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Math Questions

Pat is 20 years older than his son Patrick. In 2 years Pat will be twice as old as Patrick. How old are they now?

Pat is 20 years older than his son Patrick. In 2 years Pat will be twice as old as Patrick. How old are they now?

One number is nine more than twice another. If their sum is decreased by ten, the result is fourteen.

suppose patrick’s age is X. so pat’s age is 20+x

in two years, pat’s age will be 20+x+2

and patrick’s age will be x+2

given that 20+x+2 = 2(x+2)

22+x = 2x+4

or x = 18 i.e patrick’s age is 18 years. and pat’s age is 20+x = 20+18 = 38 years. 

let first number be x 

and 

second number be y

it is given that x = = 2x+9

and x+y - 10 =14

solve these two equations and you would get the answer


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the probability that a city bus ready for service when needed is 84%, and the probablity of a working bus with a radio is 67%. Find the probability of a bus chosen at random with a radio and that’s ready for service.

thebittersweetkingdom:

welp?

Probability that a bus is ready for service is .84 = P1
probability that the bus is ready for service and has a working radio = . 67 = P2
probability that it has a working radio and is already ready for service 

 =P2/P1

=.67/.84=.798=79.8%

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desultoryfluke asked: how come point x=0 y=0 the slope is indeterminate. I look at the graph it makes sense, but can you give me a definite answer why?

yeah. at point x= 0 and  y = 0, i.e the origin, the curve has two tangents. By the defintion of a tangent, a tangent is a line that passes through one and only point of a curve.

hope that makes sense

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3 notes &

Ask me maths: HELP WITH CALC PLEASE

desultoryfluke:

desultoryfluke:

IF YOU EXPLAIN TO ME HOW TO DO THIS QUESTION, I’LL LOVE YOU FOREVER.

So the original function is

http://www.wolframalpha.com/input/?i=2%28x%5E2%2By%5E2%29%5E2%3D25%28x%5E2-y%5E2%29

The derivative is

Man, thanks, how can I repay you, that is freaking awesome.

just share this tumblr blog. you don’t have to repay me anything. 

if you have any further queries, feel free to ask.

I might reply late, but I do reply.

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3 notes &

HELP WITH CALC PLEASE

desultoryfluke:

IF YOU EXPLAIN TO ME HOW TO DO THIS QUESTION, I’LL LOVE YOU FOREVER.

So the original function is 

http://www.wolframalpha.com/input/?i=2%28x%5E2%2By%5E2%29%5E2%3D25%28x%5E2-y%5E2%29

The derivative is 

http://www.wolframalpha.com/input/?i=%2825x-4x%5E3-4xy%5E2%29%2F%284x%5E2y%2B4y%5E3%2B25y%29

How do I find the points on the original function where the tangent line is horizontal.

Tangent is horizontal when dy/dx = 0

x (25 - 4x^2 - 4y^2) / [y (4x^2 + 4y^2 + 25)] = 0
x (25 - 4x^2 - 4y^2) = 0

x = 0 and  25 - 4x^2 - 4y^2 = 0 

=> x^2 + y^2 = 25/4

put these values back into the original equation

x = 0
2(0+y^2)^2 = 25(0-y^2)
2y^4 + 25y^2 = 0
y^2 (2y^2 + 25) = 0
y = 0 or  y^2 = -25/4( you reject this solution)

so you get a point x = 0 and  y = 0 and at this point slope is indeterminate.

x^2 + y^2 = 25/4

2(x^2+y^2)^2 = 25(x^2-y^2)
2(x^2+y^2)^2 = 25(x^2+y^2-2y^2)
2(25/4)^2 = 25(25/4-2y^2)
625/8 = 625/4 - 50y^2
50y^2 = 625/4 - 625/8
50y^2 = 625/8
y^2 = 25/16
y = 5/4 and -5/4

put values of y so obtained here in this equation

x^2 + y^2 = 25/4

you would get values of x too.


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