Water flows through a sluice gate with a 1.1-ft- high opening and is discharged with free outflow. If the upstream flow depth is 5 ft, determine the flow rate per unit width and the Froude number downstream the gate.

Water is released from a 0.8-m-deep reservoir into a 4-m-wide open channel through a sluice gate with a 0.1-m-high opening at the channel bottom. The flow depth after all turbulence subsides is 0.5 m. The rate of discharge is $(a) 0.92 m^3/s\ (b) 0.79 m^3/s\ (c) 0.66 m^3/s\ (d) 0.47 m^3/s\ (e) 0.34 m^3/s$

Find the opposite of each number. You may find a number line helpful. 90

Write the first five terms of each sequence. Assume that d represents the common difference of an arithmetic sequence and r represents the common ratio of a geometric sequence.

$$a _ { 1 } = 5 , r = - 3$$

Use direct substitution to show that the given pair of functions $x_{1}(t)$ and $x_{2}(t)$ is a solution of the given system. $x_{1}^{\prime}=-5 x_{1}-3 x_{2}, x_{2}^{\prime}=6 x_{1}+4 x_{2}, x_{1}(t)=e^{-2 t}x_{2}(t)=-e^{-2 t}$

In the division $\frac { x ^ { 4 } - 2 x ^ { 3 } + 5 x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 2 x + 3 } = x ^ { 2 } + 2 + \frac { 2 x - 5 } { x ^ { 2 } - 2 x + 3 }$ the dividend is _____ the divisor is ______, the quotient is ______, and the remainder is ______ .

For the following function, write Newton’s formula as $x_{n+1}=F(x_n)$ for solving f(x)=0.

$$f ( x ) = x ^ { 3 } + 3 x e ^ { x }$$

How can relatively weak H bonds hold the double helix together yet allow DNA to function?

Determine whether the given credit card number is a valid number. 4896-4198-8760-1970

"The aspirin substitute acetaminophen $\left( \mathrm { C } _ { 8 } \mathrm { H } _ { 9 } \mathrm { O } _ { 2 } \mathrm { N } \right)$ is produced by the following three-step synthesis:

$$\begin{array} {l}{I. \mathrm { C } _ { 6 } \mathrm { H } _ { 5 } \mathrm { O } _ { 3 } \mathrm { N } ( s ) + 3 \mathrm { H } _ { 2 } ( \mathrm { g } ) + \mathrm { HCl } ( a q ) \longrightarrow \mathrm { C } _ { 6 } \mathrm { H } _ { 8 } \mathrm { O } \mathrm { NCl } ( s ) + 2 \mathrm { H } _ { 2 } \mathrm { O } ( l ) \\ II. \mathrm { C } _ { 6 } \mathrm { H } _ { 8 } \mathrm { ONCl } ( s ) + \mathrm { NaOH } ( a q ) \longrightarrow \mathrm { C } _ { 6 } \mathrm { H } _ { 7 } \mathrm { ON } ( s ) + \mathrm { H } _ { 2 } \mathrm { O } ( l ) + \mathrm { NaCl } ( a q ) \\ III. \mathrm { C } _ { 6 } \mathrm { H } _ { 7 } \mathrm { O } \mathrm { N } ( s ) + \mathrm { C } _ { 4 } \mathrm { H } _ { 6 } \mathrm { O } _ { 3 } ( l )\longrightarrow \mathrm { C } _ { 8 } \mathrm { H } _ { 9 } \mathrm { O } _ { 2 } \mathrm { N } ( s ) + \mathrm { HC } _ { 2 } \mathrm { H } _ { 3 } \mathrm { O } _ { 2 } ( l )}\end{array}$$

The first two reactions have per cent yields of 87% and 98% by mass, respectively. The overall reaction yields 3 moles of acetaminophen product for every 4 moles of $\mathrm { C } _ { 6 } \mathrm { H } _ { 5 } \mathrm { O } _ { 3 } \mathrm { N }$ reacted. What is the percent yield by mass of step III?

How many solution s are there to the equation $x(x^2 - 4) = 0 ?$ A. $0$ B. $1$ C. $2$ D. $3$

What role did the geography of the West play in shaping patterns of migration during the late 1800s?

A person can purchase a particular model of a new car with a choice of ten colors, with or without automatic transmission , with or without four-wheel drive, with or without air conditioning , and with two, three , or four radio -CD speakers. How many different options are there for this model of the car?

A flow is isentropically expanded to supersonic speeds in a convergent-divergent nozzle. The reservoir and exit pressures are 1 and 0.3143 atm, respectively. What is the value of $A_e/A*?$