Activity 17 page 216answer:A. 1-5B. 1-2​

Answer: Part A: Translating statements into mathematical sentences. Joint variation means a variable varies directly as the product of two or more other variables. The general form is  z = kxy , where k is the constant of variation. 1.  P varies jointly as q and r.  Answer:  P = kqr 2.  V varies jointly as l, w, and h.  Answer:  V = klwh 3.  The area A of a parallelogram varies jointly as its height h and the square of the radius r.  Answer:  A = khr² 4.  The volume V of a cylinder varies jointly as its height h and the square of the radius r.  Answer:  V = khr² 5.  The heat H produced by an electric lamp varies jointly as the resistance R and the square of the current i.  Answer:  H = kRi² 6.  The force F applied to an object varies jointly as the mass m and the acceleration a.  Answer:  F = kma 7.  The volume V of a pyramid varies jointly as the area of the base B and the altitude h.  Answer:  V = kBh 8.  The area A of a triangle varies jointly as the base b and the altitude h.  Answer:  A = kbh 9.  The appropriate length s of a rectangular beam varies jointly as its width w and its depth d.  Answer:  s = kw d 10.  The electrical voltage varies jointly as the current I and the resistance R.  Answer:  V = kIR  Part B: Solving for the constant of variation and finding missing values. Problem 1:  z varies jointly as x and y, and z = 60 when x = 5 and y = 6.  a. Find z when x = 7 and y = 6. - First, find k:  60 = k(5)(6)  =>  k = 2 - Then, substitute:  z = 2(7)(6)  =>  z = 84  Answer: z = 84 b. Find x when z = 72 and y = 6. - Substitute:  72 = 2(x)(6)  =>  72 = 12x  =>  x = 6  Answer: x = 6 c. Find y when z = 80 and x = 4. - Substitute:  80 = 2(4)(y)  =>  80 = 8y  =>  y = 10  Answer: y = 10 Problem 2:  z varies jointly as x and y. If z = 3 when x = 3 and y = 15, find z when x = 6 and y = 9.  - Find k:  3 = k(3)(15)  =>  k = 1/15 - Substitute:  z = (1/15)(6)(9)  =>  z = 3.6  Answer: z = 3.6 Problem 3:  z varies jointly as the square root of the product of x and y. If z = 3 when x = 3 and y = 12, find x when z = 6 and y = 64.  - Find k:  3 = k√(3*12)  =>  3 = k√36  =>  k = 1/2 - Substitute:  6 = (1/2)√(x*64)  =>  12 = √(64x)  =>  144 = 64x  =>  x = 144/64 = 9/4  Answer: x = 9/4 Problem 4:  d varies jointly as h and g. If d = 15 when h = 14 and g = 5, find g when h = 21 and d = 8.  - Find k:  15 = k(14)(5)  =>  k = 3/14 - Substitute:  8 = (3/14)(21)(g)  =>  8 = (9/2)g  =>  g = 16/9  Answer: g = 16/9 [tex].[/tex]

Answered by mjPcontiga | 2024-10-21