Exam 18: Mathematics in Engineering

The future worth of a present value is modeled using the following function: $F ( n ) = P ( 1 + i ) ^ { n }$ where $F =$ future worth $( \$ )$ P= present value (\ ) i= interest rate (\%) n= length of investment (years) Which type of mathematical model is used here to describe the gravitational force? a. Linear model b. Nonlinear model c. Exponential model d. Trigonometric model

Find the derivative of $f ( x ) = 3 e ^ { x ^ { 2 } }$

What is the name of the following Greek alphabetic character? $\gamma$

At Snacks-R-Us, caramel corn wor $\$ 2.50$ 0 per pound is mixed with cashews wor $\$ 7.50$ r pound in order to get 20 pounds of a mixture wor $\$ 4.50$ pound.How much of each snack is used?

Calculate the average rate of change for the following functions: $f ( x ) = x ^ { 2 } \text { between } x = 0$ and $x = 2$

For many engineering situations, exponential and logarithmic models are used to describe the relationships between dependent and independent variables because they predict the actual relationships more accurately than linear models do.

Solve the following set of equations using matrices: a+b+c=6 2a+5b+c=15 -3a+b+5c=

The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: $y ( x ) = - \left( \frac { g } { 2 v _ { 0 } ^ { 2 } \cos ^ { 2 } \theta } \right) x ^ { 2 } + ( \tan \theta ) x + y _ { 0 }$ where $y =$ vertical position of football relative to the ground $y _ { 0 } =$ vertical launch position of football relative to the ground $x =$ horizontal position of football relative to launch position $g =$ magnitude of gravitational acceleration $v _ { 0 } =$ launch speed $\theta =$ launch angle relative to horizontal Which type of mathematical model is used here to describe the football's trajectory?

For many engineering situations, nonlinear models are used to describe the relationships between dependent and independent variables because they predict the actual relationships more accurately than linear models do.

The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: $\quad y ( x ) = - 0.002 x ^ { 2 } + 0.7 x + 7$ where $y =$ vertical position of football relative to the ground $( \mathrm { m } )$ $x = \text { horizontal position of football relative to launch position (m) }$ How high above the ground is the football as it leaves the quarterback's hand? a. $0.002 \mathrm {~m}$ b. $0.7 \mathrm {~m}$ c. $7 \mathrm {~m}$ d. $7.7 \mathrm {~m}$

Perform the following operations on the given matrices: [A]= 4 2 1 7 0 -7 1 -5 3 [B]= 1 2 -1 5 3 3 4 5 -7 [A[B?

Greek alphabetic characters quite commonly are used to express angles, dimensions, and physical variables in drawings and in mathematical equations and expressions.It is therefore very important to be familiar with these characters in order to communicate with other engineers.

Find the derivative of $f ( x ) = \frac { x ^ { 3 } + 3 x ^ { 2 } - 2 x + 1 } { x ^ { 2 } + x + 5 }$

What is the name of the following Greek alphabetic character? $\omega$

In general, engineering problems are mathematical models of physical situations.

The loudness $\beta$ of sound is dependent upon the sound intensity I according to the following equation: $\beta = 10 \log \left( I ^ { \times } \times 10 ^ { 12 } \right)$ .Which type of mathematical model is used in this relationship?

Minn Kota offers its sales representatives a choice between being paid a commission of 8% $8 \%$ of sales or being paid a monthly salary of $\$ 1500$ plus a commission of 1% $1 \%$ of sales.For what monthly sales do the two plans pay the same amount?

The simplest form of equations commonly used to describe a wide range of engineering situations is

The drag force acting on a car can be modeled using the following function: $F _ { d } = \frac { 1 } { 2 } C _ { d } \rho {{ V } ^ { 2 }} A$ where $F _ { d } =$ drag force $C _ { d } =$ drag coefficient $\rho =$ air density $V =$ speed of car relative to air $A =$ frontal area of car The power $P$ required to overcome air resistance can be modeled according to $P = F _ { d } V$ . When analyzing power as a function of velocity $P ( V )$ , what order is the resulting function?