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Balwyn High School is planning to establish a Balwyn Island Theme Park. One of the attractions will be the waterslide: Balwyn High Tide Slide, whose shape will form the investigation of this task. The waterslide is modelled by the functions below, where x represents the horizontal displacement from the starting point in metres, and W represents the vertical height from the ground in metres. W₁(x) = -x + 20, x € [0,10) W₂(x) = (Xx : (x - 15)* + a,x € [10,k] W₂(x)=c-loge (x-18), x € (k, 27) a. Given that W₁(x) = W₂(x) are connected, show that a = - b. Hence show that W₁ (x) and W₂ (x) are smoothly connected.

Balwyn High School is planning to establish a Balwyn Island Theme Park. One of the attractions will be the waterslide: Balwyn High Tide Slide, whose shape will form the investigation of this task. The waterslide is modelled by the functions below, where x represents the horizontal displacement from the starting point in metres, and W represents the vertical height from the ground in metres. W₁(x) = -x + 20, x € [0,10) W₂(x) = (Xx : (x - 15)* + a,x € [10,k] W₂(x)=c-loge (x-18), x € (k, 27) a. Given that W₁(x) = W₂(x) are connected, show that a = - b. Hence show that W₁ (x) and W₂ (x) are smoothly connected.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Balwyn High School is planning to establish a Balwyn Island Theme Park. One of the attractions will be the waterslide: Balwyn High Tide Slide, whose shape will form the investigation of this task. The waterslide is modelled by the functions below, where x represents the horizontal displacement from the starting point in metres, and W represents the vertical height from the ground in metres. W₁(x) = -x + 20, x € [0,10) 1 10 W₂(x)== (x-15)² + a,x E [10, k] W3(x) = c-loge(x-18), x € (k, 27] 15 a. Given that W₂(x) = W₂(x) are connected, show that a = - b. Hence show that W₁ (x) and W₂(x) are smoothly connected.
Transcribed Image Text:Balwyn High School is planning to establish a Balwyn Island Theme Park. One of the attractions will be the waterslide: Balwyn High Tide Slide, whose shape will form the investigation of this task. The waterslide is modelled by the functions below, where x represents the horizontal displacement from the starting point in metres, and W represents the vertical height from the ground in metres. W₁(x) = -x + 20, x € [0,10) 1 10 W₂(x)== (x-15)² + a,x E [10, k] W3(x) = c-loge(x-18), x € (k, 27] 15 a. Given that W₂(x) = W₂(x) are connected, show that a = - b. Hence show that W₁ (x) and W₂(x) are smoothly connected.
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