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Compare the following logarithms in base 1/2 without a calculator: log(8) and log(512)

Compare through subtraction : log 0.5 (8)- log 0.5 (512) = xUsing logarithm rule in addition/subtraction: log a (b)+log a (c) = log a (b*c) ; log a (b)-log a (c) = log a (b/c) where a,b and c are constants (...
GA
Answered by Gael A. • Maths tutor
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y=7-2x^5. What's dy/dx?Find an equation for the tangent to the curve where x=1. Is itan increasing or decreasing function when x=-2?

dy/dx=-10x^4When x-1, gradient =-10 Tangent is then: y+10x=15When x=-2, dy/dx=-160 so a decreasing function
KL
Answered by Khai L. • Maths tutor
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What does a 95% confidence interval reflect?

It reflects the set of values for which 95% of a normally distributed sample lies, which tells us with 95% confidence that the mean value lies within this interval. 95% confidence means the likelihood that o...
CP
Answered by Caitlin P. • Maths tutor
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How to sketch a cubic function

Determine intersections with the x and y axis, intersections at x axis occur when y=0 and intersections with the y axis occur when x=0.2) Differentiate function to find stationary points (by setting the diff...
AP
Answered by Anya P. • Maths tutor
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Given the two curves y1 and y2, verify the two curves intersect at (-5,0) and (2,0)

y 1 = -3x 2 - 9x + 30 , y 2 = x 2 + 3x - 10Equate two curves ( y 1 = y 2 )Obtain following simplified quadratic: x 2 + 3x + 10 = 0Factorise to obtain ( x + 5 ) ( x - 2 ) = 0 and correct x values x = -5 , x =...
JP
Answered by James P. • Maths tutor
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