8. A loaded barge is being towed by two tugboats, and the magnitude of the resultant is 6000 pounds directed along the axis of the barge (see figure). Find the tension in the tow lines fi they each make an 18° angle with the axis of the barge.     **You may use decimals.  Simply round your final answer to the hundredths place please.   **I should see work here.

Find the magnitude and direction angle of each vector: 4pts    4.

7. Forces with magnitudes of 2000 newtons and 900 newtons act on a machine part at angles of 30° and -45°, respectively with the x-axis.  Find the direction and magnitude of the resultant of these forces.     Magnitude: [mag] Direction: [dir] **You may use decimals.  Simply round to the hundredths place please.   **I should see work here.

Attach a pdf of your work for the first and last problems of this quiz.  This is the most important question to answer on the exam!  Please scan or take a picture of your handwritten work with a phone or device.  Airdrop or email it to yourself and cc: your teacher.    Find the file in your computer’s file explorer when you click “Choose a File”. (Do not drag and drop.) If you have trouble, please connect to Honorlock support by clicking the blue button with the speech bubble. They will help and document your attempt to correct the situation. Tell the support agent you are done with the test and are having trouble submitting your work. They will help you momentarily bypass the blocking program Honorlock uses to get your file uploaded properly. Remember: You are expected to make every effort to turn your work in before the exam closes. If your work is not uploaded during the exam, your teacher will contact you. If you know that there was a problem, email your teacher immediately and describe the situation and the steps that you took to correct it. Your teacher will consult the recording and Honorlock Support Log. Your proactivity and ability to explain your actions will ensure that the instance is not viewed as an Honor Code violation.

Evaluate each series. [sum1]   [sum2]   [sum3]   [sum4]   You should have work for these problems. 

7. Write an algebraic expression that is equivalent to the expression:

Please upload a clearly scanned pdf of your work for all 4 problems.  

Find the exact value of the expressions.     2pts each 4.

Pick one sine and one cosine equation from above to graph on the interval [0, 2π].  (5pts per graph) Make sure your axes are labeled. (2 points) Make sure you have at least 5 distinct points per graph. (5 points) Be sure to label which equations you are graphing. 

Solve the equation and write complex solutions in standard form. ​ ​