Mathematics2 & Engineering Economics

The space between two lines meeting at a point is called the vertex. In geometry, a vertex refers to the point where two lines or line segments intersect. Therefore, the correct answer is "angle" because an angle is formed when two lines or line segments meet at a point.

The expression (3^3)^2 can be simplified by first evaluating the exponent within the parentheses, which is 3^3. This means multiplying 3 by itself three times, resulting in 27. Then, raising 27 to the power of 2 gives us 729. Therefore, the correct answer is 729.

The break-even point refers to the level of sales at which a company's income is sufficient to cover its operating costs. It is the point where the company neither makes a profit nor incurs a loss. By reaching the break-even point, the company covers all its expenses, including fixed and variable costs. This is an important metric for businesses as it helps determine the minimum level of sales needed to cover costs and start making a profit.

The rate of return refers to the percentage of profit earned on the capital invested. It is a measure of the profitability of an investment and indicates how much return an investor can expect to earn on their investment. In this context, the ratio of annual net profit over the capital invested represents the rate of return. It shows the efficiency and profitability of the investment, as a higher rate of return indicates a higher profit relative to the capital invested.

An annuity refers to a series of equal payments occurring at equal periods of time. It is a financial product or investment that provides regular income payments for a specific period or for the rest of an individual's life. Annuities are commonly used for retirement planning or to provide a steady income stream.

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two legs. In this case, the length of the two legs are given as 7m and 10m. Using the Pythagorean theorem, we can calculate the length of the hypotenuse as follows: hypotenuse^2 = 7^2 + 10^2 = 49 + 100 = 149. Taking the square root of 149 gives us the length of the hypotenuse, which is approximately 12.207 m.

The number of board feet in a plank can be calculated by multiplying the thickness, width, and length of the plank and then dividing the result by 12. In this case, the plank is 3" thick, 1' wide, and 20' long. Multiplying these values gives 60 cubic feet. Since there are 12 board feet in a cubic foot, the number of board feet in the plank is 60.

Book value refers to the original cost of an asset minus the accumulated depreciation. It represents the net value of an asset on a company's balance sheet and is used to determine the worth of the asset at a given point in time. The book value is important for financial reporting and decision-making purposes, as it provides insight into the asset's value after accounting for depreciation.

The volume of a sphere is given by the formula 4/3(pi*r^3). This formula is derived from the fact that a sphere can be thought of as a collection of infinitely many infinitesimally thin circular disks stacked on top of each other. Each disk has a volume of pi*r^2 (the area of the disk) multiplied by a small thickness, which approaches zero. Summing up the volumes of all these disks gives us the volume of the sphere. Therefore, the correct answer is 4/3(pi*r^3).

When a body is submerged in a fluid, it displaces a certain amount of fluid equal to its own weight. This is known as Archimedes' principle. According to this principle, the loss of weight of the body is equal to the weight of the fluid displaced. Therefore, the correct answer is "equal to the weight of the fluid displaced."

The surface area of a cube can be found by multiplying the length of one side by itself, and then multiplying that by 6 (since a cube has 6 equal sides). In this case, the length of one side is given as 12 m. So, the surface area would be 12 * 12 * 6 = 864 square meters.

The correct answer is 35.29 km/hr/sec. This is because the standard acceleration due to gravity is typically measured in meters per second squared (m/s²), not in feet per second or kilometers per hour. Therefore, the option that is closest to the standard unit of measurement is 35.29 km/hr/sec.