Variety of Equations

Variety of Equations

Among the professionals you have interviewed for your article , were several state and federal government spokespersons who use linear equations in a variety of ways

1 . An employee of the National Parks Service told you about a location in Washington , DC . It is a large grassy area south of the White House known as the Ellipse . The National Tree Lighting Ceremony is held annually on the Ellipse . Because the President officiates at this event the Secret Service makes calculations which they use in planning security . The Ellipse is

actually an ellipse with major axis of length 1048 ft . and minor axis of length 898 ft . Assuming that a coordinate system is superimposed on the area in such a way that the centr is at the origin and the major and minor axes are on the x- and y- axes of the coordinate system , respectively , find an equation of the ellipse

Figure 1 . Ellipse

Equation of the Ellipse (Weisstein , 2007

So that the equation of the ellipse

2 . The Board of Governors at the Federal Reserve Bank set the prime interest rate . These rates trickle down through the economy at various rates and affect consumer spending and saving habits . The economists at the Federal Reserve follow sample households in to extrapolate information which they use in forecasting . For example , in one household they studied , the family made an investment for 1 year that earned 7 .50 simple interest . If the principal had been 25 more and the interest rate 1 less , the interest would have been the same . Find the principal and the rate

Generating two equations from the statement using the formula for simple interest I

i t with t 1 (teacherschoice .com , 2003

eqn 1 where I is the interest and

br is the principal with time is just 1 year

eqn 2 where I is interest and

is principal

We will use the process called substitution by solving for

from eqn1 and substitute it to eqn 2

Substitute to eqn 2

Using the quadratic formula 3 . Another family in the Federal Reserve study group borrowed 120 ,000 The loan is to be repaid in 13 years at 12 interest , compounded annually . How much will be repaid at the end of 13 years

Using the Future (Wikipedia , 2007 , this will be the amount repaid at the end of 13 years

4 . Twice a week , the State of Michigan runs a 6 out of 49 number lotto that pays at least 2 million . The State needs to know the probabilities of winning in to ensure that the lottery has ample reserves for payouts . You purchase a card for 1 and pick any 6 numbers from 1 to 49 If your numbers match those that the state draws , you win . How many 6-number combinations are there for the drawing ? If you buy one ticket what is your probability of winning (6 out of 6

Using the formula for permutations (Mahler Wesner , 1994 ) of...