After heating up in a teapot, a cup of hot water is poured at a temperature of 210°F. The cup sits to cool in a room at a temperature of 71°F. Newton's Law
of Cooling explains that the temperature of the cup of water will decrease
proportionally to the difference between the temperature of the water and the
temperature of the room, as given by the formula below:
T = Ta + (T. – T.)e-kt
Τα
the temperature surrounding the object
To = the initial temperature of the object
t = the time in minutes
T = the temperature of the object after t minutes
k = decay constant
The cup of water reaches the temperature of 197°F after 2.5 minutes. Using
this information, find the value of k, to the nearest thousandth. Use the
resulting equation to determine the Fahrenheit temperature of the cup of
water, to the nearest degree, after 5.5 minutes.
Enter only the final temperature into the input box.

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

No solution : there is no number of boxes that she bought

Ya i could just need to know what type of math