V= 20.8x^2 - 458.3x + 3,500 represents the value of a car from 1964 to 2002. what year did the car have the least value? (x= 0 in 1964)

See the picture for all detail, I have done it by hand.
Few important steps;
-Take the first derivative
-Put it equal to zero
-you get the x value which is equal to 11
-Now for the check that x=11 is the least value or not, take the second derivative
-As, the 2nd derivative is positive so it is the least value

As x=0 in 1964 add 11 to it so at x=11 we get 1975 so in this year car have least value

What is your question?

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