Answer to Question #246262 in Calculus for Jess

Question

19. A square gate in a wood fence has a diagonal brace. Write a formula for the area of a
square as a function of the length of its diagonal.
20. Suppose the average family spends 25% of its income I on food F, and 10% of this amount
F is spent on junk food J. Write J as a function of I.
21. Cliff left point A at 8 A.M. walking east at 3 kph. Renz left point A at 9 A.M. walking north
at 4 kph.
(a) Express the distance between Cliff and Renz as a function of the elapsed time

Answer 1

19.

The formula for the area of a square as a function of the length of its diagonal is written as:

A = s²

or

A = 1/2 * d²

20.

Income = I

Food = F

Junk food = J

The average family spends 25% of it's income on food F:

F = 0.25I

10% of this amount is spent on junk food:

J = 0.10F

J as a function of I​ :

J = (0.10) (0.25I)

J = 0.025I

21.

Cliff left point A at 8 A.M and walking east at rate of 3 kph then his coordinates are (3t, 0)

Renz left point A at 9 A.M and walking north at rate of 4 kph then his coordinates are (0, 4t)

Then distance between them using distance formula is:

= Square root (3t - 0)² + (0 - 4t)²

= Square root (9t² + 16t²)

= Square root (25t²)

= 5t

So, the distance between Cliff and Renz as a function of the elapsed time can be expressed as:

Distance = 5t

Where, t = time