What is 510° expressed in radian measure?
We can simply multiple by pi / 180 to convert from degrees to radians. This leaves us with: (510*pi) / 180 which simplifies to (17*pi) / 6
What is the equation of a circle with its center at (5,–2) and a radius of 3?
We know the equation of a circle is (x – h)^2 + (y – k)^2 = r^2 where the center is at point (h, k) with radius r. Since our center point is (5, -2) and the radius is 3, we will have: (x - 5)^2 + (y - (-2))^2 = 3^2 which simplifies to: (x - 5)^2 + (y + 2)^2 = 9
During its first week of business, a market sold a total of 108 apples and oranges. The second week, five times the number of apples and three times the number of oranges were sold. A total of 452 apples and oranges were sold during the second week. Determine how many apples and how many oranges were sold the first week.
First, let a = the # of apples and let o = the # of oranges We know a + o = 108 as this is the total number that the market sold. Next we know 5a + 3o = 452 bases on the second and third sentences of the problem. When we have two equations with two unknowns, we can use algebra to solve. Solve the first equation for o to get o = 108 - a Next, plug that into the second equation (Don't forget parentheses!) We get 5a + 3 (108 - a) = 452 Distribute: 5a + 324 - 3a = 452 Combine like terms: 2a + 324 = 452 Subtract 324 from both sides: 2a = 128 Divide both sides by 2: a = 64 Use a to find o by plugging it in above (either equation will work!) Using a + o = 108: 64 + o = 108 Subtract 65 from both sides: o = 44 Thus, our final answer is 64 apples and 44 oranges were sold in the first week.