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Some calculus problems |
2004-04-01 |
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From Weisu:
I have questions about three word problems and one
regular problem, all dealing with derivatives.
- Find all points on xy=exy where the tangent line
is horizontal.
- The width x of a rectangle is decreasing at 3 cm/s,
and its length y is increasing at 5 cm/s. At what rate
is its area A changing when x=10 and y=15?
- A car and a truck leave the same intersection, the
truck heading north at 60 mph and the car heading west
at 55 mph. At what rate is the distance between the
car and the truck changing when the car and the truck
are 30 miles and 40 miles from the intersection,
respectively?
- The production P of a company satisfies the
equation P=x2 + 0.1xy + y2, where x and y are
the inputs. At a certain period x=10 units and y=8
units. Estimate the change in y that should be made to
set up a decrease of 0.5 in the input x so that the
production remains the same.
If you could just give me some hints on these
questions, I'd really appreciate it. Thanks!
Answered by Penny Nom. |
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The intersection of two graphs |
2004-03-31 |
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From Benjanim:
How do I find the points of intersection of the two functions:
1) y = 2 - (e^-x)
2) y = 1 + (x^2)
I know that I have to set them equal to each other, but I can't solve for x. Please help :-)
Answered by Penny Nom. |
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Algebraic simplification |
2004-03-31 |
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From Chris:
Simplifying Exponents
Question
b^5d^2/b^3d^8
Answered by Penny Nom. |
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The degree sequence of a graph |
2004-03-31 |
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From Ali:
How can i find out {6,6,5,5,5,3,2}is not the sequence of the points of a simple graph,without drawing it?
Answered by Penny Nom. |
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Replacement times for TV sets? |
2004-03-31 |
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From Barb:
Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Estimate the probability that for 250 randomly selected TV sets, at least 15 of them have replacement times greater than 10.0 years.e
Answered by Andrei Volodin and Penny Nom. |
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A derivative |
2004-03-31 |
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From A student:
What is the nth derivative of f(x) =(2x)/(1-(x2))?
Answered by Harley Weston. |
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The height of a building |
2004-03-31 |
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From Nat:
Two buildings are 26.3m apart. From the top of the shorter building the angle of elevation to the top of the taller building is 35.9 degrees and the angle of depression to the base of the taller building is 54.7 degrees. What is the height of the taller building?
Answered by Penny Nom. |
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425 cc's of a saline solution |
2004-03-30 |
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From Julie:
425 cc's of a saline solution is equal to how much in lbs-weight??
Answered by Harley Weston. |
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n! > n^2 |
2004-03-30 |
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From Jose:
How can you prove by mathematical induction that:
n! > n2.
Answered by Penny Nom. |
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A stained glass window |
2004-03-29 |
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From Kay:
I'm doing a stain glass project and it's on a 4 foot across octagonal window...and I'm trying to set up the pattern and I don't know how long the sides are!
Answered by Penny Nom. |
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Numbers around a circle |
2004-03-28 |
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From Rebecca:
my maths question is use the numbers 1,2,3,4,5,6 and 7 place each number in a circle so each line adds up to 12. There are seven circles, six on the outside and one in the middle. Each number lines up with the middle number and the outside numbers line up with the one directly across from it as if a line was going through the middle number circle.
Answered by Penny Nom. |
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Percentage difference |
2004-03-28 |
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From Someone:
what is the percentage difference between 157 to 251
Answered by Penny Nom. |
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Maximizing the area |
2004-03-27 |
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From Petey:
Please could you tell me why for my coursework (where I have to find the largest area that a fence 1000m long can cover) why I should only test equilateral and isoceles triangles? We were told NOT to do right angled triangles but I was wondering why not?
Answered by Penny Nom. |
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The volume of a sphere |
2004-03-26 |
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From Mike:
I was in class today and I learned how to calculate the volume of a sphere. I understood it easily but can't find the logic behind it. So here are my questions, in the formula why is the radius cubic and not squared? And what does 4/3 have to do with it?
Answered by Penny Nom. |
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z^2 = 3 - 4i |
2004-03-26 |
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From John:
Solve: Z^2 = 3 - 4i
Answered by Harley Weston. |
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