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Mathematicians, Come And Try These Four Challenges. by Martinez39(m): 1:12pm On Feb 14, 2019 |
NB : Show your working 1) Give me the formula for the volume V of a solid formed by taking a sphere of radius R and boring a cylindrical hole of radius r through it with the centre of the sphere lying on the axis of symmetry of the cylinder. 2) Find the mass of the solid sphere of radius 5 metres whose variable density at every point on the sphere is such that it is linearly proportion to the distance from the centre of the sphere. 3) Give me the coordinates of the centre of the region in the plane bounded by the graphs of f(x) = 4 - x² and g(x) = x + 2 ? 4) I placed the following six masses : 7kg, 6kg, 5kg, 4kg, 3kg and 2kg on the cartesian plane and they have the following coordinates (2, 3), ( ½, 4), (-3, 2), (-4, 1), (3, - 2) & (1, 1) respectively. What are the coordinates of the point on which I can balance the cartesian plane on the tip on a pencil without it tipping over? |
Re: Mathematicians, Come And Try These Four Challenges. by Nobody: 3:15pm On Feb 14, 2019 |
Martinez39: Can you explain number 4 a bit further? |
Re: Mathematicians, Come And Try These Four Challenges. by Martinez39(m): 3:45pm On Feb 14, 2019 |
Darivie04:When you place various masses on a plane, there is a point on the plane at which the plane(together with the masses) would balance on a pencil tip. What is that centre of balance for the mass system I gave in question four? |
Re: Mathematicians, Come And Try These Four Challenges. by Nobody: 6:02am On Feb 15, 2019 |
Will be dropping solutions for 1,3 and 4 later. Number 2 still seems a bit confusing though..I would need some explanations on that. |
Re: Mathematicians, Come And Try These Four Challenges. by Martinez39(m): 9:00am On Feb 15, 2019 |
Darivie04:Thanks. Number 2 was incomplete. I have modified it. |
Re: Mathematicians, Come And Try These Four Challenges. by Martinez39(m): 9:55am On Feb 16, 2019 |
@Nurrex What's wrong? Why are you posting closed posts? |
Re: Mathematicians, Come And Try These Four Challenges. by Martinez39(m): 10:03pm On Feb 19, 2019 |
Mathematicians no dey Nairaland?
|
Re: Mathematicians, Come And Try These Four Challenges. by Nobody: 6:36pm On Feb 20, 2019 |
Sorry oh! I've been busy. 1 Like 1 Share |
Re: Mathematicians, Come And Try These Four Challenges. by CodeTemplar: 10:21pm On Apr 15, 2019 |
Martinez39:-0.1111, 2.03737 I will upload workings later. I am on android and can't type comfortably as I would have loved but let me try. Just start from coordinate 0,0 and treat the x and y coordinates as the x and y magnitude of the weights. This will require us to multiply the x and y value by the weight attached to each point.That gives the resultant x and y axis weight component of all loads. Next step is to add them all together ( all x axis added together separately from y axis ) finally divide by the net weight of loads available. |
Re: Mathematicians, Come And Try These Four Challenges. by CodeTemplar: 9:20am On Apr 16, 2019 |
Martinez39:Find the inspection of the two equations: 4-X² = x+2 gives X²+X-2=0 and this gives X= -2 and 1 substituting these values in the equations gives values for y as 0 and 3. This corresponds to point (1,3) and (-2,0) The centre of the equation should be answer and is (-0.5, 1.5) Please respond and tell if I got any right. |
Re: Mathematicians, Come And Try These Four Challenges. by Nobody: 9:42am On Apr 16, 2019 |
CodeTemplar:Its wrong, you can plot it and check. You're supposed to find center of the region bounded. 1 Like |
Re: Mathematicians, Come And Try These Four Challenges. by Martinez39(m): 11:06am On Apr 16, 2019 |
CodeTemplar:The sum of moments about the y-axis is: Σ(mixi) = (7 × 2) + (6 × ½) + (5 × -3) + (4 × -4) + (3 × -2) + (2 × 1) = -18 The sum of moments about the x-axis is: Σ(miyi) = (7 × 3) + (6 × 4) + (5 × 2) + (4 × 1) + (3 × -2) + (2 × 1) = 55 The sum of masses Σmi = 7 + 6 + 5 + 4 + 3 + 2 = 27. The point of balance is (a, b), where a = Σ(mixi) ÷ Σmi = -2/3 b = Σ(miyi) ÷ Σmi = 55/27 Point of balance is (-2/3 , 55/27). |
Re: Mathematicians, Come And Try These Four Challenges. by CodeTemplar: 11:16am On Apr 16, 2019 |
Martinez39: I think I made a mistake in the x-axis then. I used MS Excel thinking I could copy it into Nairaland for better formatting but, as you can see... I got -3 in the part where you got -18. 1 Like 1 Share |
Re: Mathematicians, Come And Try These Four Challenges. by CodeTemplar: 5:13pm On Apr 16, 2019 |
Darivie04:I understand you now. I was working with the assumption that the equation of the line connecting the two intersections is their middle. I think I need sum both equations and divide by two to get and equation of their average at at points. I will try that. |
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