A clock is hung on a wall so that the center is 20 cm below the ceiling. The minute hand is 10 cm long, and the hour hand is 6 cm long. Find a function m(t)that gives the distance the tip of the minute hand is from the ceiling as a function of minutes past midnight. The function should have the form m(t)=A(Bt-C)+D.

Answered: A clock is hung on a wall so that the…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

ChapterCSR: Contents Of Student Resources

Section: Chapter Questions

Problem 1.37EP

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Question

A clock is hung on a wall so that the center is 20 cm below the ceiling. The minute hand is 10 cm long, and the hour hand is 6 cm long.

Find a function m(t)that gives the distance the tip of the minute hand is from the ceiling as a function of minutes past midnight. The function should have the form m(t)=A(Bt-C)+D.

Expert Solution

Step 1

Consider the diagram as per give information,

It can be observed from the diagram the distance of tip of minute hand from the ceiling is $y$ cm and the angle $θ$ rotated by the hand in $t$ minutes.

So, the distance of minute hand's tip from the ceiling is,

$\begin{array}{rcl} y & = & C E \\ = & B E - B C \dots (1) \end{array}$