Question

or the next few problems, practice writing functions which model certa t ions 5. Suppose the product of two numbers x andy is 100, and must be positive a. Ifx 20, then y- Ifx then y= b. Write a function that gives the sum of these two numbers in terms of (Hint: we have that xy = 100, use this to get an expression for y that involves the variable x. Then set up the sum of x and y in terms of x only) What is the domain of the function in part function)? e . what are the possible x-values for the 6. A rectangle with sides of length and w has perimeter 100 yards a. Ir = 50 yards, then w= and the area A= b. Write a function that gives the area in terms of L (Hint: we have that 21 + 2 400, use this to get an expression for w that involves the variable L. Then set up the area in terms of only.) c. What is the domain of the function in part(b) i.e. what are the possible L-values for the function)? 7. A rectangular box with a square base has a volume of 10,000 cm a. If the length of the base is x 50 cm, then the height of the box h = b. Write a function that gives the surface area in terms of x. (Hints surface area is the SUM of the areas of all the sides of the box, We have that xh = 10000, use this to get an expression for h that involves the variable x. Then set up the surface area in terms of xonly.) What is the domain of the function in part (b) (e. what are the possible x-values for the function)?

Answer 1

(5) The and y 8 is Too (a) if product two nos x .: xy = 100 x=20, 2o.y = 100 = y = 100 y=5] Ang 20 - if x = 2 3 y = 150 - 22. y = 100 y = loox & y = 50x3 = (y=150 Ang (b) Now, xy=100 = y=100 The sum of two no's is : S=x+y = (x + 100 Ang (ie. x70) And Ang length (e. a70). I and width (C) As, x must be positive. And at x = 0, 10000 s is discontinuous. So Domain of s is: 10,oo) (6) The perimeter of rectangle with "W' is : 2(ltw). So, 21l+w) = 400 ltw=200 (a) if & = 50 yards 5o+w=200 [w = 150 yards ang

Now, area, A = exw A = 508 150 A = (7500yd ang (6) As ltw=200 = W = 200-l Now, A= exw A= C) A in part (bl is continuous Domain is (0,00) celine l (200-l) Any if ero. So, (7) het length of square base by 'x'am and height of box be 'hem. Now, volume of box, V = xxx xh V = x²h = x²h = 10,000 ( V= looo) (a) if x= 50cm, 7 (50)? h = 10000 = h - 1000 h = 10000 [h= 4 cm Ang (b) Now, xh = 10000 = h = loooo The surface area of rectangular box is : S = 2(16+ bh the) S= 2(. 2+ X.1000 + 10 * * S =2( + 10900 + 10000) = 2 (2+ +*) (c) Domain is at (0,0) Aug 2500 22 2