In this section, square root equations involving square roots are solved using graphs, tables, and symbolic manipulation. A graphing calculator is needed.

To review writing equations with square roots, see module 6, lesson 6.

Example 1

The velocity v (in feet per second) of a jet can be approximated by the equation

where A is the area of the wings (in square feet) and L is the lift (in Newtons).

Source: Google

1. A Boeing 747 jet has a wing area of 5825 square feet and produces a lift of 2,834,400 Newtons.

    

   Answer the questions below.

   • What is the value of L?
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     Check Your Answer

     2,834,4000 Newtons
   • What is the value of A?
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     Check Your Answer

     5825 square feet
   • What is the equation for the jet's velocity?
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     Check Your Answer

     
   • What is the jet’s velocity?
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     Check Your Answer

     194.12 feet per second
2. The velocity of an airplane is 200 ft/sec and its wing area is 4000 sq. feet.

Watch the video to see a solution to this problem.

• What is the missing value?
  Interactive popup. Assistance may be required.

  Check Your Answer

  L
• What is the value of v?
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  Check Your Answer

  200 ft/sec
• What is the value of A?
  Interactive popup. Assistance may be required.

  Check Your Answer

  4000 sq feet
• What is the equation for the jet's velocity?
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  Check Your Answer

  200 = 8.8
• What is the jet’s wings lift (in Newtons)?
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  Check Your Answer

  200 = 8.8
  
  22.73 =
  516.53 = L 4000
  516.53 (4000) = L 4000 (4000)
  2,066,116 Newtons = L

  Square both sides

  

Example 2

A sustained–release tablet or capsule is designed to dissolve slowly and release the active drug over an extended period of time. Since they keep steadier levels of the drug in the bloodstream they can be taken less frequently than instant-release formulation drugs. Indometacin is a sustained-release drug that is a non-steroidal anti-inflammatory drug commonly used to reduce fever, pain, stiffness, and swelling. Its release percent can be modeled by the equation

Release % = – 10.7 + 42.5 √t – 4t

where t is the number of hours since the medicine was ingested.

1. What percent of the drug has been released 2 1 over 2 1 2 hours after taking the medicine?
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   Check Your Answer

   r% = – 10.7 + 42.5 √2.5 – 4(2.5)
   r% = – 10.7 + 67.2 – 10
   r% = 46.5
   46.5% of the drug is released after 2½ hours

   

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2. How long after taking the medicine will the release percent reach 100%?

Watch the video to see a graphic solution to this problem.