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+259

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4/3+3m/5=41/15. Note that the both items of the left side can be reduced to the common denominator 15. (20 + 9m)/15 = 41/15. Breaking free of the denominator by multiplying both sides by 15 we get 20 + 9m = 41 => 9m = 21 =>m = 21/9 = 7/3

[input]solve(4/3+3*m/5=41/15, m)[/input]

scrutinizerSep 3, 2013

+259

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There were 360 rails of 8 meters length removed, all in all 360*8 = 2880 meters of removed rail sections. 2880/12 = 240 rails sections of 12 meters length each you need to place instead of old ones.

scrutinizerSep 3, 2013

+259

0

3(1/2)^4-2(1/2)^4+5(1/2)^2-4(1/2)+1 = (1/2)^4 + (1/2)(5*1/2 - 4) + 1 = (1/2)((1/2)^3 + 5*1/2 - 4) + 1 = (1/2)(1/8 - 3/2) + 1 = -(1/2)*(11/8) + 1 = 1 - 11/16 = 5/16

3(1/2)^4-2(1/2)^4+5(1/2)^2-4(1/2)+1

scrutinizerSep 3, 2013

0

First we need to calculate how many tons of feed each cow eats for each day.

1.92Tons/16 = 0.12Tons (So each cow eats 0.12Tons in 36 Days)
0.12Tons/36 = 1/30 Tons ( Each cow eats 1/30 Tons of food every day )
1 / 30 * 20 * 40 = 26.6 Tons (20 Cows * 40 Days * amount each cow eats every day)

GuestSep 3, 2013

+104

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Alan: a
Bob: b
Charlie: c

"Alan is twice the height of Bob" a = 2*b
"Charlie is 40cm taller than Bob" c = b+40cm

Total height: a+b+c = 410cm
2*b + b + b+40cm = 410cm = 4b + 40cm [-40cm]
4b = 410cm - 40cm = 370cm [/4]
b = 370cm/4 = 92.5cm

Insert b = 92.5cm into a = 2*b:
a = 2*92.5cm = 185cm

Insert b = 92.5cm into c = b+40cm:
c = 92.5cm + 40cm = 132.5cm

[input]solve(a+b+c=410[cm], a=2*b, c=b+40cm,a,b,c)[/input]

ApfelkuchenSep 3, 2013

+6

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poodlepotsSep 3, 2013

Sep 2, 2013

0

Basically what you are trying to find is the volume of a cylinder. To find the volume of a cylinder one needs to multiply the area of its base by its height. We know that the area of a circle is the radius squared times pi:
12x12x3.14= 452.389
Therefore you must multiply 452.389x30 to find 13571.680, or rather 13571.680 ft^2

GuestSep 2, 2013

+259

0

"Give the slope and the y intercept of the line" by what object, not clear? The slope can be determined if you express y: 3 x + 10 y = 5 => 10y = 5 - 3x => y = [5 - 3x]/10 =>

y = -0.3x + 0.5. arctan (-0.3) = -arctan (0.3)

[input]-atan(0.3)[/input]

Well, as is unclear your question about what by what is intercepted as it is, let's assume that the line intercepts Ox, we have to find x, i.e. let's assume that there such point A exists that the graph is inter-crossing Ox at the point A (x ; 0). Inserting 0 instead of y, we'll get 0 = -0.3x + 0.5 => 0.3x = 0.5 => x = 0.5/0.3 = 5/3. If we wish to find the coordinate y of the graph inter-crossing Oy, then we assume that there such point B exits, that B (0 ; y) => y = -0.3*0 + 0.5 = 0.5. Did I answer your question?

The graph is below

[input]plot(-0.3x + 0.5, x=-5..5, -5..5)[/input]

scrutinizerSep 2, 2013

+259

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Using the formulas of the sum trnasformation into the product we get (cos(80) + cos(40)) - cos(20) = 2*[cos(120/2)]*[cos(40/2)] - cos(20) = 2*[cos (60)]*[cos(20)] - cos(20) = cos (20)[2cos 60 - 1] =
= cos(20)[2*0.5 - 1] = cos(20)*0 = 0

cos(80)+cos(40)-cos(20)

scrutinizerSep 2, 2013

+259

0

You ought to rely on the fact that the sum of the angles of quadrilaterial is equal to 360 degrees. Let x be the value of one angle, y be the one of the other, z - the 3rd and w - the 4th. We have the firrst equation x + y + z + w = 360. Taken separately x = y - 11, z = 2y, w = 1.5z. Got the system {x + y + z + w = 360, x = y - 11, z = 2y, w = 1.5z}. Let's solve it for any chosen variable, y for example. In terms of y w = 1.5*2y = 3y, z = 2y, x = y - 11. Inserting them into the 1st equation, y - 11 + y + 2y + 3y = 360 => 7y = 371 = > y = 53 (degrees). Inserting into the subsequent equations we find x = 53 - 11 = 42, z = 2*53 = 106, w = 3*53 = 159 degrees. As you could possibly notice the found values satisfy the requirement of the four angles to form an ascending sequance.

[input]solve(x + y + z + w = 360, x = y - 11, z = 2y, w = 1.5z, x,y,z,w)[/input]

scrutinizerSep 2, 2013

+259

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If you have two variables then to find them you should have TWO equations system.

scrutinizerSep 2, 2013

0

Many thanks for your help - much appreciated!

GuestSep 2, 2013

0

If V is the volume of glass 1, then the volume of water in total is V*(2/3+3/4) and the volume of vinegar is v*(1/3+1/4)

The final ratio is (1/3+1/4):(2/3+3/4). You can add it on your own.

GuestSep 2, 2013

0

a better question: why did you write obelus instead of "divided by" or just "/"?

The answer to your question though is order of operations.

GuestSep 2, 2013

0

I don't think (s)he was talking about integrals.

f(x)=x^4-2x^2 = g(x)=2x^2

x^4-2x^2=2x^2

First, add 2x^2 to each side:

x^4=4x^2

Then divide by x^2

x^2=4

Then take the square root:

x=+-sqrt(4)=+-2

So there are two values for which f(x)=g(x) and those are x=2 and x=-2. Put those numbers into the equations to verify your answer

GuestSep 2, 2013

0

Well, they make $7 per t-shirt, so they need to sell $280/$7 tshirts.

GuestSep 2, 2013

0

Average Speed is distance traveled divided by the time it takes to travel that distance, in this case:

v=2.48m/(6.3*10^-6s)

That's in units of m/s

To convert units, just multiply by 1, where 1 could be for example 60s/1min and 1 inch/.0254m

So v=(2.48m*60s*1inch)/(6.3*10^-6s*1min*.0254m)

Then you get speed in units of (m*s*inch)/(s*min*m)

m and s cancel top and bottom and you have units of inch/min.

GuestSep 2, 2013

0

GuestSep 2, 2013

Sep 1, 2013

+104

0

I suppose you mean F(x) = ∫f(x)dx

F(x) = ∫f(x)dx = ∫(x^4 - 2x^2)dx = (x^5)/5 - (2x^3)/3

Solve F(x) = g(x) for x:
F(x) = g(x) = (x^5)/5 - (2x^3)/3 = 2x^2 [-2x^2]
(x^5)/5 - (2x^3)/3 - 2x^2 = 2x^2 * (x^3/10 - x/3 - 1) = 0

So we get
x_0 = 0
x_1 = 0

For the other values you could use methods like completing the square or just the polynomial division.
[input]solve((x^3)/10 - x/3 - 1 = 0)[/input]

ApfelkuchenSep 1, 2013

+104

0

Logarithm to base 11:
[input]log(73,11)[/input]

ApfelkuchenSep 1, 2013

+104

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x+y+z = f (fruits total)
x = oranges
y = apples
z = pears

"58% of the fruits at a stall are oranges" => x = f*0.58
"There are 240 more oranges than apples." => y = x - 240 = f*0.58 - 240
"The rest are apples and pears in the ratio of 3:4." => y*4/3 = (f*0.58 - 240)*4/3

x + y + z = (f*0.58) + (f*0.58-240) + (f*0.58-240)*4/3 = f
= -240-320 = f-f0.58-f0.58-f0.77333 = -0.9333333f
=> f = 560/0.93333333 = 600

ApfelkuchenSep 1, 2013

Aug 31, 2013

+104

0

ax²+bx+c = f(x)

f(0) = a0² + b0 + c = 10 => c = 10
f(1) = a1² + b1 + c = = a + b + 10 = 10.65 => a = 10.65-10-b = 0.65-b
f(2) = a2² + b2 + c = 4a + 2b + 10 = 11.34225
f(3) = a3² + b3 + c = 9a + 3b + 10 = 12.079496

Insert a into f(2):
4(0.65-b) + 2b + 10 = 11.34225 = 2.6 - 4b + 2b + 10 = 2.6 - 2b + 10
=> 2b = 12.6 - 11.34225 = 1.25775
=> b = 1.25775/2 = 0.628875

Insert b into f(3):
9a + 3(0.628875) + 10 = 9a + 1.886625 + 10 = 12.079496
=> 9a = 12.079496 - 10 - 1.886625 = 0.192871
=> a = 0.192871/9 = 0.0214301111

f(x) = 0.02x^2 + 0.63x + 10

ApfelkuchenAug 31, 2013

+104

0

abs(6x+8) = |6x+8| has to be 50.
Positive case: Replace || with ()
(6x+8) = 50 [-8]
6x = 42 [/6]
x = 7

Negative case: Replace || with -()
-(6x+8) = -6x - 8 = 50 [+8]
-6x = 58 [/-6]
x = -58/6 = -29/3

ApfelkuchenAug 31, 2013

+104

0

a/a = 1
=> (a/a+1) = 2
=> (1/a + 1)*(a/a + 1) = (1/a + 1)*2 = 2/a + 2

ApfelkuchenAug 31, 2013

+104

0

Inversely proportional means: F ~ 1/x^2
x is the distance in meters (m). F is the force in Newton (N).
Futhermore F = m*a (1N = kg*m/s^2)

1/m² is not equal to kg*m/s², so we have to add a const. value named n (as desired) with the unit kg*m^3/s^2.
Remember 1T = 1kg/(As^2)
=> kg*m^3/s^2 = T*m^3*A

So we have an equation like: F = n/x^2 with n = B*I*x^3 => F = B*I*x (have a look at the magnetic flux density)
In your case n would be 36Tm^3A

ApfelkuchenAug 31, 2013

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