A Few Problems I'm Stuck On 10 pts!?

Question

1) Suppose you have a cone filled with water and an empty cylinder. Both have a radius of 10 inches. The cone is 12 inches deep and the cylinder is 8 inches deep. You let the water drip from the tip of the cone into the cylinder:

a) Will all the water in the cone fit in the cylinder? If so, how much space (in cubic inches) remains in the cylinder? If not, how much water (in cubic inches) overflows?

b) When the level of the water in the cone is 6 inches, what is the level of the water in the cylinder?

2) e^ln(5x+6)

3) Solve for y in terms of x:

ln(y+1) = 6+x

For these don't use a calulator, give answers in exact form:

4) 5^x=17

5) tan2x = sqrt3, 0 less than equal to x < 2pi

Best answer given to the one that answers the most questions!!!

Answer 1

1.  First off, recall that the volume of a cylinder as a function of its radius (R) and height (H) is R*R*Pi*H.  The volume of a cone is (1/3)*R*R*Pi*H.

a) So the volume of the cone is 12/3 * 10 * 10 * Pi, or 400Pi.

The volume of the cylinder is 10*10*8*Pi, or 800Pi

(feel free to re-check my answers here &#039;cus I&#039;m doing this in my head).

Thus the cylinder will be half full if you empty the cone into it (4 inches of depth remaining, or 400Pi cubic inches).

b) For this problem you have to figure out how much water leaves the cone:  Figure out how much water there was originally (400Pi I&#039;m guessing), figure out how much water there is now (6/3)*10*10*Pi, subtract the two.  Then you need to work backwards to find the height in Y = 1/3 * H * R * R * Pi

2) Recall that e^ln(X) = X.

3) raise both sides as a power of e, subtract one.

4) Natural log of both sides, recall that ln(x^y) = y*ln(x), divide through by ln(5).

5) Think about what angle generates a sqrt(3) with a tan() function.  Set this angle equal to 2x, proceed from there (remember to check the opposite quadrant, i.e. add 180 degrees to each of your answers and check again).

Answer 2

2) e^ln cancels  so its 5x + 6 left

3) e^(6+x) - 1 = Y

4) log 5^x = log 17

    x log 5 = log 17

    x = log17 / log 5

5 tan(inverse) (sqrt3) = 2x

  tan inverse sqrt 3 / 2 = x

  

Answer 3

Use log and LN principles? c**p I did this stuff last semester but I forgot haha. sorry

good luck