MaplePrimes - Questions and Posts tagged with homework
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en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSat, 01 Nov 2014 10:28:39 GMTSat, 01 Nov 2014 10:28:39 GMTThe most recent questions and posts on MaplePrimes tagged with homeworkhttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with homework
http://www.mapleprimes.com/tags/homework
vector valued function, motion shuttle
http://www.mapleprimes.com/questions/202727-Vector-Valued-Function-Motion-Shuttle?ref=Feed:MaplePrimes:Tagged With homework
<p><strong>Solve, using 4000 miles for the radius of the earth. </strong></p>
<p> </p>
<p><strong>A space shuttle is in circular orbit 150 miles above the surface of the earth. Approximate </strong></p>
<ol>
<li><strong>the speed</strong></li>
<li><strong>the time required for one revolution.</strong></li>
</ol><p><strong>Solve, using 4000 miles for the radius of the earth. </strong></p>
<p> </p>
<p><strong>A space shuttle is in circular orbit 150 miles above the surface of the earth. Approximate </strong></p>
<ol>
<li><strong>the speed</strong></li>
<li><strong>the time required for one revolution.</strong></li>
</ol>202727Thu, 30 Oct 2014 17:57:49 Zlaporte bernardlaporte bernardEntropy changes in a free expansion
http://www.mapleprimes.com/questions/202714-Entropy-Changes-In-A-Free-Expansion?ref=Feed:MaplePrimes:Tagged With homework
<p>ADIABATIC FREE EXPANSION</p>
<p> </p>
<p>Suppose an ideal gas expands to four times its initial volume. From experience for this process, the initial and final </p>
<p>temperature are the same.</p>
<ol>
<li>Using a macroscopic approach, calculate the entropy change for the gas</li>
<li>Using statistical considerations, calculate the change in entropy for the gas and show that it agrees with the answer <br>you obtained in part 1.</li>
</ol><p>ADIABATIC FREE EXPANSION</p>
<p> </p>
<p>Suppose an ideal gas expands to four times its initial volume. From experience for this process, the initial and final </p>
<p>temperature are the same.</p>
<ol>
<li>Using a macroscopic approach, calculate the entropy change for the gas</li>
<li>Using statistical considerations, calculate the change in entropy for the gas and show that it agrees with the answer <br>you obtained in part 1.</li>
</ol>202714Wed, 29 Oct 2014 07:52:09 Zlaporte bernardlaporte bernardconditional probability DICE
http://www.mapleprimes.com/questions/202710-Conditional-Probability-DICE?ref=Feed:MaplePrimes:Tagged With homework
<blockquote>
<p><!--break--><!--break--><!--break--></p>
</blockquote>
<p><strong>What is the probability that the total of two dice will be greater than 9, given that the first die is a 5?</strong></p>
<p> </p><blockquote>
<p><!--break--><!--break--><!--break--></p>
</blockquote>
<p><strong>What is the probability that the total of two dice will be greater than 9, given that the first die is a 5?</strong></p>
<p> </p>202710Wed, 29 Oct 2014 07:23:31 Zlaporte bernardlaporte bernardvector-valued functions and space curves
http://www.mapleprimes.com/questions/202707-Vectorvalued-Functions-And-Space-Curves?ref=Feed:MaplePrimes:Tagged With homework
<ol>
<li>Sketch the two vectors listed after the formula for <strong>r</strong> (t).</li>
<li>Sketch, on the same plane, the curve C dterminated by r (t), and indicate the orientation for the given values of t.<br><br><strong>r</strong> (t)=t*<strong>i</strong> +4*cos (t)<strong>j</strong> +9*sin (t)<strong>k</strong>,<br><br><strong>r</strong> (0),<strong> r</strong>(Pi/4), t>=0<br><br></li>
</ol><ol>
<li>Sketch the two vectors listed after the formula for <strong>r</strong> (t).</li>
<li>Sketch, on the same plane, the curve C dterminated by r (t), and indicate the orientation for the given values of t.<br><br><strong>r</strong> (t)=t*<strong>i</strong> +4*cos (t)<strong>j</strong> +9*sin (t)<strong>k</strong>,<br><br><strong>r</strong> (0),<strong> r</strong>(Pi/4), t>=0<br><br></li>
</ol>202707Tue, 28 Oct 2014 18:55:54 Zlaporte bernardlaporte bernardconvert algebraic to parametric
http://www.mapleprimes.com/questions/202704-Convert-Algebraic-To-Parametric-?ref=Feed:MaplePrimes:Tagged With homework
<p>How to convert an algebraic equation to a parametrized one ?</p>
<p> </p>
<p>How to sketch the curve of a circular cylinder , x^2+y^3^=a^2 with the parametric equations lying on it ?</p>
<p>x=a*cos't) , y=a*sin(t) , z=b*t , if t varies from 0 to 2*Pi, the point P starts at(a,0,0) and moves upward.</p>
<p>How to show that the parametric equations are indeed lying on the cylinder ?</p>
<p>How to plot the whole things ?</p>
<p> </p><p>How to convert an algebraic equation to a parametrized one ?</p>
<p> </p>
<p>How to sketch the curve of a circular cylinder , x^2+y^3^=a^2 with the parametric equations lying on it ?</p>
<p>x=a*cos't) , y=a*sin(t) , z=b*t , if t varies from 0 to 2*Pi, the point P starts at(a,0,0) and moves upward.</p>
<p>How to show that the parametric equations are indeed lying on the cylinder ?</p>
<p>How to plot the whole things ?</p>
<p> </p>202704Tue, 28 Oct 2014 13:01:43 Zlaporte bernardlaporte bernardA concho-spiral
http://www.mapleprimes.com/questions/202690-A-Conchospiral-?ref=Feed:MaplePrimes:Tagged With homework
<p>A <strong>concho-spiral</strong> is a curve C that has a parametrization :</p>
<p><img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=064f206f260dab30e9502b761e91ecd5.gif" alt="x=a(e)^mu(t)*cos(t)"></p>
<p>y=<img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=2436ce33f655b97a3ddeeae356b56753.gif" alt="a(e)^mu(t)*sin(t)"></p>
<p><img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=e752e07e7065422e930805913491b217.gif" alt="z=b(e)^mu(t)"></p>
<p><img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=56021c1db0f528ab15753a332c9d718e.gif" alt="t>=0"></p>
<p>where a, b, <img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=fe05bfee5e2a61f9114fa931912b43d5.gif" alt="mu">, are constants.</p>
<ol>
<li>Show that C lies on the cone a^2*z^2=b^2*(x^2+y^2).</li>
<li>Sketch C for a = b = 4 and <img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=fe05bfee5e2a61f9114fa931912b43d5.gif" alt="mu">=-1.</li>
<li>Find the length of C corresponding to the t-interval [0,<img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=976bcbbc876d12a0a16947cc7f540b62.gif" alt="infinity">].</li>
</ol><p>A <strong>concho-spiral</strong> is a curve C that has a parametrization :</p>
<p><img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=064f206f260dab30e9502b761e91ecd5.gif" alt="x=a(e)^mu(t)*cos(t)"></p>
<p>y=<img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=2436ce33f655b97a3ddeeae356b56753.gif" alt="a(e)^mu(t)*sin(t)"></p>
<p><img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=e752e07e7065422e930805913491b217.gif" alt="z=b(e)^mu(t)"></p>
<p><img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=56021c1db0f528ab15753a332c9d718e.gif" alt="t>=0"></p>
<p>where a, b, <img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=fe05bfee5e2a61f9114fa931912b43d5.gif" alt="mu">, are constants.</p>
<ol>
<li>Show that C lies on the cone a^2*z^2=b^2*(x^2+y^2).</li>
<li>Sketch C for a = b = 4 and <img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=fe05bfee5e2a61f9114fa931912b43d5.gif" alt="mu">=-1.</li>
<li>Find the length of C corresponding to the t-interval [0,<img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=976bcbbc876d12a0a16947cc7f540b62.gif" alt="infinity">].</li>
</ol>202690Sun, 26 Oct 2014 14:48:12 Zlaporte bernardlaporte bernarddirectional derivatives, gradient
http://www.mapleprimes.com/questions/202646-Directional-Derivatives-Gradient?ref=Feed:MaplePrimes:Tagged With homework
<p> 1) find the direction in which f(x,y) increases most rapidly at the point P(1,2), and find the maximum rate of increase<br>of f at P.</p>
<p>Interpret 1) using the graph of f.</p>
<p> </p>
<p>Let f(x,y) = 2+x^2 +1/4*(y^2)</p><p> 1) find the direction in which f(x,y) increases most rapidly at the point P(1,2), and find the maximum rate of increase<br>of f at P.</p>
<p>Interpret 1) using the graph of f.</p>
<p> </p>
<p>Let f(x,y) = 2+x^2 +1/4*(y^2)</p>202646Wed, 22 Oct 2014 07:11:16 Zlaporte bernardlaporte bernardhow do you insert a tangent line onto a graph or merge graphs etc?
http://www.mapleprimes.com/questions/202609-How-Do-You-Insert-A-Tangent-Line-Onto?ref=Feed:MaplePrimes:Tagged With homework
<p>I need to make two graphs. 1st take the equation y= ln3x+3 and graph it and it's derivative. Then find the equation of the tangent line and the normal line to the given function at x=e Then I need to create a single graph containing the function, the tangent line, and it's normal line. Any pointers or help would be greatly appreciated. I can graph the equation and it's derivative ok but I don't know how to make a graph with multiple stuff on it. Thanks</p><p>I need to make two graphs. 1st take the equation y= ln3x+3 and graph it and it's derivative. Then find the equation of the tangent line and the normal line to the given function at x=e Then I need to create a single graph containing the function, the tangent line, and it's normal line. Any pointers or help would be greatly appreciated. I can graph the equation and it's derivative ok but I don't know how to make a graph with multiple stuff on it. Thanks</p>202609Fri, 17 Oct 2014 01:38:09 ZJazen1Jazen1Least Squares to Fit Curve
http://www.mapleprimes.com/questions/202581-Least-Squares-To-Fit-Curve?ref=Feed:MaplePrimes:Tagged With homework
<p>From some scientific experiments, the following set of data is available<br>(1.0, 2.33),(2.0, 0.0626),(3.0, −2.16),(4.0, −2.45),(5.0, −0.357),(6.0, 2.21),(7.0, 2.75),(8.0, 0.636),(9.0, −2.45).</p>
<p>We need to use least squares method to fit the curve to the data<br>y = a + b cos(x) + c sin(x) + d cos(2x) + e sin(2x)</p>
<p><br>Show your solution procedure in Maple and get the best fit for the coefficients. Finally<br>plot the data and the y curve together on the same graph to visualize the fitting. For the<br>data, use blue circles while for the y curve, use red solid line style. Use the leastsquares<br>command we learned in LinearAlgebra package.</p><p>From some scientific experiments, the following set of data is available<br>(1.0, 2.33),(2.0, 0.0626),(3.0, −2.16),(4.0, −2.45),(5.0, −0.357),(6.0, 2.21),(7.0, 2.75),(8.0, 0.636),(9.0, −2.45).</p>
<p>We need to use least squares method to fit the curve to the data<br>y = a + b cos(x) + c sin(x) + d cos(2x) + e sin(2x)</p>
<p><br>Show your solution procedure in Maple and get the best fit for the coefficients. Finally<br>plot the data and the y curve together on the same graph to visualize the fitting. For the<br>data, use blue circles while for the y curve, use red solid line style. Use the leastsquares<br>command we learned in LinearAlgebra package.</p>202581Mon, 13 Oct 2014 02:55:25 ZdgemdgemSolving system of Equations
http://www.mapleprimes.com/questions/202580-Solving-System-Of-Equations?ref=Feed:MaplePrimes:Tagged With homework
<p>What is the solution to the following system? Is the solution unique? Use<br>the reduced row echelon form to explain why.<br>x + 2y + 3z = 1,<br>4x + 5y + 6z = 1,<br>7x + 8y + 9z = 1</p><p>What is the solution to the following system? Is the solution unique? Use<br>the reduced row echelon form to explain why.<br>x + 2y + 3z = 1,<br>4x + 5y + 6z = 1,<br>7x + 8y + 9z = 1</p>202580Mon, 13 Oct 2014 02:52:52 ZdgemdgemHow to estimate the largest eigenvalues?
http://www.mapleprimes.com/questions/202579-How-To-Estimate-The-Largest-Eigenvalues?ref=Feed:MaplePrimes:Tagged With homework
<p>Find the eigenvalues and eigenvectors for</p>
<p>A =<br>2 0.37 0<br>0 1.1 −4.29<br>1.6 0 2.2</p>
<p><br>Can you estimate the largest eigenvalues (in absolute value) using Power method for this<br>problem? Try to explain why if you can</p><p>Find the eigenvalues and eigenvectors for</p>
<p>A =<br>2 0.37 0<br>0 1.1 −4.29<br>1.6 0 2.2</p>
<p><br>Can you estimate the largest eigenvalues (in absolute value) using Power method for this<br>problem? Try to explain why if you can</p>202579Mon, 13 Oct 2014 02:51:59 ZdgemdgemFinding Quadratic Equation
http://www.mapleprimes.com/questions/202578-Finding-Quadratic-Equation?ref=Feed:MaplePrimes:Tagged With homework
<p>Find the quadratic polynomial which interpolates (2, 0),(6, 1),(8, 0). Solve this with Maple. Start the problem by setting f(x) = ax2 + bx + c for example, then the unknowns are a, b, c.</p><p>Find the quadratic polynomial which interpolates (2, 0),(6, 1),(8, 0). Solve this with Maple. Start the problem by setting f(x) = ax2 + bx + c for example, then the unknowns are a, b, c.</p>202578Mon, 13 Oct 2014 02:50:20 ZdgemdgemPartial Differentiation
http://www.mapleprimes.com/questions/202567-Partial-Differentiation?ref=Feed:MaplePrimes:Tagged With homework
<p>Hello,</p>
<p> </p>
<p>A flate metal plate lies on an xy plane such that the temperature T at (x,y) is given by T=10(x^2+y^2)^2 , where T is in degrees and x and y are in centimeters.</p>
<p>Find the instantaneous rate of change of T with respect to distance at (1,2) in the direction of<br><br></p>
<p>a) the x-axis</p>
<p>b) the y-axis</p><p>Hello,</p>
<p> </p>
<p>A flate metal plate lies on an xy plane such that the temperature T at (x,y) is given by T=10(x^2+y^2)^2 , where T is in degrees and x and y are in centimeters.</p>
<p>Find the instantaneous rate of change of T with respect to distance at (1,2) in the direction of<br><br></p>
<p>a) the x-axis</p>
<p>b) the y-axis</p>202567Sat, 11 Oct 2014 11:02:26 Zlaporte bernardlaporte bernardtangent circles
http://www.mapleprimes.com/questions/202540-Tangent-Circles?ref=Feed:MaplePrimes:Tagged With homework
<p>How to get the equations of circles A, B, C, such as circle A with center (1,1) is drawn in the first quadrant.</p>
<p>Circle B with radius 2 and circle C are placed so that each circle is tangent to the other 2 circles and the x-axis.</p>
<p>THe 3 circles are on the first quadrant.</p>
<p>1) do it with Maple</p>
<p>2) do it by hand</p>
<p>3) draw the figure</p>
<p> </p>
<p>Regards</p><p>How to get the equations of circles A, B, C, such as circle A with center (1,1) is drawn in the first quadrant.</p>
<p>Circle B with radius 2 and circle C are placed so that each circle is tangent to the other 2 circles and the x-axis.</p>
<p>THe 3 circles are on the first quadrant.</p>
<p>1) do it with Maple</p>
<p>2) do it by hand</p>
<p>3) draw the figure</p>
<p> </p>
<p>Regards</p>202540Wed, 08 Oct 2014 11:01:12 Zlaporte bernardlaporte bernardModifying A Loop
http://www.mapleprimes.com/questions/202528-Modifying-A-Loop?ref=Feed:MaplePrimes:Tagged With homework
<p>N := 8;</p>
<p>b := 2 ∗ P i;<br>data := [];<br>for n f rom 0 to N do<br>data := [op(data), [n ∗ b/N, sin(n ∗ b/N)]];<br>od;</p>
<p>Since exact points are not needed, changed the loop (and reinitialize) to:</p>
<p>data := [];</p>
<p>for n from 0 to N do<br>data := [op(data), [evalf(n ∗ b/N), sin(evalf(n ∗ b/N))]];<br>od;</p>
<p>Modify the second example so that it can be used to graph the sin function<br>over any interval from a to b. (You should suppress the output from the for-loop in your<br>example, so that you <strong>do not fill up the worksheet with an unwieldy amount of output.</strong>)</p><p>N := 8;</p>
<p>b := 2 ∗ P i;<br>data := [];<br>for n f rom 0 to N do<br>data := [op(data), [n ∗ b/N, sin(n ∗ b/N)]];<br>od;</p>
<p>Since exact points are not needed, changed the loop (and reinitialize) to:</p>
<p>data := [];</p>
<p>for n from 0 to N do<br>data := [op(data), [evalf(n ∗ b/N), sin(evalf(n ∗ b/N))]];<br>od;</p>
<p>Modify the second example so that it can be used to graph the sin function<br>over any interval from a to b. (You should suppress the output from the for-loop in your<br>example, so that you <strong>do not fill up the worksheet with an unwieldy amount of output.</strong>)</p>202528Sun, 05 Oct 2014 04:08:14 Zdgemdgem