What is the length of a 36° arc of a circle with radius 25?
Since the 360° arc of a circle is given by the formula for the perimeter of a circle (P = Pi * Diameter), to get a fraction of that all we need to do is multiply the perimeter of this particular circle times the ratio of the given angle to the total of the circumference, as follows: 36° / 360° = 0.10 Diameter = 2 * radius = 50 P = Pi * 50 = 50 Pi Arc of 36° = P * 0.10 = (50 Pi) * 0.10 = 5 Pi Arc of 36° = 5 Pi = 15.708
Jane gets paid 8 dollars an hour when she works shifts during the week (Monday-Friday) and gets paid an extra 2 dollars per hour when she works a shift during the weekend (saturday and Sunday). If she is working a 4 hour shift every day from Monday to Friday, and two 4 hour shifts daily on the weekends, how many weeks does she need to work following this schedule in order to save up 11,000 dollars, if she's spending 100 dollars per week on transportation and food?
The first step in this problem is figuring out how much money Jane is making each week. To do this, we multiply the amount of dollars time the number of hours she's working at each rate, time the number of days at those specific rates, and then sum those quantities: 8 x 4 = 32 dollars daily from Mon-Fri 32 x 5 = 160 dollars during the week (Mon-Fri) (8+2) x 8 = 80 dollars daily on the weekend 80 x 2 = 160 dollars during the weekend 160 + 160 = 320 dollars total during the whole week Now that we know how much money she's making during an entire week (320 dollars), we substract the amount she's spending weekly on transportation and food. 320 - 100 = 220 dollars net profit per week After figuring this out, we only need to divide the desired amount of money to be saved up, by the profit per week. 11,000/220 = 50 weeks
Given the equation x^2 + 15x + 54, which value or values of x would make this equal to zero?
There are two ways to go about this: 1.- Using the general quadratic equation, assuming ax^2 + bx + c = x^2 + 15x + 54, which would in turn give us two answers ( x = -6, x = -9) 2.- Perhaps the easier and quicker way in this case, is just finding out which combination of two numbers summed is 15, and multiplied is 54 (a.k.a. factoring this equation into two multiplying expressions). With some quick examination, one can come to the conclusion that these numbers are 6 and 9, resulting in the fllowing: x^2 + 15x + 54 = (x + 6)(x + 9) = 0 The values of x needed for this to be true, are those that make it so the expressions inside the parenthesis are equal to zero, as follows: If x + 6 = 0 then x = -6 If x + 9 = 0 then x = -9