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Mathematics: Post your doubts here!
The book answer is correct. dy/dx =2x At the point (2, 4), gradient of tangent =2(2)=4, and hence gradient of normal = -1/4 Equation of normal is y-4 = -1/4 ( x-2) = -1/4 x +1/2 ie y = -1/4x +9/2 When this normal cuts the curve again, we set x^2 = -1/4x... -
Mathematics: Post your doubts here!
Differentiating y=9x+1/x wrt to x on both sides gives dy/dx = 9 -1/x^2 When the tangent is horizontal, dy/dx=0 =====> 9 -1/x^2 =0 x^2 =1/9 x= 1/3 or -1/3 When x=1/3, y= 6 When x= -1/3, y= -6 Hence, the required coordinates are (1/3, 6) and (-1/3, -6) (shown) Hope this helps. Peace. -
Mathematics: Post your doubts here!
You can sketch out the graph related to the function, and look at the set of x values specified for observation in the problem (ie the domain of the function). In this window of observation, locate the maximum and minimum y-values-these would give you the range of the function. Hope this... -
Mathematics: Post your doubts here!
Because the scalar product of (5, 0, 0) and the normal to the plane (2, -2, -1) equals 10, hence the point (5, 0, 0) lies on the plane. You can always choose another point if you want to, so long as the scalar product of that point and the normal to the plane equals 10. For example you could... -
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Mathematics: Post your doubts here!
Full solutions for vectors problem 6(i) and (ii) here: Hope this helps. Peace. -
Mathematics: Post your doubts here!
You are most welcome. Peace. -
Mathematics: Post your doubts here!
Previously solved 10(i) here, for your reference first: Solutions for 10(i) Hope this helps. Peace. -
Mathematics: Post your doubts here!
ln(1+y²) =2 x + 1/ln5 1+y²= e^ (2 x + 1/ln5) y²= e^ (2 x + 1/ln5) -1 (shown) Hope this helps. Peace. -
Mathematics: Post your doubts here!
Workings for Q5(ii) here: Hope it helps. Peace. -
Mathematics: Post your doubts here!
Get you started off first. For your Q9, I have solved this previously on my website which you can view here: http://www.whitegroupmaths.com/2011/10/applications-of-integration.html (look at Q3) Hope this helps. Peace. -
Mathematics: Post your doubts here!
Here you are: Solutions to Q7 Peace. -
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Mathematics: Post your doubts here!
Here are the full solutions for Q10: Hope this helps. Peace. -
Mathematics: Post your doubts here!
Q10 for you first here: Hope this helps. Peace. -
Mathematics: Post your doubts here!
For N = e^50ksin(0.02t) + ln125 , recognising that sin (0.02t) will reside between -1 and +1 inclusive, we can surmise that minimum value of sin (0.02t) will be exactly = -1. Hence, minimum value of N = e^50 * (0.01)(-1) +ln 125 = -5.185 * 10^(19) (shown) Hope this helps. Peace. -
Mathematics: Post your doubts here!
I post them right out of my head. -
Mathematics: Post your doubts here!
There you, Q7: Solutions for Q10 coming soon. Hope this helps. Peace. -
Mathematics: Post your doubts here!
For the former, you can rewrite 4(cos3x)^2 as 4 [ (cos6x+1)/2 ] = 2 cos6x +2 (Note this is achieved through the cosine double angle formula) For the latter, is k a constant or variable? Peace. -
Mathematics: Post your doubts here!
No problem, am glad it helped. Peace.
