Alan

"A)State an interval in which the  x -coordinate of the maximum turning point on the graph of y=−x(x+2)(x−3)  must lie.

B)Use a numerical method to zoom in on this interval and hence estimate the position of the maximum turning point of the graph with the  x -coordinate correct to 1 decimal place."

Here's one approach:

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Yes.  Enter log(a, b) to get the logarithm to the base b of a.

eg log(49,7) followed by Enter results in log₇(49) = 2

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Area of semicircle: A1 = (1/2)*pi*4^2

Area of complete circle: A2 = pi*r^2

If A1 = A2 then pi *r^2 = (1/2)*pi*4^2

r^2 = (1/2)*16

r^2 = 8

r = sqrt(8)  or r = 2*sqrt(2) cm

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4x - 7 > 29

Add 7 to both sides

4x > 36

Divide both sides by 4

x > 9

x usually represents the domain.

90 = (4*87 + 2*w)/6. where w is the average weight of the last two tortoises.

Rearrange:

w = (6*90 - 4*87)/2 

w = 96 pounds

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The probability of drawing a heart first time is 13/52.

If the card is replaced the probability of drawing a heart the second time is also 13/52.

The probability of drawing a heart both times is therefore (13/52)^2 = (1/4)^2 = 1/16 =  0.0625

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When angles are very small the following approximations hold:

sin(theta) ≈ theta

tan(theta) ≈ theta

(Where theta is measured in radians), so sin and tan return very nearly the same value.

2.3 degrees is 2.3*pi/180 radians → 0.0401 radians. This is small!

More precisely:

sin(2.3degrees) ≈ 0.040131792533

tan(2.3degrees) ≈ 0.040164148968

S + L = 44

S = L - 22

Use the second equation in the first:

L - 22 + L = 44

2L = 66

L = 33

S = 33 - 22

S = 11

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