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Solved: 3336. Circular motion Find parametric equations

Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs ISBN: 9780321947345 167

Solution for problem 33 Chapter 10.1

Calculus: Early Transcendentals | 2nd Edition

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Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs

Calculus: Early Transcendentals | 2nd Edition

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Problem 33

3336. Circular motion Find parametric equations that describe the circular path of the following objects. For Exercises 3335, assume 1x, y2 denotes the position of the object relative to the origin at the center of the circle. Use the units of time specified in the problem. There is more than one way to describe any circle. A go-cart moves counterclockwise with constant speed around a circular track of radius 400 m, completing a lap in 1.5 min. 3

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Chapter 3: Court Procedures Procedural Rules  Provide a framework for every dispute o Specify what must be done at each age of litigation process  Procedural rules are complex  Rules vary from court to court and state to state  Procedures depend on whether case is civil or criminal  Trials involve “due process” o Requires adequate notice and fair and impartial hearing o Example: Civil trials in federal district courts are governed by Federal Rules of Civil Procedure (FRCP) Stages of Litigation  Three phases o Pre-trial o Trial o Post-trial Consulting with Attorney  Generally the first step of process  Types of Attorneys’ Fees o Fixed fees  Charged for performance of services as drafting and simple will o Hourly fees  Charged for matters that involve an intermediate period of time o Contingency fees  Fixed as percentage (between 25% and 40%) of client’s recovery in certain types of lawsuits  Personal injury lawsuit  If lawsuit is unsuccessful attorney receives no fee  Client must reimburse attorney for all out-of-pocket costs incurred  Settlement considerations o Once attorney is retained, he/she is required to pursue resolution of the matter on client’s behalf Pre-Trial Procedures  Involves o Filing of pleadings o Gathering of evidence (Discovery) o Possible pretrial conference/jury selection  Pleadings o The complaint and answer taken together o Pleadings inform each party of other’s claims and specify issues involved in case o Plaintiff’s complaint  Contains statement alleging:  Facts showing that court has subject-matter and personal jurisdiction  Facts establishing plaintiff’s basis for reliefs  The remedy the plaintiff is seeking  Can be lengthy or brief  Depends on complexity of case and rules of jurisdiction o Service of Process  Court must have proof that defendant was notified lawsuit  Plaintiff must deliver copy of complaint  Summons  A notice requiring defendant to appear in court and answer complaint  Default judgement  If other party fails to respond to allegations o Method of Service  Depends on rules of court or jurisdiction in which lawsuit is brought  Server hands summons and complaint to defendant or leaves is at defendant’s residence/place of business o Waiver of Formal Service  When defendant is willing to waive (give up) her/his rights to be served personally  Defendant receives additional time to respond to complaint  (60 days instead of 20) o Defendant’s response  The form of an answer  Defendant either admits or denies allegations in plaintiff’s complaint  Any allegations not denied by defendant is deemed by court to have been admitted  Affirmative defenses  To raise new facts to show that other party should not be held liable for damages  Defendants in both civil/criminal cases can raise affirmative defenses  Counterclaims  Denying party’s allegations and set forth own claim that the accident occurred  Dismissals and Pre-Trial Judgement o Motion  A procedural request submitted to court by attorney on behalf of her/his client  Filing party must send opposing party a notice of motion  Informs opposing party that motion has been filed  Pretrial motions  Include motion to dismiss, motion for judgement on pleadings, and motion for summer judgement o Motion to Dismiss  Asks court to dismiss case for reasons stated in motion  Normally the defendant requests dismissal  If judge grants motion to dismiss, plaintiff is given time to file amended complaint o Motion for Judgement on Pleadings  Asks court to decide the issue solely on pleadings without proceeding trial o Motion for Summary Judgement  Asks court to grant judgement in party’s favor without trial  Motion can be made before or during trial  Party can submit evidence obtained at any point before trial that refutes other party’s factual claim  Affidavits: copies of documents (contracts, email, letters) obtained through course of discovery Discovery  The process of obtaining information from the opposing party or from witnesses prior to trial  Includes gaining access to: o witnesses o documents o records o other types of evidence  Prevents surprises at trial by giving both parties access to evidence that might be hidden  Serves to narrow issues so trial time is spent productively  Discovery Rules o FRCP/similar state rules set guidelines for discovery activity o Discovery is allowed regarding any matter relevant to claim or defense of any party o Rules attempt to protect witnesses/parties from undue harassment and material disclosure o Court may deny request if it involves privileged or confidential business information o Court can limit scope of discovery in a number of ways  Depositions o Sworn testimony recorded by authorized court official (court reporter) o Impeach  Challenge the credibility of something o Deposition can be used as testimony if witness is not available at trial  Interrogatories o Written questions directed towards the party (under oath)  Not to a witness (difference from depositions)  Requests for Admissions o Written request of truth of matter relation to trial  Requests for documents, objects, and entry upon land  Requests for Examinations o If physical or mental condition of one party is in question  Electronic Discovery o Information stored electronically o E-evidence  Electronic evidence consisting of computer-generated or electronically recorded information (email, voicemail, tweets, spreadsheets, etc.) o Metadata  Electronics that record certain information about files on their hard drives  Can only be obtained from the file in its electronic format  No print-outs Pre-Trial Conference  A hearing  After discovery has taken place and before trial begins attorneys meet with judge Right to a Jury Trial  7 Amendment guarantees right to jury trial o For cases at law in federal courts when amount in controversy exceeds $20  Does not need to be exercised  Jury Selection o Voir Dire (to tell the truth) o Party may challenge certain number of prospective jurors peremptorily  Ask an individual not to be sworn in as juror without reasoning o Alternatively, party may challenge prospective juror “for cause”  Provide reason why individual should not be sworn in as juror The Trial  Opening statements o The facts that both attorneys prove during trial o Provides opportunity for each lawyer to give a brief version of facts and supporting evidence being used during trial  Rules of evidence o A series of rules the courts have created to ensure that any evidence presented during trial is fair/reliable o Evidence Must Be Relevant to Issues  Evidence that proves/disproves a fact in questions or establish degree of probability of fact or action o Hearsay Evidence Not Admissible  Testimony someone gives in court about a statement made by someone else who was not under oath at time of statement  Examination of Witnesses and Potential Motions o Direct examination  Calling first witness for plaintiff, and examining, or questioning, witness o Cross-examination  The interrogation of a witness by one’s opponent o Two types of witnesses  Expert  Fact (average person) o Expert Witnesses  A person who has specialized knowledge in a particular area beyond an average person  When witnesses are qualified as experts they can offer their opinions and conclusions about evidence in that field o Potential Motion and Judgement  Motion for judgement as a matter of law  When the defendant’s attorney may ask judge to direct the verdict for defendant on the ground that plaintiff has presented no evidence to support her/his claim o Defendant’s Evidence  Defendant’s attorney presents evidence and witnesses for defendant’s case  Rebuttal  Offering additional evidence that refutes defendant’s case  Rejoinder  Refute evidence o Closing Arguments, Jury Instructions, and Verdict  Closing Argument  Each attorney summarizes facts and evidence presented to trial  Indicates why facts and evidence support his/her client’s claim  Jury instructions  Instructions often called charges  In civil trial, standard of proof is a preponderance of evidence  In criminal trial, standard proof must prove its case beyond a reasonable doubt  Verdict  Specifies jury’s factual findings Post-trial Motions  Motion for new trial o Only if she/he believes the jury was in error and it is not appropriate to grant judgement for other side  Motion for Judgement N.O.V. (notwithstanding the verdict o If the defendant’s attorney moved earlier for directed verdict The Appeal  Either party may appeal verdict during trial o Appellants must have legitimate grounds  Filing Appeal o Contains all pleadings, motions, and other documents filed with court o Contains complete written transcript of proceedings, including:  Testimony  Arguments  Jury instructions  Judicial rulings o Brief  A formal legal document outlining facts and issues of case, judge’s rulings, or jury’s findings that should be reversed or modified  Appellate Review o Court has following options after reviewing case:  Affirm trial court’s decision  Reverse trial court’s judgement if trial court erred  Remand (send back) case to trial court for further proceedings  Affirm or reverse decision in part  Modify a lower court’s decision  Higher Appellate Courts o Losing party does not have right to have case heard by higher appellate court Enforcing the Judgement  Requesting court assistance in collecting judgement o Writ of execution  An order directing the sheriff to seize and sell the defendant’s nonexempt assets, or property  Availability of Assets o Plaintiff checks if defendant has sufficient assets before suit is filed

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Chapter 10.1, Problem 33 is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

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Solved: 3336. Circular motion Find parametric equations