A dietician works in a hospital and prepares meals under the guidance of a physician. Suppose that for a particular patient, a physician prescribes a meal to have 850 calories, 60g of protein, and 320 mg of vitamin C. The dietician decides to prepare the meal using steak (each 3-oz serving contains 300 Cal, 20 g of protein, and no vitamin C), baked potatoes (one baked potato contains 100 Cal, 5 g of protein, and 20 mg of vitamin C), and Brussels sprouts (one 156-g serving contains 50 Cal, 5 g of protein, and 100 mg of vitamin C). How many servings of each food are required to satisfy the physician's requirements?

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12