The science of physics, specifically projectile motion, goes hand in hand with the mathematics of trigonometry. We need the math of trigonometry to model the flight path of an object moving through the air. Describe another connection between a math topic and a non-math topic, where the math topic is needed to explain and model the non-math topic.

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explanation:

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step-by-step explanation:

i hope this is what you were looking for.

see attached graph

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.