Alan

Re: Jam question

If 4 parts = 1kg then 1 part = 1/4 kg and 3 parts = 3/4 kg.  So you would need 3/4kg of sugar.

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You can write y = k*x² where k is a constant

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Use Pythagoras:  h = √(0.992^2 + 0.213^2) metres

$${\mathtt{h}} = {\sqrt{{{\mathtt{0.992}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{0.213}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{h}} = {\mathtt{1.014\: \!609\: \!777\: \!205\: \!01}}$$

h ≈ 1.015 metres

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The mean is the average obtained by adding all the values and dividing the result by the number of values.

The median is the middle value when they are sorted in order of size.

The mode is the most common value.

The range is the difference between the largest and the smallest.

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Corrected 2nd line to say median not mean!! Thanks Anonymous4338.

Use sin(22°) = 689/h  where h is the length of the gondola wire, to get h = 689/sin(22°) feet.

Then divide h by 130 feet per minute to get the ride time in minutes.

ride time = 689/(sin(22°)*130) minutes

$${\frac{{\mathtt{689}}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{22}}^\circ\right)}{\mathtt{\,\times\,}}{\mathtt{130}}\right)}} = {\mathtt{14.148\: \!175\: \!961\: \!532\: \!953\: \!6}}$$

ride time = 14 minutes to the nearest minute.

Multiply every term by 3 to get rid of the fraction.  You are then left with:

2x - 15 = 3x - 9

Can you take it from here?

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We can rewrite the equation  as

y² - 150y + 35 = -x²

(y - 75)² - 5625 + 35 = -x²

(y - 75)² - 5590 = -x²

(y - 75)² = 5590 - x²

Now the right-hand side has a maximum value of 5590, because as x moves away from zero, in either the positive or negative direction, x² is positive and subtracts from 5590.  Therefore the maximum value of y is obtained when x is zero:

(y - 75)² = 5590

y = 75 + √5590 ≈ 150

So c. gives the maximum height.

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1.  Set f(k) = 25

k² + 2k + 1 = 25 

k² + 2k - 24 = 0

(k - 4)(k + 6) = 0

So two limiting values in the domain are -4 and 6

2. Set f(k) = 64

k² + 2k + 1 = 64

k² + 2k - 63 = 0

(k - 7)(k + 9) = 0

So the other two limits are -9 and 7

The domain is  [-9, -4] ∪ [6, 7]

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1). Take log to the base 10 of the number log(2014^2022) = 2022*log(2014)

$${\mathtt{2\,022}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{2\,014}}\right) = {\mathtt{6\,680.808\: \!240\: \!691\: \!985\: \!784\: \!6}}$$

2) Take the integer part (6680) and add 1 to get 6681.  That's how many digits there are.

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slope = (y2 - y1)/(x2 - x1)  = (5 - 8)/(-8 - -11) = -3/3 = -1

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