As follows:
The four numbers must be 1, 2, 4, 4
You can work out their sum.
Chris has given the point tht intersects the x-axis. To find the point that intersects the y-axis, set x = 0 and calculate the corresponding value of y from the equation y = 2x + 5.
x and r are directly proportional means we can write; x = k*r where k is a constant.
To find k use the fact that x = 5 when r = 25, so 5 = k*25 . You should be able to find k from this.
Then use that to find x when r is 40: x = k*40
Another way is to notice that every term in the series is less than 20^2. Since there are 20 terms in all we must have S20 < 20*20^2, which means that 20A < 20*20^2, or A < 20^2 or A < 400. Hence e) is the answer.
Replace x by y and f(x) by x in the function definition, then rearrange to find y:
\(x = \frac{2y-1}{y+5}\) so \(x(y+5)=2y-1\)
Collect the y's \(y(x-2)+5x = -1\) or \(y = \frac{-5x-1}{x-2}\)
which means \(f^{-1}(x)=\frac{-5x-1}{x-2}\)
So a /c= -5/1
Use Pythagoras to get the length of one side, then square it to get the area.
32a = 13b means 3a + 2 = b + 3
b = 3a - 1
Smallest possible a is 4, so: a = 4, hence b = 11, and a+b = 15
The mean value theorem here says:
Can you finish from here?
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