||| - Official Maths / Science Thread - |||

[DVSTT]

The Sharp EL-W516X is by far the best I have ever used thus far!

I have that one! Rell bess! It have quiz and stuff lol

[Corn Bird]

anyone has nice shortcuts to share? like easy ways of calculated long questions?

see this guy:

Ms. Arroyo asked the class to see if they could find the sum of the first 50 odd numbers. As everyone settled down to their addition, Terry ran to her and said, "The sum is 2,500." Ms. Arroyo thought, "Lucky guess," and gave him the task of finding the sum of the first 75 odd numbers. Within 20 seconds, Terry was back with the correct answer of 5,625.

How does Terry find the sum so quickly?

this is actually a story about gauss

Another famous story has it that in primary school after the young Gauss misbehaved, his teacher, J.G. Büttner, gave him a task : add a list of integers in arithmetic progression; as the story is most often told, these were the numbers from 1 to 100. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant Martin Bartels.

http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss


for the sum of the first fifty odd numbers, the method is to duplicate the sum in reverse order. so the following fifty terms

1 + 3 + 5 + ... + 97 + 99

added to

99 + 97 + 95 + .... + 3 + 1

gives

(1 + 99) + (3 + 97) + ... + (99 + 1)

= 100 + 100 + ... + 100 (50 times)
=5000

and then divide by 2 to account for the duplication to get 5000/2=2500. exactly the same idea is used to prove the sum of n terms in an a.p.

see

http://en.wikipedia.org/wiki/Arithmetic_progression

[Ronaldo95163]

APs and GPs are so awesome

@DVSTT Drill mode FTW!

[Corn Bird]

ok this is mess. lol

An area in the first Cartesian coordinate is bounded by one function, the line x = 1, and the x axis (y = 0).

The boundary function is y = (1/x) starting at x =1 and it goes to x = infinity.

Rotate this area about the x axis so it creates a volume.

Calculate the surface area and the volume of this object.

got the volume as pi and the surface area as infinite

*edit* for the surface area, can in fact get

(1+x)^{1/2}>1

for x>0 which is what we would need in this case

[stev]

^^^correcto!!!

that was the answer!!! well done corn bird

[redmanjp]

How bout this

A carpenter makes tables and chairs. Each table can be sold for a profit of £30 and each chair for a profit of £10. The carpenter can afford to spend up to 40 hours per week working and takes six hours to make a table and three hours to make a chair. Customer demand requires that he makes at least three times as many chairs as tables. Tables take up four times as much storage space as chairs and there is room for at most four tables each week.

To get maximum profit, how much tables & chairs should he make & how much profit would he get?

[Corn Bird]

How bout this

A carpenter makes tables and chairs. Each table can be sold for a profit of £30 and each chair for a profit of £10. The carpenter can afford to spend up to 40 hours per week working and takes six hours to make a table and three hours to make a chair. Customer demand requires that he makes at least three times as many chairs as tables. Tables take up four times as much storage space as chairs and there is room for at most four tables each week.

To get maximum profit, how much tables & chairs should he make & how much profit would he get?

let t denote tables and c denote chairs. this looks like an integer linear programming problem with objective function

P=30t+10c

and constraints

6t+3c \leq 40
3t \leq c
t+(c/4) \leq 4
0 \leq t
0 \leq c


using this formulation, maple gives

that is max profit is 140 at chairs=8 and tables=2

[Corn Bird]

^^^correcto!!!

that was the answer!!! well done corn bird

thks stve

[nervewrecker]

for the electrical dudes:

resistor bands, 4,5 and 6

http://samengstrom.com/5107960/en/read/ ... 613,610938

inductance

http://www.consultrsr.com/resources/eis/induct5.htm

wire resistance chart

http://www.cirris.com/testing/resistance/wire.html

some conversions
• Speed
• Length
• Temperature
• Acceleration
• Angles
• Area
• Astronomy
• Computer
• Cooking
• Density
• Electric capacitance
• Energy
• Flow rate (Mass)
• Force
• Frequency
• Iluminance
• Luminance
• Power
• Torque
• Viscosity dynamic
• Viscosity kinematic
• Viscosity oil
• Volume
• Weight
• Pressure

http://www.krstarica.com/eng/conversion ... ednost=4.7

more here:

http://www.amb.org/audio/

scroll down to online calculators.

[Ronaldo95163]

Nice! @Corn Bird

Simple Differentiation question for you guize

Given the curve y=2x^3-21x^2+78x-98
Calculate:
a)The gradient at the point (3,1)
b)The x-coordinate of the point at which the tangent to the curve is parallel to the tangent (3,1)


BTW nice stuff there nerve

[Trini Hookah]

Nice post there nerve.

[stev]

nice post nerve.

here's a little one for u guys:

How can you add eight 8's to get the number 1,000? (only use addition)

[Trini Hookah]

888 + 88 + 8+ 8 + 8 = 1000

[Ronaldo95163]

Nice^

re-re-re-re-related rates
A sphere is increasing in volume at the rate of 20∏cm^3/s. Given that the volume of a sphere of radius r is (4/3)∏r^3, calculate the radius of the sphere at the instant when the radius is increasing at the rate of 0.2cm/s

The surface area of a sphere is increasing at a constant rate of 6cm^2/s. Given that the surface area of a sphere of radius r is 4∏r^2 and the volume is (4/3)∏r^3, find the rate of increase of the radius and the volume at the instant when the radius is 5cm

[matthewmazda]

888 + 88 + 8+ 8 + 8 = 1000

had to add it to believe it

[Ronaldo95163]

Corn Bird what version of Maple is that?

[Corn Bird]

Corn Bird what version of Maple is that?

maple 14 -- i think it is a couple years old. latest version is maple 16

[Ronaldo95163]

I got a copy of Maple 15....just installed it. It's awesome!

[stev]

[Ronaldo95163]

bump

[KURMAman]

Maths Goblin will be proud!

[Ronaldo95163]

Ched ded bai......will post some more calculus problems when I get a chance.....I posted a few higher up as well

[DVSTT]

Nice^

re-re-re-re-related rates
A sphere is increasing in volume at the rate of 20∏cm^3/s. Given that the volume of a sphere of radius r is (4/3)∏r^3, calculate the radius of the sphere at the instant when the radius is increasing at the rate of 0.2cm/s

The surface area of a sphere is increasing at a constant rate of 6cm^2/s. Given that the surface area of a sphere of radius r is 4∏r^2 and the volume is (4/3)∏r^3, find the rate of increase of the radius and the volume at the instant when the radius is 5cm

These kind of questions are so damn annoying! Always get trouble with it!

[Ronaldo95163]

Nice^

re-re-re-re-related rates
A sphere is increasing in volume at the rate of 20∏cm^3/s. Given that the volume of a sphere of radius r is (4/3)∏r^3, calculate the radius of the sphere at the instant when the radius is increasing at the rate of 0.2cm/s

The surface area of a sphere is increasing at a constant rate of 6cm^2/s. Given that the surface area of a sphere of radius r is 4∏r^2 and the volume is (4/3)∏r^3, find the rate of increase of the radius and the volume at the instant when the radius is 5cm

These kind of questions are so damn annoying! Always get trouble with it!

Give them a shot. Write down given information in terms of calculus...things like formulae, derivatives etc ... take for example the first one

dV/dt = 20pi
V=4/3pi(r)^3
r=?
dr/dt=0.2

V=4/3pi(r)^3
dV/dt = 4/3pi.3r^2dr/dt(Implicit differentiation) + 0.r^3
dV/dt = 4pir^2dr/dt
20pi = 4pir^2(0.2)
r = sqrt(20pi/4pi(0.2)
r = 5

Radius = 5cm

[Ronaldo95163]

Ched ded

Hold this fellas

The three-week-long cycling race, Tour de France, is said to be one of the most grueling sporting events in the world.

i) If a cyclist of mass 70kg uses a bicycle of mass 7kg, how much work must the cyclist do against gravity in order to ascend to 2100m from sea level(0m)?
ii)One particular descent goes from 2100m to 1600m. Assuming the work done against friction is 90% of the potential energy change of the cyclist and the cycle, what increase in speed in km/h can a rider attain by the end of the descent?
iii)What is the average rate of energy conversion of the cyclist and cycle if the descent in part(ii) takes 1 minute at constant speed?

Use acceleration due to gravity as 10ms^-2

[Corn Bird]

i) If a cyclist of mass 70kg uses a bicycle of mass 7kg, how much work must the cyclist do against gravity in order to ascend to 2100m from sea level(0m)?
ii)One particular descent goes from 2100m to 1600m. Assuming the work done against friction is 90% of the potential energy change of the cyclist and the cycle, what increase in speed in km/h can a rider attain by the end of the descent?
iii)What is the average rate of energy conversion of the cyclist and cycle if the descent in part(ii) takes 1 minute at constant speed?

Use acceleration due to gravity as 10ms^-2

(i) mgh=(77)(10)(2100)
(ii) increase in kinetic energy=(.1)(77)(10)(500); assuming that cyclist begins descent at
zero velocity then increase in speed dv is the square root of (2)(.1)(10)(500). it's probably
a little harder to show that if the cyclist starts at positive speed then the increase in
speed will be smaller than this
(iii) no energy is converted to k.e. as cyclist travels at constant speed.
cyclist converts/loses his p.e. of (77)(10)(500) to friction in 60 s, so rate of conversion is
(77)(10)(500)/60 W


by the way gracen, this site for math students at any level may be interesting

http://math.stackexchange.com/

while this site

http://mathoverflow.net/

is apparently for research mathematicians

[Ronaldo95163]

i) If a cyclist of mass 70kg uses a bicycle of mass 7kg, how much work must the cyclist do against gravity in order to ascend to 2100m from sea level(0m)?
ii)One particular descent goes from 2100m to 1600m. Assuming the work done against friction is 90% of the potential energy change of the cyclist and the cycle, what increase in speed in km/h can a rider attain by the end of the descent?
iii)What is the average rate of energy conversion of the cyclist and cycle if the descent in part(ii) takes 1 minute at constant speed?

Use acceleration due to gravity as 10ms^-2

(i) mgh=(77)(10)(2100)
(ii) increase in kinetic energy=(.1)(77)(10)(500); assuming that cyclist begins descent at
zero velocity then increase in speed dv is the square root of (2)(.1)(10)(500). it's probably
a little harder to show that if the cyclist starts at positive speed then the increase in
speed will be smaller than this
(iii) no energy is converted to k.e. as cyclist travels at constant speed.
cyclist converts/loses his p.e. of (77)(10)(500) to friction in 60 s, so rate of conversion is
(77)(10)(500)/60 W


by the way gracen, this site for math students at any level may be interesting

http://math.stackexchange.com/

while this site

http://mathoverflow.net/

is apparently for research mathematicians

Niceeee. I did the question earlier but I didn't get your answers for the last two parts...my mistake was that I used 0.9 instead of 0.1




Thanks for the links as well

[Ronaldo95163]

More Calculus

A box with square base has no top. If 64cm^2 of the material is used, what is the maximum possible volume for the box?

[nervewrecker]

More Calculus

A box with square base has no top. If 64cm^2 of the material is used, what is the maximum possible volume for the box?

or cm^3?

[nervewrecker]

oh, wait, I not get the question, is the 64cm^2 of material that make up the 5 sides?