BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2, Problem 12P
To determine

To find: The function that models the length (L) of shadow of woman standing near a street lamp in terms of her distance (d) from the base of the lamp.

Expert Solution

Answer to Problem 12P

The function that models L   in terms of d is L(d)=57d,d>0 .

Explanation of Solution

The geometric figure of the situation is shown below,

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2, Problem 12P

Figure (1)

In triangle AOB as shown in Figure (1), OA is height of street lamp, CD is height of woman, L is the length of shadow of woman and d is the distance of woman from base of street lamp.

Height of woman is 5ft . and height of street lamp is 12ft

Triangles AOB and CDB are similar and corresponding sides of similar triangles are in same proportion.

Mathematically,

CDAO=BDBO

Substitute 5 for CD, 12 for AO, L for BD and BO for L+d in above equation.

512=LL+d5(L+d)=12L[ab=cdad=cb]5L+5d=12L

Subtract (5L) from both the sides of above equation.

5L+5d5L=12L5L5d=7LL=57d

Thus, the function that models L in terms of d is L(d)=57d,d>0 .

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