geno3141

This is a compound problem:  A  =  P(1 + r)^t

A = final amount = 305 million         P = beginning amount = 281 million

r = rate per year (as a decimal)         t = number of years = 8 years

--->   305,000,000  =  281,000,000(1 + r)⁸

Divide both sides by 281,000,000

--->   1.4663  =  (1 + r)⁸

Now, find the 8^th root of both sides:

--->   1.0103  =  1 + r

Subtract 1 from both sides:

--->   r  =  0.0103   --->   r  =  1.03%

First, find the amount of increase:

--->   1, 120, 000, 000, 000 - 700, 000, 000, 000  =  420, 000, 000, 000

Then divide this answer by the original number.

--->   420, 000, 000, 000 ÷ 700, 000, 000, 000  =  0.60

Finally, turn this into a percentage by multiplying by 100 and attaching a % sign.

--->   0.60 x 100  =  60%

Since A = (-4,5) and A' is the reflection image wrt y-axis, A' = (4, 5).

Since B = (-5,-4) and B' is the 90° anticlockwise rotation, B' = (4,-5)

To determine whether or not A'B is perpendicular to AB', find the slopes of A'B and AB'. If they are negative reciprocals, then the lines will be perpendicular.

Is this enough help?

Example:   sin(Angle)   =  opposite / hypotenuse

If the   angle = 40°  and   the opposite side = 10   and   the hypotenuse is unknown:

--->   sin(40°)  =  10/x

--->   x · sin(40°)  =  10                  (multiply both sides by x)

--->   x  =  10 / sin(40°)                 (divide both sides by sin(40°))

--->   x  =  15.6

Use the Pythagorean Theorem:  c²  =  a² + b²

a  and  b  represent the lengths of the legs; so,  a = 8  and  b = 8  (since the triangle is isosceles)

--->   c²  =  8² + b²   --->   c²  =  64 + 64   --->   c²  =  128   --->   c  =  √128

This question is rather confused ...

First, find the amount of increase by subtracting the original value (120) from the final value (250).

Then, divide that answer by the original value.

Turn this into a percent by multiplying by 100 and attaching a percent symbol.

250 - 120  =  130

130 ÷ 120  =  1.08333...

1.08333... x 100  =  108.33 %  (approximately)

Use a calculator to find 1.045^10 and then multiply that answer by 82000.

(Your answer should be slightly over 127,400.)

Compound Interest Formula:     A  =  P(1 + r/n)^(n·t)

A = final amount = $6000.00         P = beginning amont = $2000.00         t = time (in years)

r = rate (as a decimal) = 0.03        n = number of compounding periods per year = 1

--->   6000  =  2000(1 + 0.03/1)^(n·1)

--->   6000  =  2000(1.03)ⁿ

--->   3  =  (1.03)ⁿ 

--->   log(3)  =  log(1.03)ⁿ             Now, since exponents come out as multipliers:

--->  log(3)  =  n·log(1.03)             Divide both sides by log(1.03):

--->  log(3) / log(1.03)  =  n          Use a calculator to make this division, and round your answer.