Exam 6: Equations

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If a projectile (such as a bullet)is fired into the air with an initial velocity v at an angle of elevation θ  (see the figure), then the height h of the projectile at time t is given by h = -16 t 2 + vt sin  θ If a projectile (such as a bullet)is fired into the air with an initial velocity v at an angle of elevation θ  (see the figure), then the height h of the projectile at time t is given by h = -16 t <sup>2</sup> + vt sin  θ   Give the equation for the height, if v is 1,600 feet per second and θ  is 30°. (Leave your answer in exact value form.) ​ Give the equation for the height, if v is 1,600 feet per second and θ  is 30°. (Leave your answer in exact value form.) ​

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Find all solutions if Find all solutions if   . Round your answer to the nearest tenth.   ​ . Round your answer to the nearest tenth. Find all solutions if   . Round your answer to the nearest tenth.   ​ ​

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Solve the equation for x  if Solve the equation for x  if   . Give your answer in radians using exact values only.  . Give your answer in radians using exact values only. Solve the equation for x  if   . Give your answer in radians using exact values only.

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​ ​   ,   ,  , ​   ,   ,  , ​   ,   ,

Solve for θ  if Solve for θ  if   .  . Solve for θ  if   .

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Eliminate the parameter t in the following: Eliminate the parameter t in the following:       ​   Eliminate the parameter t in the following:       ​ ​

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Eliminate the parameter t from the following and then sketch the graph: Eliminate the parameter t from the following and then sketch the graph:   ​ ​

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Solve the equation for x if Solve the equation for x if   .   ​ . Solve the equation for x if   .   ​ ​

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Use your graphing calculator to find the solutions to the equation to the nearest tenth of a degree in the interval Use your graphing calculator to find the solutions to the equation to the nearest tenth of a degree in the interval    by defining the left side and right side of the equation as functions and then finding the intersection points of their graphs. Make sure your calculator is set to degree mode.  sin  θ - 4 = 7sin  θ  by defining the left side and right side of the equation as functions and then finding the intersection points of their graphs. Make sure your calculator is set to degree mode. sin  θ - 4 = 7sin  θ

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Solve the equation for θ  if Solve the equation for θ  if   . Do not use a calculator.  . Do not use a calculator. Solve the equation for θ  if   . Do not use a calculator.

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Solve for θ  if Solve for θ  if   .  . Solve for θ  if   .

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Find all solutions if Find all solutions if   . Use exact values only. Verify your answer graphically.   ​ . Use exact values only. Verify your answer graphically. Find all solutions if   . Use exact values only. Verify your answer graphically.   ​ ​

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Solving the following equation will require you to use the quadratic formula. Solve the equation for θ  between 0° and 360°, and round your answers to the nearest tenth of a degree. Solving the following equation will require you to use the quadratic formula. Solve the equation for θ  between 0° and 360°, and round your answers to the nearest tenth of a degree.

(Short Answer)
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Eliminate the parameter t from the following and then sketch the graph: Eliminate the parameter t from the following and then sketch the graph:       ​   Eliminate the parameter t from the following and then sketch the graph:       ​ ​

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Solve for θ  if Solve for θ  if   .   ​ . Solve for θ  if   .   ​ ​

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Eliminate the parameter t in the following: Eliminate the parameter t in the following:

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Eliminate the parameter t in the following: Eliminate the parameter t in the following:        Eliminate the parameter t in the following:    

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The formula below gives the relationship between the number of sides n , the radius r , and the length of each side l in a regular polygon. Find n , if l = r . The formula below gives the relationship between the number of sides n , the radius r , and the length of each side l in a regular polygon. Find n , if l = r .     n = __________ The formula below gives the relationship between the number of sides n , the radius r , and the length of each side l in a regular polygon. Find n , if l = r .     n = __________ n = __________

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Eliminate the parameter t in the following: Eliminate the parameter t in the following:

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Solve the equation for x if Solve the equation for x if   .   ​ . Solve the equation for x if   .   ​ ​

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Eliminate the parameter t in the following: Eliminate the parameter t in the following:        Eliminate the parameter t in the following:    

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