Give the first five terms of the following:

$\bold{i}$. The arithmetic sequence whose first two terms are $1, 7$ $\bold{ii}$. The geometric sequence whose first two terms are $2, 8$

Determine the common difference and common ratio for the sequences

Broadcasters use a parabolic microphone on football sidelines to pick up field audio for broadcasting purposes. A certain parabolic microphone has a reflector dish with a diameter of $28$ inches and a depth of $14$ inches. If the receiver of the microphone is located at the focus of the reflector dish, how far from the vertex should the receiver be positioned?

Depth A trough is $12$ feet long and $3$ feet across the top (see figure). Its ends are isosceles triangles with altitudes of $3$ feet.
If water is being pumped into the trough at $2$ cubic feet per minute, how fast is the water level rising when $h$ is $1$ foot deep?

A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is $2 \mathrm{~m}$ and volume is $8 \mathrm{~m}^3$. If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?

Some college students collected data on the intensity of light at various depths in a lake. Here are their data.

$$\begin{array}{|c|c|c|c|} \hline \begin{array}{c} \text { Depth } \\ \text { (m) } \end{array} & \begin{array}{c} \text { Light intensity } \\ \text { (lumens) } \end{array} & \begin{array}{c} \text { Depth } \\ \text { (m) } \end{array} & \begin{array}{c} \text { Light intensity } \\ \text { (lumens) } \end{array} \\ \hline 5 & 168.00 & 9 & 44.34 \\ \hline 6 & 120.42 & 10 & 31.78 \\ \hline 7 & 86.31 & 11 & 22.78 \\ \hline 8 & 61.87 & & \\ \hline \end{array}$$

Using your chosen model, calculate and interpret the residual for the measurement at 11 meters.

What was the first neurotransmitter discovered in the CNS?

In a study of frost penetration it was found that the temperature T at time t (measured in days) at a depth x (measured in feet) can be modeled by the function T(x,t)=T0+T1e^-λx sin(wt-λx) where w = 2π/365 and λ is a positive constant. Find ∂T/∂t. What is its physical significance?

The antenna of a radio telescope is a paraboloid measuring 81 feet across with a depth of 16 feet. Determine, to the nearest tenth of a foot, the distance from the vertex to the focus of this antenna.

A student is using a straw to drink from a conical paper cup, whose axis is vertical, at a rate of 3 cubic centimeters per second. If the height of the cup is 10 centimeters and the diameter ofits opening is 6 centimeters, how fast is the level of the liquid falling when the depth of the liquid is 5 centimeters?

Broadcasters use a parabolic microphone on football sidelines to pick up field audio for broadcasting purposes. A certain parabolic microphone has a reflector dish with a diameter of 28 inches and a depth of 14 inches. If the receiver of the microphone is located at the focus of the reflector dish, how far from the vertex should the receiver be positioned?

Near a buoy, the depth of a lake at the point with coordinates $(x, y)$ is $z = 200 + 0.02x^2 - 0.001y^3,$ where $x, y,$ and $z$ are measured in meters. A fisherman in a small boat starts at the point (80, 60) and moves toward the buoy, which is located at (0, 0). Is the water under the boat getting deeper or shallower when he departs? Explain.

The volume of a bubble that starts at the bottom of a lake at 4.55 °C increases by a factor of 10 as it rises to the surface where the temperature is 18.45 °C and the air pressure is 0.965 atm. Assuming that the density of the lake water is $1.00\;\mathrm{g/cm^3}$, determine the depth of the lake. (Hint: You will need to use Equation 10.1.)

A new store is being built in the shape of a rectangle with a parking lot in the shape of an isosceles trapezoid. The parking lot and the store will share a side. The area of the store is to be 154 square meters. If the depth is given as $\frac{1}{14} x^2+\frac{15}{14} x$, find the value of x.

A 7

B 11

C 14

D 28

(a) Determine the horizontal hydrostatic force on the 2309-m-long Three Gorges Dam when the average depth of the water against it is 175 m. (b) If all of the 6.4 billion people on Earth were to push horizontally against the Three Gorges Dam, could they generate enough force to hold it in place? Support your answer with appropriate calculations.