Questions by MathsGee

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Interactive Content: Berry Info Wall

asked Jan 31 in Mathematics | 4 views

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Solve the following equation and round your answer off to three decimal places: \[ 2^x=3 \]

asked Jan 22 in Mathematics | 13 views

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Simplify the following using the laws of logarithms:

asked Jan 22 in Mathematics | 14 views

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Prove that \(\log _a x=\frac{\log _b x}{\log _b a}\)

asked Jan 22 in Mathematics | 11 views

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Simplify \(\frac{\log 16}{\log 4}\)

asked Jan 22 in Mathematics | 9 views

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SImplify \(\frac{\left(\log _2 8\right)^2}{\log _2 8^2}\)

asked Jan 22 in Mathematics | 11 views

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simplify \(\log _3 \sqrt{27}\)

asked Jan 22 in Mathematics | 11 views

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Simplify \(\log _3 \frac{1}{27}\)

asked Jan 22 in Mathematics | 12 views

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simplify \(-\log 4-\log 25\)

asked Jan 22 in Mathematics | 12 views

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simplify \(\log 20+\log 30-\log 6+\log _4 1\)

asked Jan 22 in Mathematics | 12 views

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Simplify using laws of logs \(\log _3 27-\log _3 3\)

asked Jan 22 in Mathematics | 12 views

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Simplify \(\log _9 27+\log _9 3\)

asked Jan 22 in Mathematics | 11 views

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Prove that \(\log _a a=1\)

asked Jan 22 in Mathematics | 14 views

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Using the laws of logarithms, expand \(\log _4\left(\frac{5}{x}\right)\)

asked Jan 22 in Mathematics | 11 views

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Expand \(\log_{3}5x\)

asked Jan 22 in Mathematics | 7 views

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Prove that \(\log _a x^m=m \log _a x \)

asked Jan 22 in Mathematics | 17 views

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Prove that \(\log _a\left(\frac{x}{y}\right)=\log _a x-\log _a y \)

asked Jan 22 in Mathematics | 14 views

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Prove that \(\log _a(x \times y)=\log _a x + \log _a y \)

asked Jan 22 in Mathematics | 14 views

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Determine the domain of the function \(f(x)=\log _2(1-2 x)\).

asked Jan 22 in Mathematics | 11 views

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The function \(f: x \rightarrow \log _a x\) passes through the point \((4 ;-2)\).

asked Jan 22 in Mathematics | 19 views

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What is the inverse function of \(g(x)=\left(\frac{1}{2}\right)^x\)

asked Jan 22 in Mathematics | 11 views

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What is the inverse function of \(f(x)=\frac{1}{2} x+3\)?

asked Jan 22 in Mathematics | 13 views

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What is the inverse function of \(f(x)=2 x-4\)?

asked Jan 22 in Mathematics | 10 views

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Define an inverse function

asked Jan 22 in Mathematics | 15 views

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What is the horizontal line test for functions?

asked Jan 22 in Mathematics | 9 views

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What is the vertical line test for functions?

asked Jan 22 in Mathematics | 11 views

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What is fractional calculus?

asked Jan 22 in Mathematics | 10 views

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Are one-to-many relations considered as functions?

asked Jan 22 in Mathematics | 10 views

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What is a many-to-one function?

asked Jan 22 in Mathematics | 9 views

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What is a one-to-one function?

asked Jan 22 in Mathematics | 12 views

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In an arithmetic sequence \(S_n=n^2-2 n\). Use your formula in 2 to determine the value of:

asked Jan 21 in Mathematics | 10 views

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Show without multiplying the terms out.

asked Jan 21 in Mathematics | 10 views

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If \(\sum_{m=1}^5(x-3 m)=\sum_{m=1}^8(x-3 m)\), prove that \(\sum_{r=1}^{13}(x-3 m)=0\).

asked Jan 21 in Mathematics | 16 views

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If \(a^2(c-b) ; a(c-b) ; b-a\) forms a geometric sequence, prove that \(a ; b ; c\) forms an arithmetic sequence.

asked Jan 21 in Mathematics | 8 views

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If \(a x^2+2 b x+c=0\) has equal roots, prove that \(a ; b ; c\) forms a geometric sequence.

asked Jan 21 in Mathematics | 14 views

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Solve simultaneously for

asked Jan 21 in Mathematics | 16 views

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Consider the geometric sequence: \(\quad 8 x^2 ; 4 x^3 ; 2 x^4 ; \ldots \ldots \ldots\)

asked Jan 21 in Mathematics | 10 views

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What is the greatest value of \(p\) for which the series \(\sum_{k=1}^p 10(3)^{k-1}<2300\) ?

asked Jan 21 in Mathematics | 10 views

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The sum of a geometric series is 364 of which the first term is 243 and the last term is 1 . Determine the constant ratio of the series.

asked Jan 21 in Mathematics | 16 views

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A rubber ball dropped from a height of \(20 \mathrm{~m}\) loses \(20 \%\) of its previous height on each rebound.

asked Jan 21 in Mathematics | 11 views

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For which values of \(x\) will the series \(2(3 x-1)+2(3 x-1)^2+2(3 x-1)^3+\ldots \ldots\) converge?

asked Jan 21 in Mathematics | 13 views

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Calculate the difference between \(S_{\infty}\) and \(S_7\) of \(4+\frac{4}{3}+\frac{4}{9}+\ldots\)

asked Jan 21 in Mathematics | 8 views

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The 3rd and 12th terms of an arithmetic progression are 12 and \(-24\) respectively. Determine the 49th term.

asked Jan 21 in Mathematics | 13 views

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The 11th term of an arithmetic sequence is 32 and the sum of the first 11 terms is 187 . Calculate the 21st term.

asked Jan 21 in Mathematics | 11 views

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\(2 ; x ; y\) are the first three terms of an arithmetic sequence. If the 2nd term is decreased by 1 , the three terms will form a geometric sequence. Calculate \(x\) and \(y\).

asked Jan 21 in Mathematics | 15 views

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Calculate \(n\) if \(\quad \sum_{k=1}^n(3 k+1)=650\)

asked Jan 21 in Mathematics | 6 views

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Calculate, by using an appropriate formula: \(3-1+\frac{1}{3}-\ldots \ldots \ldots \ldots \ldots+\frac{1}{243}\)

asked Jan 21 in Mathematics | 11 views

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Write each of the following series in sigma notation:

asked Jan 21 in Mathematics | 13 views

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A ball bounces \(\frac{1}{2}\) of its previous height on each bounce. Find the total distance covered by the ball, until it comes to rest, if it is dropped from a height of 20 metres.

asked Jan 21 in Mathematics | 8 views

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A specific tree grows \(1,5 \mathrm{~m}\) in the 1st year. Its growth each year thereafter is \(\frac{2}{3}\) of its growth in the previous year. What is the greatest height it can reach?

asked Jan 21 in Mathematics | 8 views