Intermediate Algebra

The formula is C=4d^-1/3b

D= 23,245 because it is the pounds

B= 13.5 because that is the height of the mast

C=4(23,245)^-1/3(13.5)

Because the exponent was negative it needed to be dropped down to the numerator. The fact that it was a fraction meant that 92980 needed to be cubed, since it was a 1/3 exponent. Then it could be multiplied with the B. value, which was 13.5 / This left the final answer to be 283.693745115.

C=4d^-1/3b

d=64b3/c3

In order to solve for D. you needed to move 4 and the variable D. To the other side. Then you have to log both sides, which leaves an exponent of 3 instead of -1/3.

This formula could definitely be very important in the real world. For one, it is needed to be able to properly sail a boat in various conditions. It is extremely important to understand the conditions in which any boat can capsize. As such, it is important to use the formula in the real world to understand o much weight can be utilized in a boat of various length without the threat of capsizing. This is especially important to understand before getting out on the water, where Mother Nature can throw storms and swells that would only further complicate the situation.

Problem 104

A. S=16 AD^-2/3

A=810 square feet

D= 23.345

S=16(810) (23.345)^-2/3

S=12960 * (23.245^-2/3)

S=12960 * .00122776

S= 15.9 Knots

B. S=16 AD^-2/3

D=(S/16A)^-2/3

In order to solve this problem, one had to replace the values given with the problem with the numbers given. As such, there was an 810 square feet area and a D. value of 23.345, because it represented the pound value provided. As such, it was necessary to drop the -2/3 exponent to the dominator. From there the 23.345 pounds was then squared to the appropriate amount based on the fractional exponent. This resulted in the fraction that translated into the decimal .00122776.

Again, this is incredibly useful because it helps forecast a situation before the people sailing actually get on the open ocean. With so much at risk, it is important to understand the details of one's boat in order to be able to push it to its limits without putting anyone's life in danger.