Introduction to battery-management systems- COURSERA WEEK 01 Specialization prerequisite quiz

 Introduction to battery-management systems- COURSERA WEEK 01  Specialization prerequisite quiz

1.

Question 1

This quiz asks questions from the prerequisite topic areas for this specialization. If you do well on this quiz, then you have the general skills to do well in the specialization (although you will gain further skills in each of these areas as you proceed through the specialization). If you do NOT do well on certain areas of this quiz, you should consider studying those particular areas before continuing with the specialization.

(Note that this is not a quiz on topics covered in this lesson. It is a quiz for you to be able to assess whether you have adequate background preparation to succeed in the specialization.)

Differential calculus: If $f(x)=5x^3+3x+1$, then what is d$f(x)/$d$x$?

H​int: See https://learner.coursera.help/hc/en-us/articles/208279916-Math-assignments for instructions on how to enter equations in Coursera.

1 / 1 point

$15 x^{2} + 3$

15*x^2+3

Correct

Yes. That is the correct response.

2.

Question 2

Integral calculus: If $g(t)=\exp(-0.5 t)$, what is $\int_0^\infty g(t)$ d$t$?

H​int: See https://learner.coursera.help/hc/en-us/articles/208279916-Math-assignments for instructions on how to enter equations in Coursera.

1 / 1 point

2

Correct

Yes. That is correct.

3.

Question 3

Differential equations: If $\dot{x}(t) = -2x(t) + 2u(t)$, $x(0)=0$, and u(t)=\cases{0 & t ≤ 0\\1 & t>0}, what is $x(t)$ for $t>0$? Enter your answer as a mathematical expression. Note that $\dot{x}(t) =$d$x(t)/$d$t$.

H​int: See https://learner.coursera.help/hc/en-us/articles/208279916-Math-assignments for instructions on how to enter equations in Coursera.

0 / 1 point

$1 + e^{- 2 t}$

Please note: "e" will not be interpreted as the mathematical constant. For the mathematical constant, please use upper case "E".

e^(-2*t)+1

Incorrect

Sorry. That is not the correct response. Please check your answer for errors and consider refreshing your skills in differential equations.

4.

Question 4

Linear circuits: Consider the following electric circuit:

What is the voltage $v$ (in volts)?

1 / 1 point

4

Correct

Yes. That is correct.

5.

Question 5

Linear circuits: Consider the following electric circuit:

Before time $t=0$, the capacitor is completely discharged and the switch is open. At time $t=0$, the switch is closed. Enter a mathematical expression for the capacitor voltage that is valid for all time $t>0$.

H​int: See https://learner.coursera.help/hc/en-us/articles/208279916-Math-assignments for instructions on how to enter equations in Coursera.

1 / 1 point

$4 - 4 e^{- t}$

4-4*exp(-t)

Correct

Yes, that is correct.

6.

Question 6

Linear algebra: Consider the two vectors,

$x=\left[\begin{array}{c} 1\\2\\3\end{array}\right]$ and $y=\left[\begin{array}{c} 4\\5\\6\end{array}\right]$.

What is $x^Ty$?

1 / 1 point

32

Correct

Yes. That is correct.

7.

Question 7

Linear algebra: Consider the following matrix and vector,

$A=\left[\begin{array}{ccc} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{array}\right]$ and $x=\left[\begin{array}{c} 1\\0\\1\end{array}\right]$.

What is $x^TAx$?

1 / 1 point

20

Correct

Yes. That is correct.

8.

Question 8

Linear algebra: Consider the following matrix,

$A=\left[\begin{array}{ccc} 3 & 0 & 0\\ 0 & -10 & 0\\ 0 & 0 & 13 \end{array}\right]$.

What is the maximum eigenvalue of $A$?

0 / 1 point

10

Incorrect

Sorry. That is not the correct response. Please check your answer for errors and consider refreshing your skills in linear algebra.

9.

Question 9

Programming: Consider the following code segment (written in either the Octave or MATLAB programming language),

What is the value of the variable "x" after this code segment executes?

1 / 1 point

6

Correct

Yes. That is correct.

10.

Question 10

Programming: Consider the following code segment (written in either the Octave or MATLAB programming language),

What is the value of the variable "x" after this code segment executes?

1 / 1 point

8

Correct

Yes. That is correct.