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Interactive Content: Berry Info Wall
asked
Jan 31
in
Mathematics
|
4
views
interactive
content
berry
info
wall
quiz
2
like
0
dislike
1
answer
Solve the following equation and round your answer off to three decimal places: \[ 2^x=3 \]
asked
Jan 22
in
Mathematics
|
13
views
solve
equation
round
your
answer
decimal
places
2
like
0
dislike
1
answer
Simplify the following using the laws of logarithms:
asked
Jan 22
in
Mathematics
|
14
views
logarithms
grade12
expression
exponents
calculate
function
calculus
2
like
0
dislike
1
answer
Prove that \(\log _a x=\frac{\log _b x}{\log _b a}\)
asked
Jan 22
in
Mathematics
|
11
views
logarithms
exponents
prove
law
calculate
calculus
function
2
like
0
dislike
1
answer
Simplify \(\frac{\log 16}{\log 4}\)
asked
Jan 22
in
Mathematics
|
9
views
expression
logarithms
number
simplify
grade12
problem-solving
calculus
2
like
0
dislike
1
answer
SImplify \(\frac{\left(\log _2 8\right)^2}{\log _2 8^2}\)
asked
Jan 22
in
Mathematics
|
11
views
logarithms
expression
grade12
simplify
number
problem-solving
algebra
2
like
0
dislike
1
answer
simplify \(\log _3 \sqrt{27}\)
asked
Jan 22
in
Mathematics
|
11
views
expression
simplify
grade12
logarithms
problem-solving
exponents
calculate
2
like
0
dislike
1
answer
Simplify \(\log _3 \frac{1}{27}\)
asked
Jan 22
in
Mathematics
|
12
views
grade12
expression
simplify
logarithms
problem-solving
exponents
calculate
2
like
0
dislike
1
answer
simplify \(-\log 4-\log 25\)
asked
Jan 22
in
Mathematics
|
12
views
logarithms
expression
grade12
simplify
problem-solving
exponents
number
2
like
0
dislike
1
answer
simplify \(\log 20+\log 30-\log 6+\log _4 1\)
asked
Jan 22
in
Mathematics
|
12
views
calculate
expression
logarithms
grade12
exponents
function
calculus
2
like
0
dislike
1
answer
Simplify using laws of logs \(\log _3 27-\log _3 3\)
asked
Jan 22
in
Mathematics
|
12
views
logarithms
grade12
expression
exponents
simplify
problem-solving
calculate
2
like
0
dislike
1
answer
Simplify \(\log _9 27+\log _9 3\)
asked
Jan 22
in
Mathematics
|
11
views
expression
simplify
grade12
logarithms
problem-solving
exponents
2
like
0
dislike
1
answer
Prove that \(\log _a a=1\)
asked
Jan 22
in
Mathematics
|
14
views
logarithms
exponents
prove
law
calculate
function
calculus
2
like
0
dislike
1
answer
Using the laws of logarithms, expand \(\log _4\left(\frac{5}{x}\right)\)
asked
Jan 22
in
Mathematics
|
11
views
function
calculus
logarithms
calculate
exponents
grade12
expression
2
like
0
dislike
1
answer
Expand \(\log_{3}5x\)
asked
Jan 22
in
Mathematics
|
7
views
logarithms
exponents
function
expand
2
like
0
dislike
1
answer
Prove that \(\log _a x^m=m \log _a x \)
asked
Jan 22
in
Mathematics
|
17
views
prove
logarithms
exponents
law
calculate
function
calculus
2
like
0
dislike
1
answer
Prove that \(\log _a\left(\frac{x}{y}\right)=\log _a x-\log _a y \)
asked
Jan 22
in
Mathematics
|
14
views
logarithms
exponents
prove
law
function
calculus
calculate
2
like
0
dislike
1
answer
Prove that \(\log _a(x \times y)=\log _a x + \log _a y \)
asked
Jan 22
in
Mathematics
|
14
views
logarithms
exponents
law
prove
2
like
0
dislike
1
answer
Determine the domain of the function \(f(x)=\log _2(1-2 x)\).
asked
Jan 22
in
Mathematics
|
11
views
determine
domain
function
graph
intercepts
2
like
0
dislike
1
answer
The function \(f: x \rightarrow \log _a x\) passes through the point \((4 ;-2)\).
asked
Jan 22
in
Mathematics
|
19
views
equation
line
parallel
point
calculate
angle
collinear
2
like
0
dislike
1
answer
What is the inverse function of \(g(x)=\left(\frac{1}{2}\right)^x\)
asked
Jan 22
in
Mathematics
|
11
views
differential
function
equation
initial-conditions
point
bounded
continuity
2
like
0
dislike
1
answer
What is the inverse function of \(f(x)=\frac{1}{2} x+3\)?
asked
Jan 22
in
Mathematics
|
13
views
function
real
differentiable
open-set
subset
local
maximum
2
like
0
dislike
1
answer
What is the inverse function of \(f(x)=2 x-4\)?
asked
Jan 22
in
Mathematics
|
10
views
function
inverse
graph
domain
integral
sine
jee
2
like
0
dislike
1
answer
Define an inverse function
asked
Jan 22
in
Mathematics
|
15
views
function
inverse
differential
equation
initial-conditions
error
graph
2
like
0
dislike
1
answer
What is the horizontal line test for functions?
asked
Jan 22
in
Mathematics
|
9
views
vertical
functions
test
line
function
graph
horizontal
2
like
0
dislike
1
answer
What is the vertical line test for functions?
asked
Jan 22
in
Mathematics
|
11
views
vertical
line
test
functions
2
like
0
dislike
1
answer
What is fractional calculus?
asked
Jan 22
in
Mathematics
|
10
views
fractional
calculus
leibniz
2
like
0
dislike
1
answer
Are one-to-many relations considered as functions?
asked
Jan 22
in
Mathematics
|
10
views
one-to-many
relations
considered
domain
range
functions
2
like
0
dislike
1
answer
What is a many-to-one function?
asked
Jan 22
in
Mathematics
|
9
views
domain
range
many-to-one
function
2
like
0
dislike
1
answer
What is a one-to-one function?
asked
Jan 22
in
Mathematics
|
12
views
function
calculus
domain
range
2
like
0
dislike
0
answers
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
sequence
calculate
general
terms
sum
value
prove
2
like
0
dislike
0
answers
Show without multiplying the terms out.
asked
Jan 21
in
Mathematics
|
10
views
calculus
function
theorem
expression
binomial
partial
expand
2
like
0
dislike
0
answers
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
algebra
solution
matrices
equations
infinitely
unique
homogenous
2
like
0
dislike
0
answers
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
prove
lines
convex
quadrilateral
angles
equation
roots
2
like
0
dislike
0
answers
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
prove
convex
lines
quadrilateral
angles
equation
roots
2
like
0
dislike
0
answers
Solve simultaneously for
asked
Jan 21
in
Mathematics
|
16
views
matrix
simultaneous
equations
solve
method
substitution
elimination
1
like
0
dislike
0
answers
Consider the geometric sequence: \(\quad 8 x^2 ; 4 x^3 ; 2 x^4 ; \ldots \ldots \ldots\)
asked
Jan 21
in
Mathematics
|
10
views
arithmetic
sum
calculate
sequence
terms
general
value
1
like
0
dislike
0
answers
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
series
converge
sum
infinite
sequence
equation
grade12
1
like
0
dislike
0
answers
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
grade12
series
prove
geometric
convergent
paper1
calculations
1
like
0
dislike
0
answers
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
distance
height
ball
velocity
mass
speed
tower
1
like
0
dislike
0
answers
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
converge
solve
solutions
equation
bisection
method
newton-raphson
1
like
0
dislike
0
answers
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
series
calculate
sequence
sum
terms
general
arithmetic
1
like
0
dislike
0
answers
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
sequence
grade12
calculate
arithmetic
questions
equations
unknown
1
like
0
dislike
0
answers
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
sequence
grade12
calculate
arithmetic
questions
geometric
people
1
like
0
dislike
0
answers
\(2 ; x ; y\) 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
sequence
grade12
calculate
questions
arithmetic
geometric
people
1
like
0
dislike
0
answers
Calculate \(n\) if \(\quad \sum_{k=1}^n(3 k+1)=650\)
asked
Jan 21
in
Mathematics
|
6
views
series
infinite
sequence
function
convergent
value
divergent
0
like
0
dislike
0
answers
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
sequence
prove
real
positive
proof
permutation
induction
0
like
0
dislike
0
answers
Write each of the following series in sigma notation:
asked
Jan 21
in
Mathematics
|
13
views
notation
sigma
series
standard
write
sum
information
0
like
0
dislike
0
answers
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
velocity
height
distance
speed
tower
ball
mass
0
like
0
dislike
0
answers
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
components
distance
vector
parallel
vectors
euclidean
planes
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