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2 unit maths revision (1 Viewer)

cutemouse

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It's 60 degreez.



Cross multiply x=


Alternatively, grab a protracter and hold it against your clock and measure the angle when it's 2:00.
Okay my bad. I thought I wrote 2:15. Derp.

I should really start using pen and paper for maths...
 

AAEldar

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If we square x, don't we square
Wouldn't it be (Don't go harsh on me)
Nope, what he's doing is putting the under the square root sign. So . It's like making a common denominator on a fraction, you're just multiplying by in that case, and here you're putting the under the square root sign by making it .
 
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NEW QUESTION:

Use simpsons rule with 4 sub intervals to estimate the area enclosed by the curve y= e^(x) +1 , and the lines y=1.5 , y=3.5 and x=0.

give answer to two decimal places
 
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cutemouse

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You need to split the area into two integrals. Take one of them with abs value maybe.
 
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You need to split the area into two integrals. Take one of them with abs value maybe.
yeh but looking back at it , there wouldnt be a way whereby you could use 5 function values and still isolate the "negative" part of the integral and take its absolute value. thats what happens when you make questions up on the spot
 

Squishxmishyx

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Nope, what he's doing is putting the under the square root sign. So . It's like making a common denominator on a fraction, you're just multiplying by in that case, and here you're putting the under the square root sign by making it .
THANKS BRO!! <3 <3 <3

Someone do this... preferably before tonight =]

Question.
a) The sum of the radii of two circles is 100cm. If one of the circles has a radius of x cm, show that the sum of the areas of the two circles is given by


b) Find the value of x for which A is least.
 
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A= 2 pi ( x^2 -100x +5000 )

dA/dx = 2 pi ( 2x -100 ) [ note the constants remain out front, and we differentiate the inside ]

set equal to zero

so 2x-100 =0

x=50

now the second derivative is 2 pi ( 2 ) = 4 pi, which is positive, so the graph is concave down, and thus gives a minium value
 
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for part a.

let radii be x and y

therefore x+y = 100

and the Area of the two circles = pi x^2 + pi y^2 = pi ( x^2 +y^2 )

now rearrage the first eqn for y, ie y=100-x, and sub into the above

A= pi ( x^2 + ( 100-x)^2 )
expand

A= pi [ x^2 + 10000-200x +x^2 ]

factor out a factor of 2

so A = 2pi [ x^2 -100x +5000]
 

SpiralFlex

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Let the radius be such that the other radius is

Now,











Working on second question now. Too late, Bored beat me to it.
 

Squishxmishyx

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Thank you Matthew Goodwin, you're my hero!
And SpiralFlex, are you doing maths accelerated o.o.
How come you know how to do this...

I'll continue the questions so I don't seem like a whore.
The distance between the sun and the earth is approximately . The sun subtends an angle of approximately at a point on the earth. Calculate the approximate diameter of the sun.
 
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Thank you Matthew Goodwin, you're my hero!
And SpiralFlex, are you doing maths accelerated o.o.
How come you know how to do this...

I'll continue the questions so I don't seem like a whore.
The distance between the sun and the earth is approximately . The sun subtends an angle of approximately at a point on the earth. Calculate the approximate diameter of the sun.

isnt that a worked example in cambridge??

its just using the arc length formula

l= r theta


where theta is in radians
 

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