Find the curvature K of the curve at the point $r(t)={e}^{t}\mathrm{cos}t\cdot i+{e}^{t}\mathrm{sin}t\cdot j+{e}^{t}k,P(1,0,1)$

illusiia
2020-12-28
Answered

Find the curvature K of the curve at the point $r(t)={e}^{t}\mathrm{cos}t\cdot i+{e}^{t}\mathrm{sin}t\cdot j+{e}^{t}k,P(1,0,1)$

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Bella

Answered 2020-12-29
Author has **81** answers

Differentiate

Find Magnitude

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Differentiate

Find Magnitude

Recall that

Result

asked 2021-08-16

Classify each of the studies as either descriptive or inferential. Explain your answers. In an article titled “Teaching and Assessing Information Literacy in a Geography Program” (Journal of Geography, Vol. 104, No. 1, pp. 17-23), Dr. M. Kimsey and S. Lynn Cameron reported results from an on-line assessment instrument given to senior geography students at one institution of higher learning. The results for level of performance of 22 senior geography majors in 2003 and 29 senior geography majors in 2004 are presented in the following table. Level of performance Met the standard: 36−48 items correct Passed at the advanced level: 41−48 items correct Failed: 0−35 items correct Percent in 2003 82%50%18% Percent in 2004 93%59%7%
Level of performance
Met the standard:
36−48 items correct

Passed at the advanced level: 41−48 items correct

Failed: 0−35 items correct

Percent in 2003

82%

50%

18%

Percent in 2004

93%

59%

7%

Passed at the advanced level: 41−48 items correct

Failed: 0−35 items correct

Percent in 2003

82%

50%

18%

Percent in 2004

93%

59%

7%

asked 2022-05-20

Counting routes from home to office if you only return home if you realize you have forgotten something before you reach the office

The following is how you can go to the office from home:

Home $\to $ Four Roads $\to $ Schools $\to $ Three Roads $\to $ University $\to $ Five Roads $\to $ Parks $\to $ Two Roads $\to $ Offices

You are forgetful minded. You may have forgotten something at home. You remember what you forgot at home, either at your school or university or in the park, and you go back to pick it up. Then the journey continues from the beginning again. You forget one thing at most during the day and when you reach the office you do not go back to take back what you have left. So how many different routes are possible for you?

I have tried this way:

Case 1: I remember what I forgot at school:

In this case, I can go to school in 4 ways and come back in 4 ways and go back in 4 ways. Then I can start the journey from there in $3\cdot 5\cdot 2$ ways.

Case 2: I remember what I forgot at university:

In this case, I can go to university in $4\cdot 3$ ways and come back in $4\cdot 3$ ways and go back in $4\cdot 3$ ways. Then I can start the journey from there in $5\cdot 2$ ways.

Case 3: I remember what I forgot at park:

In this case, I can go to park in $4\cdot 3\cdot 5$ ways and come back in $4\cdot 3\cdot 5$ ways and go back in $4\cdot 3\cdot 5$ ways. Then I can start the journey from there in 2 ways.

Case 4: I go to office without remembering:

In this case, I can go to the office in $4\cdot 3\cdot 5\cdot 2$ ways.

So, total ways would be $=(4\cdot 3+3\cdot 5\cdot 2)+(4\cdot 3\cdot 3+5\cdot 2)+(4\cdot 3\cdot 5\cdot 3)+2+4\cdot 3\cdot 5\cdot 3$ ways.

The following is how you can go to the office from home:

Home $\to $ Four Roads $\to $ Schools $\to $ Three Roads $\to $ University $\to $ Five Roads $\to $ Parks $\to $ Two Roads $\to $ Offices

You are forgetful minded. You may have forgotten something at home. You remember what you forgot at home, either at your school or university or in the park, and you go back to pick it up. Then the journey continues from the beginning again. You forget one thing at most during the day and when you reach the office you do not go back to take back what you have left. So how many different routes are possible for you?

I have tried this way:

Case 1: I remember what I forgot at school:

In this case, I can go to school in 4 ways and come back in 4 ways and go back in 4 ways. Then I can start the journey from there in $3\cdot 5\cdot 2$ ways.

Case 2: I remember what I forgot at university:

In this case, I can go to university in $4\cdot 3$ ways and come back in $4\cdot 3$ ways and go back in $4\cdot 3$ ways. Then I can start the journey from there in $5\cdot 2$ ways.

Case 3: I remember what I forgot at park:

In this case, I can go to park in $4\cdot 3\cdot 5$ ways and come back in $4\cdot 3\cdot 5$ ways and go back in $4\cdot 3\cdot 5$ ways. Then I can start the journey from there in 2 ways.

Case 4: I go to office without remembering:

In this case, I can go to the office in $4\cdot 3\cdot 5\cdot 2$ ways.

So, total ways would be $=(4\cdot 3+3\cdot 5\cdot 2)+(4\cdot 3\cdot 3+5\cdot 2)+(4\cdot 3\cdot 5\cdot 3)+2+4\cdot 3\cdot 5\cdot 3$ ways.

asked 2021-08-16

We have a recursively defined sequence $a}_{n$ .

${a}_{0}=0,{a}_{1}=3$ , and $a}_{n}=3{a}_{n-1}-2{a}_{n-2$ for $n\ge 2$

We would like to prove that f or all$n\ge 0,{a}_{n}=3\cdot {2}^{n}-3$ .

Prove this using the stronger mathematical induction.

We would like to prove that f or all

Prove this using the stronger mathematical induction.

asked 2022-06-25

What is the contradiction (no I do not mean negation) of this statement: "The sum of ANY two positive integers is positive"

I believe that it can be rewritten in the form: "If two integers are positive then their sum is positive.". i.e. $A\to B$.

My math teacher believes that the contradiction is: "There exists two positive integers whose sum is nonpositive.".

But I believe that it is: "The sum of any two positive integers is nonpositive.".

Please note the main difference between my answer and his is the difference between "there exists and any". i.e. $\mathrm{\exists}$ and $\mathrm{\forall}$

I believe that it can be rewritten in the form: "If two integers are positive then their sum is positive.". i.e. $A\to B$.

My math teacher believes that the contradiction is: "There exists two positive integers whose sum is nonpositive.".

But I believe that it is: "The sum of any two positive integers is nonpositive.".

Please note the main difference between my answer and his is the difference between "there exists and any". i.e. $\mathrm{\exists}$ and $\mathrm{\forall}$

asked 2022-06-14

How to use structural induction on lists?

I don't really understand structural induction and how to use it. The question is use structural induction on lists to prove that $\mathrm{rev}(\mathrm{rev}(L))=L$. You may use the lemma that $\mathrm{rev}{\textstyle (}\mathrm{app}(L,M){\textstyle )}=\mathrm{app}{\textstyle (}\mathrm{rev}(M),\mathrm{rev}(L){\textstyle )}.$.

So far I believe the base cases are:

$L=[\phantom{\rule{thickmathspace}{0ex}}]$

But after that I am little confused as to how to go through the proof. Any help would be appreciated!

I don't really understand structural induction and how to use it. The question is use structural induction on lists to prove that $\mathrm{rev}(\mathrm{rev}(L))=L$. You may use the lemma that $\mathrm{rev}{\textstyle (}\mathrm{app}(L,M){\textstyle )}=\mathrm{app}{\textstyle (}\mathrm{rev}(M),\mathrm{rev}(L){\textstyle )}.$.

So far I believe the base cases are:

$L=[\phantom{\rule{thickmathspace}{0ex}}]$

But after that I am little confused as to how to go through the proof. Any help would be appreciated!

asked 2022-01-19

The number of terms in $(x+y+z)}^{30$ is 496.

How many terms would there be if the same terms were combined? How can we find out?

How many terms would there be if the same terms were combined? How can we find out?

asked 2022-07-18

Let P be the power set of {a,b,c} Define a function from P to the set of integers as follows: $f(A)=|A|.(|A|$ is the cardinality of A.) Is f injective? Prove or disprove. Is f surjective? Prove or disprove.

I'm having a hard time understanding what this question is asking (as I have with most discrete math problems). What does it mean by "Let P be the power set of..."?

I'm having a hard time understanding what this question is asking (as I have with most discrete math problems). What does it mean by "Let P be the power set of..."?