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Trigonometry-basics/40533: This question is from textbook
Can you please check my answer? Our professor has shown us how to get these answers in decimal, and the book shows how to get them with radicals.
Question: A child pulls a wagon with a force of 40 lbs. The handle of the wagon makes a angle of 30° with the ground. Express the force vector F in terms i and j.
Answer: 17.32i+10j
Thank You
1 solutions
Answer 25992 by longjonsilver(2297)   on 2006-06-03 19:37:33 (Show Source):
You can put this solution on YOUR website!draw a simple line diagram...basically a right angled triangle. I assume that i is in the horizontal and j is in the vertical directions. Assuming this to be the case, we have the angle 30 degrees and the hypotenuse is 40.
What we are basically doing is "resolving" this into 2 component parts, at right angles to each other:
Horizontally, let this portion/projection of the 40 lb force be called H say, so that using trig:
cos30 = adj/hyp
Vertically, we get an equivalent for the projection, V:
sin30 = opp/hyp
So, the vector of the force pulling the handle can be thought of as  and 20j.
Force is 
Your answer is not correct - from a directional point of view it is fine, but the magnitude of 17.32i + 10j is not 400, it is  -->  which is 20.
jon.
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Polynomials-and-rational-expressions/40573: A viedo game has three villans which appear on screen at different intervals. One villan appears every 3 seconds, a second villan appears every 5 seconds, and a third villan appears every 12 seconds. When will all three villans appear at the same time? List all the possibilites ihn an organized way.
A)in 120 seconds B)in 150 seconds C)in 60 seconds D)in 30 seconds
1 solutions
Answer 25986 by longjonsilver(2297) on 2006-06-03 19:15:18 (Show Source):
You can put this solution on YOUR website!the answers have to be multiples of all 3 numbers: 3, 5 and 12.
Looking at 5 and 12, we have 60, 120, 180, 240, etc.
3 also goes into each of these, so this set of numbers is the answer.
Jon.
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Polynomials-and-rational-expressions/40186: Joe's Dairy Farm has 100 gallons of milk that is 4.6% butterfat. How much skimmilk (no butterfat) should be mixed with it to make milk that is 3.2% fat?
________gallons of milk should be added.
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A chemist has one solution that is 80% acid and another soulution that is 30% acid. How much of the first (80%) solution is needed to make a 400L solution that is 62% acid?
__________liters of the 80% solution is required.
Thanx
1 solutions
Answer 25619 by longjonsilver(2297) on 2006-06-01 06:01:09 (Show Source):
You can put this solution on YOUR website!read my Lesson on Mixtures. That should help you understand this type of question.
Anyway:
1. We cannot think about "amounts of butterfat, since the skimmed has none: its percentage is zero. So i have turned it around and considered the percentage of non-fat milk in the milk: the skimmed will be 100%.
100*0.954 + x*1.00 = (100+x)*0.968
95.4 + x = 96.8 + 0.968x
x - 0.968x = 96.8 - 95.4
0.032x = 1.4
x = (1.4)/(0.032)
x = 43.75 gallons
2. Start with 80% acid and a 30% acid.
--> Let there be x litres of the 80% solution acid. So, how much of the 30%? Answer is "the rest of the 400 litres ie (400-x). This is the tricky bit you need to "see".
So, 0.80x + 0.30(400-x) = 0.62*400
0.80x + 120 - 0.30x = 256
0.80x - 0.30x = 256 - 120
0.50x = 136
x = 272
So we need 272 litres of the 80% acid
and we need 128 litres of the 30% acid
jon.
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Geometric_formulas/40114: This question is from textbook geometry, measuring, reasoning, applying
The endpoints of a diameter of a circle are (-2,1) and (6, -5).
Write the standard equationof the circle?
1 solutions
Answer 25550 by longjonsilver(2297) on 2006-05-31 17:33:10 (Show Source):
You can put this solution on YOUR website!1. find the origin of the circle by finding the midpoint between the 2 quoted points.
2. Calculate the length of the diameter using the standard formula for length of a line. Find the radius from this length by dividing by 2.
3. Find the standard equation of a circle and put in the values of the coordinates of the centre and the length of the radius.
Done.
Jon.
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decimal-numbers/40023: Cany someone help me solve this problem?
Find the least common multiple of 24 and 48.
Thanks,
Sher
1 solutions
Answer 25430 by longjonsilver(2297) on 2006-05-31 09:11:30 (Show Source):
You can put this solution on YOUR website!multiples of 5 are 5,10,15,20,25,30,...etc
so we need to work out a few for both 24 and 48. When we reach a number that is in both the list for 24 and 48, then we stop...this is the lowest common multiple.
OK, 24 first.
24,48,... here we have 48 which is the other number. So straight away we have the lowest common multiple of 24 and 48 is 48.
jon.
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Numeric_Fractions/40024: Can someone help me with this problem?
Add:
4 2/7 + 1 5/7
Thanks,
Sher
1 solutions
Answer 25428 by longjonsilver(2297) on 2006-05-31 09:05:50 (Show Source):
You can put this solution on YOUR website!strictly, you do not need to do this method with this fractional sum, but practice it anyway:
4 and 2/7 is how many 7ths in total? 4 complete "pies" each divided into 7ths is a total of 28 7ths. Plus the other 2 gives a total of 30/7.
Similarly, 1 and 5/7 is 7/7 and 5/7 --> 12/7 in total
So, we have 30/7 + 12/7 which is 42/7 which happens to be 6.
jon.
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Graphs/39986: This question is from textbook algebra 1
can anybody tell me how to graph a function out of an equation
for example like f(x)= -2x^2 + 4x + 1
1 solutions
Answer 25427 by longjonsilver(2297) on 2006-05-31 09:00:27 (Show Source):
You can put this solution on YOUR website!when you say graph, you mean plot, on graph paper?
If so, pick values of x...your choice. Pick some easy ones like 0,1,2,3,4. Possibly -1,-2,-3 -4 too. For each, put it into the equation and find the value of f(x) ie "y".
Hopefully you will have picked enough x-values that your graph will cover the "interesting" part of the curve, namely the place it turns.
So...give it a go :-)
jon
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Polynomials-and-rational-expressions/40013: If a number is subtracted from its square, the result is 2. Find the number.
The length of a rectangle is 4 cm longer than the width. If the perimeter of the rectangle is 20 cm what is the area? Area=___cm^2
thanx
1 solutions
Answer 25422 by longjonsilver(2297) on 2006-05-31 08:44:30 (Show Source):
You can put this solution on YOUR website!Let number be x.
Its square is therefore 
So: a number is subtracted from its square: 
and this equals 2 --> 
so,  is a quadratic to solve.
(x-2)(x+1) = 0
(x-2) = 0 or (x+1) = 0
x=2 or x=-1
these are your 2 possible answers
jon.
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Polynomials-and-rational-expressions/40016: The sum of the digets of a two digit number is 10. if the digets were reversed, the new number would be 54 less than the original number. find the original number.
thanx
1 solutions
Answer 25421 by longjonsilver(2297) on 2006-05-31 08:37:54 (Show Source):
You can put this solution on YOUR website!Well, from just thinking about it:
19 and 91 --> difference is 72
28 and 82 --> difference is 54
37 and 73 --> difference is 46
46 and 64 --> difference is 18
so you have your answer there: 28 and 82
OK, algebraically:
Let the number be written as xy where x+y=10
xy means the number is (10x+y) like 28 is (10*2 + 8)
and yx is the reversed version: (10y+x)
and we are told that new number = old number - 54
--> 10y+x = 10x+y - 54
9y-9x = -54
or 9x-9y = 54 (just swapping all the signs over --> like moving the lefthand terms to the right hand side and vice versa)
So, we have:
9x-9y = 54
x+y = 10
9x-9y = 54
9x+9y = 90
Now, add the 2 equations together:
18x = 144
x = 144/18
x = 8
and so y must be 2.
So answer is: original number, xy, is 82
jon.
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Matrices-and-determiminant/39449: Use Cramer's Rule to solve this equation.
2x-5y=18
-x+3y=10
1 solutions
Answer 24882 by longjonsilver(2297) on 2006-05-25 18:02:21 (Show Source):
You can put this solution on YOUR website!M = 
Its determinant, D is:
D = (2)(3)-(-1)(-5)
D = 6-5
D = 1
Now repeat on
Dx = (18)(3)-(10)(-5)
Dx = 54+50
Dx = 104
and also on
Dy = (2)(10)-(-1)(18)
Dy = 20+18
Dy = 38
So, x = Dx/D
--> x = 104/1
--> x = 104
So, y = Dy/D
--> y = 38/1
--> y = 38
CHECK:
2x-5y
2(104)-5(38)
208-190
18... CORRECT
and -x+3y
-(104)+3(38)
-104+114
10... CORRECT
jon.
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Exponential-and-logarithmic-functions/39439: I need this for work ASAP.
What is the derivative
I need this for work ASAP.
What is the derivative
d/dx( f(x) ^ g(x) )
where ^ is the sign of EXPONENTIATION and f and g are function of x.
Please NOTE AGAIN that I am not talking about a compound function, I am talking about one function taken TO THE DEGREE of another.
thanks
1 solutions
Answer 24879 by longjonsilver(2297) on 2006-05-25 17:54:10 (Show Source):
You can put this solution on YOUR website!have a read of this i found on google:
http://www.physicsforums.com/showthread.php?t=87992
basically... take natural logs first then differentiate the whole thing.
Good luck :-)
Jon.
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