Answer: a) a= (3/4)t 4a = 3t b = (5/2)t 2b = 5t b)See explanation below c) It will take 30.075 hours for the whole business to make at least $500 profit Step-by-step explanation: a) First we would represent the information given in terms of amount of bracelet produced and time spent in production with variables in order to convert to linear equations Let number of bracelet Darrelle makes = a Number of bracelet Danica makes = b Let the time spent in producing them in hours = t Darrelle takes 4 hours to make 3 bracelets: Rate of producing bracelet = (number of bracelet produced)/time Rate = a/t = 3/4 4a = 3t Linear equation form: y = mx + c a= (3/4)t The above equation is in the slope-intercept form indicating the intercept = 0 and slope = 3/4 4a - 3t = 0 (equation in standard form ) Danica makes 5 bracelets every 2 hours: Rate of producing bracelet = (number of bracelet produced)/time Rate = b/t = 5/2 2b = 5t Linear equation form: y = mx + c b = (5/2)t The above equation is in the slope-intercept form indicating the intercept = 0 and slope = 5/2 2b - 5t = 0 (equation in standard form) b) The equations are linear equations, hence they can be graphed. But as regards graphing using special functions, this answer can only be answered by you as I'm not aware of the special functions discussed in the course. c) Darrelle makes $10.50 in profit per bracelet. Danica makes $3.50 in profit per bracelet Since Darrelle and Danica work the same amount of time, we have to find the relationship between their profit, the number of bracelets produced and the time. Profit for Darrelle for 'a' number of bracelet product = $10.50 × a = $10.50a Profit for Danica per 'b' number of bracelet product = $3.50 × b = $3.50b Let P = total profit made by both P = $10.50a + $3.50b Relationship of profit in terms of time spent in production when they work same amount of time: P = $10.50(3/4 ×t)+ $3.50(5/2 × t) P = 16.625t When P = $500, t = ? 500 = 10.50(3/4 ×t)+ 3.50(5/2 × t) 500 = 7.875t + 8.75t 500 = 16.625t t = 30.075 hours It will take 30.075 hours for the whole business to make at least $500 profit
The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π. So, a coefficient of b=1 is equivalent to a period of 2π. To get the period of the sine curve for any coefficient b, just divide 2π by the coefficient b to get the new period of the curve.
