Accuracy and Scientific Notation
Write 0.0000832 in scientific notation.
8.32*10^(-5)
Find the common difference of the arithmetic sequence:
6, 10, 14, 18, ...
d=4
$2000 is invested at 5% simple interest for 3 years. Find the final value.
$2300
Simplify:
(x^7*x^3)/(x^4)
x^6
Find the coefficient of x2 in the expansion of
(x+1)^4
6
Round 0.0067841 to 3 significant figures.
0.00678
Find the common ratio of the geometric sequence:
81, 27, 9, 3, ...
r=1/3
$2000 is invested at 5% interest compounded annually for 3 years. Find the final value.
$2315.25
Rewrite in logarithmic form:
5^3=125
log_5(125)=3
Expand:
(x+2)^3
x^3+6x^2+12x+8
Calculate and give your answer in scientific notation.
(4*10^6)(3*10^(-2))
1.2*10^5
Find the sum of the first 20 terms of the arithmetic sequence:
5, 8, 11, 14, ...
670
$8000 is invested at 5.4% annual interest compounded monthly for 4 years. Find the final value.
Approximately $9924.01
8000(1+0.054/12)^(48)
Write as a single logarithm:
ln(5)+ln(7)
ln(35)
Find the coefficient of x4 in the expansion of
(x-2)^6
60
A length is recorded as 12.6 cm, correct to the nearest 0.1 cm. State the error interval.
12.55 <= L < 12.65
Find the sum of the first 20 terms of the arithmetic sequence
5, 8, 11, 14, ...
765
A car is purchased for $28,500 and depreciates by 13% each year. Find its value after 5 years.
Approximately $14,205.00
28500(0.87)^5
Given log(2)=p and log(3)=q, express log(18) in terms of p and q.
p+2q
Show that
(x+4)^2-7 ≡ x^2+8x+9
LHS=(x+4)2-7
=x2+8x+16-7
=x2+8x+9
=RHS
A measured length is 73.8 cm. The accepted value is 72.5 cm. Find the percentage error.
1.79%
An infinite geometric series has first term 18 and sum to infinity 30. Find the common ratio.
r=0.4
Because:
30=18/(1-r)
$6000 is invested for 10 years. Account A earns 5% simple interest. Account B earns 4.5% interest compounded annually. Which account has more money, and by how much?
Account B by approximately $317.82
Solve and give you answer to 3 significant figures.
2^(x+1)=5^(x-2)
x=4.27
(x+1)ln(2)=(x-2)ln(5)
Given x>7, show that
x/(x^2-8x+7)*(x^2-1)/(x+1) = x/(x-7)
LHS=x/((x-1)(x-7))*((x-1)(x+1))/(x+1) =x/(x-7) =RHS
using x^2-8x+7=(x-1)(x-7)
and x^2-1=(x-1)(x+1)