WTSN 112 Lecture Assignments

Approximately 95.5% of the values for a normal distribution appear... (a) Between ±3σ (b) Between ±1σ (c) Between ±2σ (d) To the left of µ (e) To the right of µ

(c) Between ±2σ

Use MATLAB to find the integral of i(t) = t*sin(5t) and select the correct answer below. Assume i(0) = 0. Show your MATLAB program in your engineering notebook.

(sin(5t)/25)-((t*cos(5t))/5)

What are the standard acceptable requirements verification methods (check all that apply)? - Inspection - Demonstration - Test - Analysis

- Inspection - Demonstration - Test - Analysis

Use Euler's formula to express e^πi in the form a + bi. (Note π = 3.14159 radians.) Show your calculations in your engineering notebook.

-1

Find the determinant of the matrix shown. Show your calculations in your engineering notebook. [ 3 2 ] [ 2 -5 ]

-19

Find the dot product of these two vectors: a = 1.3i + 2.5j b = 1.2i - 2.0j Select the best answer. Show your calculations in your engineering notebook.

-3.44

Find the determinant of the following matrix. Show your calculations in your engineering notebook. [ 1 3 7 ] [ 9 3 4 ] [ 3 2 4 ]

-5

What is the time shift of this sinusoid? Select the best answer. y(t) = 10sin(2πt + π/8)

0.063

A biomedical engineer measures the velocity profile of a belted car occupant during a 20 m/s frontal collision and determines that the velocity profile is v(t) = 20cos(62.5πt) The biomedical engineer also measures the velocity profile of a non-belted car occupant during a 20 m/s frontal collision and determines that the velocity profile is v(t) = 20cos(12.5πt) How much more is the displacement of the non-belted occupant than the belted occupant? Show your calculations in your engineering notebook.

0.4074

What is the approximate area under a standard normal distribution between μ-σ and μ+2σ?

0.819

Express 2e^(π/3)i the form a + bi. (Note: π = 3.14159 radians.) Show your calculations in your engineering notebook.

1 + 1.732i

What is the linear frequency of this sinusoid? Select the best answer. y(t) = 10sin(2πt + π/8)

1.000

Find the cross product of these two vectors: a = 3.3i - 1.5j b = -1.2i + 4.0j Select the best answer. Show your calculations in your engineering notebook.

11.4

An airplane is flying at an air speed of 150 mph at a heading of 30 north of east (Vpa), as shown in the figure below. If the velocity of the wind is 10 mph due west (Vag), determine the resultant speed of the plane with respect to the ground. Select the best answer. Show your calculations in your engineering notebook.

141.4

Recall from an earlier lecture that the relationship between the current through an inductor and the voltage across it is given by v(t) = L(di/dt) What is the current through a 10 mH inductor if 1 V is applied across it for exactly 20 ms? Assume that initially there is no current through the inductor. Show your calculations in your engineering notebook.

2.0 A

What is the standard deviation of the following set of data? Assume the set is the entire population of data. Show your calculations in your engineering notebook. 1.1, 2.4, 7.6, 3.4, 5.2, 2.2, 6.1, 4.0

2.0427

What is the peak-to-peak amplitude of this sinusoid? Select the best answer. y(t) = 10sin(2πt + π/8)

20

What is the final value of voltage on the capacitor in the figure approach after the switch is closed?

20 V

Express -1 - 3i in the form re^iθ. (Assume θ is in degrees.) Show your calculations in your engineering notebook.

3.1623e^251.56i

What is the median of the following set of data? Show your calculations in your engineering notebook. 1.1, 2.4, 7.6, 3.4, 5.2, 2.2, 6.1, 4.0

3.7

What is the mean of the following set of data? Show your calculations in your engineering notebook. 1.1, 2.4, 7.6, 3.4, 5.2, 2.2, 6.1, 4.0

4.0

What is the magnitude of this vector: R = 2.3i + 4.5j - 1.2k Select the best answer. Show your calculations in your engineering notebook.

5.19

Find V_out in this circuit. (Angles in answers shown are in degrees.) Show your calculations in your engineering notebook.

5.3e^57.9i

Express 45 - 25i in the form re^iθ. (Assume θ is in degrees.) Show your calculations in your engineering notebook.

51.48e^-29.055i

What is the angular frequency of this sinusoid? Select the best answer. y(t) = 10sin(2πt + π/8)

6.283

What is the range of the following set of data? Show your calculations in your engineering notebook. 1.1, 2.4, 7.6, 3.4, 5.2, 2.2, 6.1, 4.0

6.5

Find the angle in degrees between these two vectors: a = 0.3i + 4.5j b = -3.2i + 2.0j Select the best answer. Show your calculations in your engineering notebook.

61.8

For a biomedical engineering study tissue samples are taken from a population of harbor seals and weighed. A sample of the weights in grams is: 9.1, 7.9, 8.9, 5.6, 8.7, 8.8, 9.5, 9.9, 6.7, 7.6, 6.5, 7.7, 7.8, 8.9, 9.1, 9.3, 6.7, 8.2, 8.8. & 7.8. What are the mean and standard deviation of the weights?

8.175 and 1.136

For the matrix shown below, find the value of cofactor C₁₃. Show your calculations in your engineering notebook. [ 1 3 7 ] [ 9 3 4 ] [ 3 2 4 ]

9

When writing a requirement, the preferred verb is "should." for example, "The 'RoboButler' should weigh no more than 50lb." True or false?

False

Verification is the confirmation that a component, sub-system, or full system appropriately meets its design function of intended use. True or false?

False.

Use matrix algebra to solve for I₁ and I₂ in the following circuit. Show your calculations in your engineering notebook. -----WWWW-------------WWWW---- | . . . . . 6Ω . . . . . . | . . . . . . 8Ω . . . .| | . . . . . . . . . . . . . | . . . . . . . . . . . . . | 18V . . . . . . . . . . . < . . . . . . . . . . . . . . | | . . I₁ (clockwise) .< 4Ω . . . . . . . . . . . | | . . . . . . . . . . . . . .< . . . . I₂ . . . . . . . | | . . . . . . . . . . . . . .. | . . (c-clockwise) . | | . . . . . . . . . . . .. . ..| . . . . . . . . . . . . . | ----------------------------------

I₁≈1.6154 I₂≈0.4615

In the following table of test results for yield strength what is the approximate probablility of the result being in bin 68000? Bin , Frequency ------------- 56000 , 0 57000 , 1 58000 , 1 59000 , 1 60000 , 1 61000 , 4 62000 , 7 63000 , 7 64000 , 9 65000 , 7 66000 , 5 67000 , 4 68000 , 3 69000 , 1 70000 , 1 71000 , 1 72000 , 0

None of the above. (0.5660)

An allocated requirement is any requirement that is made from dividing a higher-level requirement into more than one lower-level requirement. True or false?

True

Requirements specify the design that must be accomplished, but not how the design is to be done. True or false?

True

You will be required to use the analysis verification method for each of your project requirements. True or false?

True.

Find te inverse of this matrix using the adjoint method. Show your calculations in your engineering notebook. [ 1 3 7 ] [ 9 3 4 ] [ 3 2 4 ]

[ -0.8 -0.4 1.8 ] [ 4.8 3.4 -11.8 ] [ -1.8 -1.4 4.8 ]

Find the inverse of this matrix using the method of matrix row operations. Show your calculations in your engineering notebook. [ -1 5 2 ] [ -2 4 0 ] [ 0 3 1 ]

[ -2/3 -1/6 4/3 ] [ -1/3 1/6 2/3 ] [ 1 -1/2 -1 ]

Add these two matrices. Show your calculations in your engineering notebook. [ 9 -3 ] + [ 7 0 ] [ 2 -5 ] [ -2 -1 ]

[ 16 -3 ] [ 0 -6 ]

Multiply these two matrices in the order shown. Show your calculations in your engineering notebook. [ 7 0 ] X [ 9 -3 ] [ -2 -1 ] [ 2 -5 ]

[ 63 -21 ] [ -20 11 ]

Multiply these two matrices in the order shown. Show your calculations in your engineering notebook. [ 9 -3 ] X [ 7 0 ] [ 2 -5 ] [ -2 -1 ]

[ 69 3 ] [ 3 5 ]

Which of the following is the best written performance requirement? a) The "RoboButler" should operate for 4 hours on a fully charged battery. b) The "RoboButler" shall operate for 4 hours on a fully charged battery. c) The "RoboButler" shall operate for at least 4 hours on a fully charged battery. d) The "RoboButler" shall operate for more than 4 hours on a fully charged battery. e) The "RoboButler" shall operate for at least 4 hours on a battery.

c) The "RoboButler" shall operate for at least 4 hours on a fully charged battery.

Which of the following are "Types of Requirements?" a) Environmental b) Interface c) Functional d) Performance e) All of the above

e) All of the above

Given a capacitor, C = 100mF, and the capacitor voltage v(t) = t*e^(-2t), find the capacitor current i(t). Show your calculations in your engineering notebook.

i(t) = 0.1e^(-2t)(-2t + 1)

The current flowing in a resistor is given by i(t) = (t-1)² A Knowing that i(t) = d(q(t))/dt , where q(t) is charge find an expression for the charge q(t). The initial charge q(0) = 0. Show your calculations in your engineering notebook.

q(t) = (1/3)(t-1)^3+(1/3) Amps

The position of a particle is defined by x(t) = (1/3)t³ - 5t² + 21t + 5 feet. When is the particle at a local maximum position? Assume time is in seconds. Show your calculations in your engineering notebook.

t = 3 sec.

Given an inductor, L = 100 mH, and the inductor current i(t) = e^(-3t), find the inductor voltage v(t). Show your calculations in your engineering notebook.

v(t) = -0.3e^(-3t)

Find the velocity of a vehicle that starts from rest and is subject to the following acceleration: a(t) = 4sin(2t)cos(2t) m/s² Hint: Use trigonometric identities. Show your calculations in your engineering notebook.

v(t) = sin(2t)^2 m/s

The position of a particle is defined by x(t) = (1/3)t³ - 5t² + 21t + 5 feet. Find the particle's position when the speed is zero. Show your calculations in your engineering notebook.

x = 32 ft. and x = 21 1/3 ft.

What is the sum of these two sinusoids? Select the best answer. y₁(t) = 3sin(5t) and y₂(t) = 4sin(5t)

y = 7sin(5t)