Find the force $P$ needed to hold the $3 -\text{m}$-wide rectangular gate as shown if: (a) $l=2 \mathrm{~m}$ (b) $l=4 \mathrm{~m}$ (c) $l=5 \mathrm{~m}$

A plane gate of uniform thickness holds back a depth of water as shown. Find the minimum weight needed to keep the gate closed.

Use Eq. and show that the force $F$ in Fig. acts one-third the way up on a vertical rectangular area and also on a sloped rectangular area. Assume the sloped gate to be on an angle $\alpha$ with the horizontal.

Calculate the force $P$ necessary to hold the $\textrm{4-m}$ wide gate in the position shown in Fig. if: (a) $H=6 \mathrm{~m}$ (b) $H=8 \mathrm{~m}$ (c) $H=10 \mathrm{~m}$

A teacher predicts that the distribution of grades on the final exam will be and they are recorded in Table 11.27.

$$\begin{matrix} \text{Grade} & \text{Proportion}\\ \text{A} & \text{0.25}\\ \text{B} & \text{0.30}\\ \text{C} & \text{0.35}\\ \text{D} & \text{0.10}\\ \text{Table 11.27}\\ \end{matrix}$$

The actual distribution for a class of 20 is in Table 11.28.

$$\begin{matrix} \text{Grade} & \text{Proportion}\\ \text{A} & \text{7}\\ \text{B} & \text{7}\\ \text{C} & \text{5}\\ \text{D} & \text{1}\\ \text{Table 11.28}\\ \end{matrix}$$

p-value = ______

A $6-\text{ft}$-wide, $\textrm{10-ft-high}$ vertical rectangular gate has its top edge $6 ~\mathrm{ft}$ below the water level. It is hinged along its lower edge. What force, acting on the top edge, is necessary to hold the gate shut?

The top of each gate shown in figure lies $4 \mathrm{~m}$ below the water surface. Find the location and magnitude of the force acting on one side assuming a vertical orientation.

Estimate the pressure in the water pipe shown in figure. The manometer is open to the atmosphere. (A) $10 ~\mathrm{kPa}$ (B) $9 ~\mathrm{kPa}$ (C) $8 ~\mathrm{kPa}$ (D) $7 ~\mathrm{kPa}$

The triangular gate shown in figure has its $6$-$\mathrm{ft}$ side parallel and $30 ~\mathrm{ft}$ below the water surface. Calculate the magnitude and location of the force acting on the gate if it is: (a) Vertical (b) Horizontal (c) On a $45^{\circ}$ angle sloped upward.

A meteorologist states that the barometric pressure is $28.5$ inches of mercury. Convert this pressure to kilopascals. (A) $98.6 ~\mathrm{kPa}$ (B) $97.2 ~\mathrm{kPa}$ (C) $96.5 ~\mathrm{kPa}$ (D) $95.6 ~\mathrm{kPa}$

Freshwater and seawater flowing in parallel horizontal pipelines are connected to each other by a double U-tube manometer, as shown in the figure. Find the pressure difference between the two pipelines. Take the density of seawater at that location to be $\rho=1035 \mathrm{~kg} / \mathrm{m}^3$. Can the air column be ignored in the analysis?

The sides of a triangular area measure $2 \mathrm{~m}, 3 \mathrm{~m}$, and $3 \mathrm{~m}$, respectively. Calculate the force of water on one side of the area if the 2-m side is horizontal and $10 \mathrm{~m}$ below the surface and the triangle is: (a) Vertical (b) Horizontal (c) On a $60^{\circ}$ angle sloped upward.

How can you convert the string "3.14" into the floating-point number 3.14? How can you convert the floating-point number 3.14 into the string "3.14"?

Write a program that reads in two floating-point numbers and tests whether they are the same up to two decimal places. Here are two sample runs. Enter a floating-point number: 2.0 Enter a floating-point number: 1.99998 They are the same up to two decimal places. Enter a floating-point number: 2.0 Enter a floating-point number: 1.98999 They are different.