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Answers by Miguel M.

balloon question (answer)

Melissa, Slope = Δy/Δx or rise/run.  Consider where the balloon was tied to be x = 0. The balloon is 65 ft to the right of where it was tied, so now x = 65 ft. The horizontal change or run = 65 ft. Given that the ground is y = 0, when the balloon is at 20 ft, the vertical change or rise...

-3 (5 – 2y) = (answer)

I assume there is no answer to the right of the = sign. So this is a simplification problem. Get rid of the parentheses by multiplying everything inside the parentheses by -3. Remember that - x - = +: -3 x 5 - (-3)x 2y = -15 + 6 y.  

Let's call Chip X and Dale Y. When X gets 1 acorn from Y, it increased to X +1, and Y decreases to Y -1. But at that point they are supposed to be equal: X+1 = Y - 1, thus X = Y - 2 Now if X gives Y an acorn, Y increases to Y + 1. But now the number of Dale's acorns is double...

If the castle has dimensions of 60 ft and 45 ft, then the outer area would have dimensions of 2m +60 and 2m +45, This is because you have the m width of the moat all around the castle, contributing 2m to both width and length. Thus, for #1, area = (2m+60)(2m+45). For #2, substitute...

Solve for Y (answer)

Divide both sides by 3, since 15 can be divided by 3 to get a whole number: [3(2Y-9)]/3 = 15/3 The 3 cancels on the left side and you get 5 on the right side: 2Y-9 = 5 Now add 9 to both sides to leave Y by itself: 2Y-9+9 = 5+9 2Y = 14 Now divide by sides by 2...

Use the expression (x1+x2/2, y1+y2/2) to get the x and y coordinates of the midpoint. So add up the x values and divide by 2 to get x at the midpoint, and add up the y values and divide by 2 to get y at the midpoint. 

Assuming constant water density, pressure increases by 1 atm (  about 100.9 kPa ) with each 10 m of depth below the surface. So at 10 m, the pressure is 2 atm (1 atm of air + 1 atm of water) or 201.8 kPa.  At 18 atm, the pressure is 282.3 kPa. Now for Boyle's law, you now have...