Explanation Given information : Two ships start from point P at two speeds 8 knots and 12 knots in north and 60 degree east to north directions respectively. And distance between both the ships at a particular time t is let represented by s . Formula used : Here we have that Distance=Speed × Time , so distance covered by both ships after t seconds will be 8 ( t + 1 ) (because second ship takes 1 hour more) and 12t respectively after t second from leaving.Now, it is applied following cosine rule in above formed triangle PQR, cos θ = a 2 + b 2 − c 2 2 a b Where θ = 60 0 , a = P Q = 8 ( t + 1 ) , b = P R = 12 t c = Q R = s Calculation : On plug in these values in above cosine formula, cos 60 = ( 8 ( t + 1 ) ) 2 + ( 12 t ) 2 − s 2 2 ( 8 ( t + 1 ) ) ( 12 t ) ⇒ 1 2 = 64 t 2 + 128 t + 64 + 144 t 2 − s 2 192 ( t 2 + t ) ⇒ 96 t 2 + 96 t = 208 t 2 + 128 t + 64 − s 2 ⇒ s 2 = 208 t 2 + 128 t + 64 − 96 t 2 − 96 t ⇒ s 2 = 112 t 2 + 32 t + 64 ...... ( i ) That is the desired relation between s and t

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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Chapter 3.7, Problem 56PS

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To find the rate of increase in the distance between two ships that are heading towards north and east of north direction at different speeds at 2 P.M. and 5 P.M.

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Chapter 3.7, Problem 55PS

Chapter 3.7, Problem 57PS

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8:38 *** TEMU TEMU -3 -2 7 B 2 1 & 5G. 61% 1 2 -1 Based on the graph above, determine the amplitude, period, midline, and equation of the function. Use f(x) as the output. Amplitude: 2 Period: 2 Midline: 2 ☑ syntax error: this is not an equation. Function: f(x) = −2 cos(πx + 2.5π) +2× Question Help: Worked Example 1 ☑ Message instructor Submit Question ||| <

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To find the rate of increase in the distance between two ships that are heading towards north and east of north direction at different speeds at 2 P.M. and 5 P.M.

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To find the rate of increase in the distance between two ships that are heading towards north and east of north direction at different speeds at 2 P.M. and 5 P.M.

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Chapter 3 Solutions