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Show using mathematical induction that 8^n - 1 is divisible by 7 for n=1,2,3,...

First step: n=1 we have 8 1 -1=7 which is divisible by 7. Assumption step: 8 k -1 is divisible by 7. Induction step: Using the previous step we have that 8 k -1=7x. So 8 k = 7x+1. Therefore, 8 k+1 - 1=8(8 k ...
MC
Answered by Mike C. • Maths tutor
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Differentiate the expression x^6+5x^4+3 with respect to x

Using the general rule d/dx(a*x^n) = a *n * x^(n-1) and the linearity of the derivative operator, we obtain: 6x^5+20x^3+0 = 6x^5+20x^3
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Explore the significance of aspects of dramatic tragedy in the following passage and in relation to the play as a whole.

Introduction Shakespeare creates dramatic tragedy in the passage through Lear’s fatal decision to ‘divide in three our kingdom’. The irony of Lear’s action is heavy and the passage is infused with tragic imp...
SH
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Calculate (7 + √3)(7 - √3)

(7 + √3)(7 - √3) = 7 2 + 7√3 - 7√3 - (√3) 2 = 49 - 3 = 46Alternatively you can go straight to identifying that this is the difference between two squares, using the fact that (a + b)(a - b) = a 2 - b 2
IB
Answered by Isabel B. • Maths tutor
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State the interval for which sin x is a decreasing function for 0⁰ ≤ x ≤ 360⁰.

Draw a diagram of the graph y=sin x between the stated interval. Identify the two extrema. Required interval is in between the two points.
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