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3 notes &

I’m not sure what to do :/
it is clearly given that the median is bisecting the opposite side
for a)
you need to get only the cordinates of P to write the equation of line passing through P and O
p is mid point of BA
so p has cordinates 
(2b+2a)/2 , (2c+0)/2
or b+a, c
so equation is
y-y1 = m(x-x1) m is slope
y-0 = (c-0)/(b+a-0)(x-0)
simplify, you will get your answer

b) can be done the same way

c) now you have equation of two medians
op and aq
solve them to get the point of their intersection at G
compute equation or BR the same way I did for Op
to prove that third median passes through point of intersection G of medians op and aq, put the coordinates of G in equation of BR
it will satisfy and hence it is proved

I’m not sure what to do :/

it is clearly given that the median is bisecting the opposite side

for a)

you need to get only the cordinates of P to write the equation of line passing through P and O

p is mid point of BA

so p has cordinates 

(2b+2a)/2 , (2c+0)/2

or b+a, c

so equation is

y-y1 = m(x-x1) m is slope

y-0 = (c-0)/(b+a-0)(x-0)

simplify, you will get your answer

b) can be done the same way

c) now you have equation of two medians

op and aq

solve them to get the point of their intersection at G

compute equation or BR the same way I did for Op

to prove that third median passes through point of intersection G of medians op and aq, put the coordinates of G in equation of BR

it will satisfy and hence it is proved

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16 notes &

talk so little, say so much: FREE MATH TRICKS WOWOWVery simple math tips from a would-be math...

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FREE MATH TRICKS WOWOW

Very simple math tips from a would-be math teacher!!

1) multiplying big numbers.

instead of tackling things all at once, break them down.

for example, let’s do 34 X 15. Not many people can do this so readily in their heads, so here’s a different approach. Think of it…

awesome stuff

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1 note &

Transforming Linear Functions

Let g(x) be the indicated combined transformation of f(x)=x. Write the rule for g.

horizontal stretch by a factor of 5 followed by a horizontal shift right 2 units.



That’s what the problem says. I don’t really understand how you transform linear functions at all. I don’t know if I said enough in the above question for you to help me with it or not ^^;

horizontal stretch of a graph by a factor of n makes f(x) as f(x/n)

since your graph is stretched by a factor of 5, your f(x) is transformed to f(x/5) = x/5

a horizontal shift of n units right transforms f(x) to f(x-n)

in your graph, it is 2 units, so your function becomes f(x-2) = (x-2)/5

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0 notes &

Let g(x) be the indicated combined transformation of f(x)=x. Write the rule for g.

horizontal stretch by a factor of 5 followed by a horizontal shift right 2 units.

That’s what the problem says. I don’t really understand how you transform linear functions at all. I don’t know if I said enough in the above question for you to help me with it or not ^^;

horizontal stretch of a graph by a factor of n makes f(x) as f(x/n)

since your graph is stretched by a factor of 5, your f(x) is transformed to f(x/5) = x/5

a horizontal shift of n units right transforms f(x) to f(x-n)

in your graph, it is 2 units, so your function becomes f(x-2) = (x-2)/5

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0 notes &

Can you help with word problems?

1.) Train A goes 12mph slower than Train B. Train A travels 230 miles in the same time that Train B travels 290 miles. Find the speed of each train.

2.) Zeno takes 3 hr longer to paint a floor than it takes Lia. When they work together, it takes them 2 hrs. How long would each take to do the job alone?

3.) A boat travels 15 km/h in still water. If the boat travels 140 km downstream in the same time it takes to travel 35 km upstream. What is the speed of the river?

I’m not sure what sort of equations to use in order to set up the problem..

Any help would be great, thanks :)

very simple

1) let speed of train A is Va, B be Vb

given, Va = Vb - 12………………eqn 1

speed= distance/time

time taken is same for each of the train, let it be t

given, distance traveled by A/ speed of A = distance traveled by B/speed of B…just equating time

or

230/Va = 290/Vb

put Vb= Va + 12 from equation 1 and solve 

2) Let time taken by Lia to paint a floor be x hours.

Thus, time taken by Zeno would be x + 3 hours.

This simply means when alone, in 1 hour,

Lia completes 1/x of the floor, while

Zeno completes 1/(x+3) of the floor.

If working together, in 1 hour,

Both will complete 1/x + 1/(x+3) of the floor

Since if working together, it takes them 2 hours to complete the job, in 1 hour they would complete 1/2 of the whole floor, or in other word:

1/x + 1/(x+3) = 1/2

[(x+3) + x] / [(x)(x+3)] = 1/2

(2x+3)/(x^2+3x) = 1/2

2(2x+3)=(x^2+3x)

4x+6=x^2+3x

x^2-x-6=0

Solving for x, x=3 hours or x=-2 (Not acceptable, as time taken to paint a floor can’t be negative)

3) Let F = the downstream speed of the water.
Then the boat’s upstream speed is: 15 - F
The boat’s downstream speed is: 15 + F
Assume both the journeys mentioned take T hours, then using “speed x time = distance” we get:
Downstream journey: (15 + F)T = 140
Upstream journey: (15 - F)T = 35
Add the two formulae together:
(15 + F)T + (15 - F)T = 140 + 35
15T + FT + 15T - FT = 175
30T = 175
T = 35/6
Use one of the equations to find F:
(15 + F)T = 140
15 + F = 140/T
F = 140/T - 15
F = 140/(35/6) - 15
F = 24 - 15
F = 9
i.e. the downstream speed of the water is 9 kph
Therefore, the boat’s speed downstream is 15 + F = 15 + 9 = 24 kph.

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2 notes &

So will you math ed guys do me a favor?

kat523719:

Actually, any of you who would be willing please do it. I had to make this learning module for a class. Would you guys look at it and tell me what you think?

http://katsmathy.wordpress.com/learning-module/

it is very good, you used google docs to create your quizzes,

if you want to include grading too in google docs quizzes, like after a student finishes the test, he should be able to see his grades too, let me know.

or if you want to include multimedia too in the questions, let me know.

(Source: fangirlspiral0913)

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