1 Class Exercises2015
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Transcript of 1 Class Exercises2015
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Linear Mathematics and Matrices
Class exercises. January 14th, 2015 1. Which of the following algebraic expressions are linear equations? Explain! a. 5x +3.7y = sin 32( ) b. 9 4a+ 9x c. 7m+ n 7.5 = y
d. x + 2y2 + z = 81 e. 34+ ab 7 = c f. 7x a = x + y3 2. First: translate the problem into a (system of) linear equation(s). Second: find the solution. a. In June 2010 the world largest beach towel was displayed in Las Palmas (Spain). It had a perimeter of 224.68 meters, and a length of 87.14 meters. What was the width of the towel? b. A carpenter needs to make a circular table leaf with a perimeter of 3 meters. What will be the diameter of this table leaf? c. Your neighbor has a car loan charging 0.75% interest per month and a loan for his speedboat that charges 0.5% interest per month. How much does he owe on each account if he pays a total of 395.50 monthly interest on a total debt of 62,200 ? 3. Bring the following linear equations in standard form, and find their solution.
a. 4b 7+ 2b =1+ 2b+8 b. 13 2x 1( ) =54 x +
3112
c. 2 x 1( ) 4 = 4 1+ x( )+ 2x + 2 d. 6210 x 1( ) 4 =4210 x 2x( )
4. You are given the following system of linear equations: 7x1 + x5 = 2x2 x3 =1x4 + x5 =
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Which of the three 5-tuples below are solutions of the system?
a. 2,8,4,1, 3"
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&' b. 1,8, 7, 5,5( ) c. 0,177,176, 2, 2( )
5. The receipts for last weekends showing of a classic Disney movie in your neighborhood cinema theater were 410 for an audience of 100 people. Children paid 3 for a ticket, seniors paid 5. The regular price was 6. Twice as many childrens tickets as regular admission tickets were purchased. Determine how many of each type of ticket were sold.