:
I am having trouble integrating the following expression by parts: ex sin(x) I used the integrator at http://www.integrals.com/ to find the solution, ? 1/2 ex cos(x) + 1/2 ex sin(x). This is easy to confirm by differentiation, however I am confounded as how to arrive at the answer.
Answered by Penny Nom and Claude Tardif. |
|
|
|
|
|
|
The volume of air flowing in windpipes |
2003-05-02 |
|
From James:
The volume of air flowing in windpipes is given by V=kpR4, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: Ro - R = cp, where Ro is the windpipe radius when p=0 & c is a positive constant. R is restricted such that:
0 < 0.5*Ro < R < Ro,
find the factor by which the radius of the windpipe contracts to give maximum flow?
Answered by Penny Nom. |
|
|
|
|
|
|
positive multiples of 10 that are the sum of four consecutive integers |
2003-05-01 |
|
From Taurus:
How many positive multiples of 10 that are less than 1000 are the sum of four consecutive integers?
Answered by Penny Nom. |
|
|
|
|
|
|
A circle, tangent to two circles and a line |
2003-04-30 |
|
From Keith:
I have a horizontal line (that is treated as a datum line or the X axis), with two circles having their center points at different heights from that line (X1,Y1 & X2,Y2). The two circles are also at different diameters (R1 & R2). Both circles and the line (X-Axis) do not intersect nor are they tangent. My goal is to determine the maximum diameter of an inscribed circle that will fit between all three.
Answered by Chris Fisher and Harley Weston. |
|
|
|
|
|
|
A binomial probability |
2003-04-30 |
|
From Erica:
In a biathlon, athletes shot at 20 targets. A particular athlete had a probability of 0.18 of missing a target. Assuming a binomial distribution, what is the probability, to the nearest thousandth, that the athlete hit exactly 16 targets?
Answered by Andrei Volodin. |
|
|
|
|
|
|
Some shapes |
2003-04-29 |
|
From Suzanne:
- What shape has 12 edges all the same length?
- What shape has 3 surfaces and 1 is curved?
Answered by Penny Nom. |
|
|
|
|
|
|
Profit for a dance studio |
2003-04-28 |
|
From Craig:
A dance studio charges $80 per student for a series of 2 hour lessons. The studio's costs are $30 per hour for the instructor, $15 per lesson for the room rental, and $3 per student for miscellaneous expenses. If x is the number of students enrolled in the class, express the studio's profit P(x) in terms of x. Find the profit if 10 students are enrolled in the class.
Answered by Penny Nom. |
|
|
|
|
|
|
A skill testing question |
2003-04-27 |
|
From Allan:
it is a contest Labatt Blue can you please give me the answer some people are saying 154 and some 34
Answered by Leeanne Boehm and Harley Weston. |
|
|
|
|
|
|
20% of 40% of 500 |
2003-04-27 |
|
From A student:
What is 20% of 40% of 500
Answered by Penny Nom. |
|
|
|
|
|
|
The product of four consecutive integers is 3024. |
2003-04-25 |
|
From pillar:
The product of four consecutive integers is 3024. What are those numbers.
Answered by Penny Nom. |
|
|
|
|
|
|
Gallons of rain |
2003-04-25 |
|
From Jocelyn:
If you have a surface of 6500 square feet and 1 inch of rain falls on the surface, how many gallons of water does this equal?
Answered by Penny Nom. |
|
|
|
|
|
|
38 minus 10 plus 12 divided by 4 times 16 |
2003-04-23 |
|
From James:
please help me work this math problem 38 minus 10 plus 12 divided by 4 times 16
Answered by Harley Weston. |
|
|
|
|
|
|
Hidden by the curvature of the Earth |
2003-04-23 |
|
From Shirley:
There are 2 six foot men. What would the distance be between them before one could not be seen because of the curvature of the earth?
Answered by Penny Nom. |
|
|
|
|
|
|
Two intersecting graphs |
2003-04-23 |
|
From Patty:
a) graph the equation x2 - y - 4 = 0
x2 + y2 = 9 on the same set of coordinate axes. I did not have a problem with this. The problem is part (b) of the question ask: Find all solutions of the system in part (a) algebraically. Express answers in decimal form, accurate to two decimal places.
Answered by Penny Nom. |
|
|
|
|
|
|
8 faces, 12 vertices, and 18 edges |
2003-04-22 |
|
From Thomas:
I would like to know the proper name for this geometrical solid. It has 8 faces, 12 vertices, and 18 edges?
Answered by Penny Nom. |
|
|
