Alan

"A new scooter is valued at $15 000. At the end of each year its value is reduced by 15% of its value at the start of the year. What will it be worth after 3 years?"

At the end of the first year the value is $0.85*15000       (because 0.85 = 1 - 0.15)

at the end of the second year the value is $0.85*0.85*15000 → $0.85²*15000

at the end of the third year the value is $0.85*0.85²*15000 → $0.85³*15000

etc.

A quick graph shows pro35hp is clearly correct:

1revolution = 360 degrees

90 revolutions = 90*360 degrees

1 minute = 60 seconds

Therefore wheel turns through 90*360/60 → 540 degrees per second

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"Write x / (x2-1) - (x + 1) / (x - 1) as a single fraction in simplest form."

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Just use the calculator to work out each side of the equality.

Let n be the number of cheaper calculators. Then

n*2.95 + 40*8.20 = 387

n*2.95 = 387 - 40*8.20

n = (387 - 40*8.20)/2.95

n = 20

This graph might help:

First set h = 0, then divide each term by -8 to get:

2t^2 + 3t - 20 = 0. This factors as:

(2t - 5)(t + 4) = 0

The only positive solution is given by 2t - 5 = 0 or t = 5/2

So t = 2.5 seconds

"A geosynchronous satellite is stationary over a point on the equator (zero degrees latitude) at the same longitude as Seattle, Washington. Seattle's latitude is 47.6°. If you want to communicate with the satellite, at what angle above the horizon must you point your communication device? The Earth's radius is 6.38×106 m. The orbital radius of a geosynchronous satellite was found in a previous problem (you can also calculate it using the mass of the Earth: 5.97×1024 kg)"

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Slope of line joining A and B is (4 - (-2))/(6 - 2) = 3/2  Hence slope of perpendicular line is -2/3

Midpoint of A and B is ( (2+6)/2, (-2+4)/2 )  or (4, 1)  

Equation of perpendicular bisector is  y - 1 = -(2/3)(x - 4)  or  y = -(2/3)x + 11/3

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