Alan

"As salt water boils, the only thing that evaporates is the water – the amount of salt in the mixture remains constant. As a consequence, the concentration of the salt in the mixture increases over time. Suppose the concentration of salt in a pot of boiling water is given by c= 200/v  , where c  is the concentration of salt (mg/L) and v is the total amount of mixture in the pot (L). Determine the rate at which the salt concentration is changing at the moment there are 5.2 liters of liquid in the pot if at that moment water is evaporating at the rate of 0.13 L/min."

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Solution as follows:

I think this question is probably meant to read:

"An urn contains different colored marbles. The probability of drawing two green marbles from the urn without replacement is 3/20 , and the probability of drawing one green marble is 2/5 .

What is the probability of drawing a second green marble, given that the first marble is green?"

If so, then:

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The following diagram should help. 

 \(\cos(73°)=c/b \\\sin(\theta)=c/b\\73°+\theta=?\)

Hmm.

Both methods are correct. 

Melody has made a small numerical error in solving the last quadratic for reaching the rear of the truck. The value under the square root sign should be 601 rather than 761.

The other differences are due to small differences used for the numerical approximations used for 1/root2.  (I get values for velocity between 15.83 and 17.04 m/s).

Terminating decimal values for k occur when 1+2x is a power of 5, so: \(\sum k=\sum_{p=1}^\infty 5^{-p}=\frac{1}{4}\)

First, use s = v₁t + (1/2)gt² to find v₁, the velocity at s = 1m (g = 9.81 m/s², t = 0.05 s).

Then use v₁²= 2gh to find the distance, h, from the top of the bridge to 1 m above the water (assuming rock is dropped with zero initial velocity).

Then height of bridge = h + 1 m

You don't say how the circles are arranged!  Here are a couple of possibilities:

In one case we have length = 80 + 20pi, in the other, length = 60 + 20pi

Make repeated use of the chain rule.  For example: