## Question 1: Identify the dependent and independent variables for the following problems.

 (a) P = 64d (b) F(C) = 9/5 C + 32 (c) C(F) = 5/9 (F – 32)

Solution

(a). P = 64d

This equation is used to find the pressure P on an object immersed in saltwater.(saltwater is denser than common water!) ‘d’ is the depth of the object below the surface. Pressure ‘P’ varies as depth ‘d’ is varied. Here,
Independent variable = d (this you can choose according to your need)
Dependent variable = P

(b). F(C) = 9/5 C + 32

This is the equation for converting centigrade scale reading of temperature into Fahrenheit scale. It gives the corresponding Fahrenheit value, F of a given Centigrade scale value, C.
Independent Variable = C
Dependent Variable = F

(c). C(F) = 5/9 (F-32)

This equation converts Fahrenheit value of temperature into centigrades. For a certain Fahrenheit degree of temperature the corresponding value in centigrade scale is determined.
Independent Variable = F
Dependent Variable = C

(d). s = f(r, θ) = rθ

This equation relates the linear displacement to the angular displacement. It says the linear displacement ‘s’ is a function of the radius ‘r’ and angular displacement θ of a rotating object (like wheel).
Independent Variables = r, θ
Dependent Variable = s

(e). F = θ(m,a) = ma

The force ‘F’ applied on a body of mass ‘m’ is equal to m times the acceleration produced.
Independent Variable = m, a
Dependent Variable = F

(e). F = θ(m,a) = ma

The force ‘F’ applied on a body of mass ‘m’ is equal to m times the acceleration produced.
Independent Variable = m, a
Dependent Variable = F

(f). SA = θ(l, w, h) = 2lw + 2lh + 2wh

The function represents the surface area of a cuboid with length = l, width = w and height = h. Its surface area is, then,
SA = 2lw + 2lh + 2wh
Independent Variables (we can choose them as input variables) = l, w, h
Dependent Variable = SA (Surface area of the cuboid). What is a cuboid?

Hint: A square is to cube as a rectangle to a cuboid.

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2. Saifurrehman

Grt

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