True or False. A special case of the Law of Cosines is the Pythagorean Theorem.

Determine whether the below statement is true or false.$\newline$ "The Pythagorean theorem is a special case of the Law of Cosines."

A lie detector will show a positive reading (indicate a lie) 10% of the time when a person is telling the truth and 95% of the time when the person is lying. Suppose two people are suspects in a one-person crime and (for certain) one is guilty and will lie. Assume further that the lie detector operates independently for the truthful person and the liar. What is the probability that the detector gives a positive reading for either or both of the two suspects?

The following data were obtained for flow of 20°C water at 20 m³/h through a badly corroded 5-cm-diameter pipe that slopes downward at an angle of 8°:

$$p_1 = 420 kPa, z_1 = 12 m, p_2 = 250 kPa, z_2 = 3 m$$

. Estimate (a) the roughness ratio of the pipe and (b) the percentage change in head loss if the pipe were smooth and the flow rate the same.

Determine whether the below statement is true or false.$\newline$ "If an obtuse triangle is isosceles, then knowing the obtuse angle and a side adjacent to it is sufficient to solve the triangle."

Determine whether the following statement is True or False.

The Law of Cosines states that the square of one side of a triangle equals the sum of the squares of the other two sides, minus twice their product.

If two sides and the included angle of a triangle are given, the Law of _____ is used to solve the triangle.

Identify the elements represented by (a) $1s^22s^22p^63s^23p^1$, (b) $1s^22s^22p^63s^23p^64s^23d^{10}$, and (c) $1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^2$.

The angle of elevation from a rowboat moored 75 feet from a cliff is $60 ^ { \circ } .$ Find the height of the cliff.

A Ferris wheel has 16 evenly spaced cars. The distance between adjacent chairs is 15.5 ft. Find the radius of the wheel (to the nearest 0.1 ft).

Suppose a balloon is filled with $5000\ \mathrm{cm}^{3}$ of helium. It then loses one fourth of its helium each day. How much helium will be left in the balloon at the start of the tenth day? How can you write a sequence of numbers to represent this situation? Is the sequence arithmetic, geometric, or neither? How can you write a formula for this sequence?

A Little League baseball diamond has four bases forming a square whose sides measure 60 feet each. The pitcher’s mound is 46 feet from home plate on a line joining home plate and second base. Find the distance from the pitcher’s mound to third base. Round to the nearest tenth of a foot.

Find the flux of the vector field F across

$$\sigma$$

in the direction of positive orientation.

$$\mathbf { F } ( x , y , z ) = e ^ { - y } \mathbf { i } - y \mathbf { j } + x \sin z \mathbf { k } ; \sigma$$

is the portion of the elliptic cylinder

$$\mathbf { r } ( u , v ) = 2 \cos v \mathbf { i } + \sin v \mathbf { j } + u \mathbf { k }$$

with

$$0 \leq u \leq 5,0 \leq v \leq 2 \pi$$

.

What makes the Richter scale different from the scales we use to measure mass or distance?