(1) The curved surface area A of a cone of height and base radius is pie R squareroot H square+T square.
(a) Make H the subject of the formula.
(b) Find the height of a cone of area 550cm Square and base radius 7cm, taking pie to be 22/7.
(2) if nSquare _ 1 over m = 4.
(a) Express n in terms of m .
(b) Hence find n when m=12.
Please somebody help if I don't do think assignment I will be flogged.
(1)
(a) To make H the subject of the formula, we need to isolate H on one side of the equation.
Given formula: A = πR√(H^2 + T^2)
Step 1: Square both sides of the equation
A^2 = (πR√(H^2 + T^2))^2
A^2 = π^2R^2(H^2 + T^2)
Step 2: Divide both sides of the equation by π^2R^2
A^2 / (π^2R^2) = (H^2 + T^2)
Step 3: Subtract T^2 from both sides of the equation
A^2 / (π^2R^2) - T^2 = H^2
Step 4: Take the square root of both sides of the equation
√(A^2 / (π^2R^2) - T^2) = H
Therefore, the formula for H is: H = √(A^2 / (π^2R^2) - T^2)
(b) Using the given values:
A = 550 cm^2
R = 7 cm
π = 22/7
Step 1: Substitute the values into the formula for H
H = √((550^2) / ((22/7)^2 * (7^2)) - T^2)
Step 2: Since T is not given, we can assume it to be zero (as it represents slant height in this context)
H = √((550^2) / ((22/7)^2 * (7^2)) - 0^2)
Step 3: Simplify the expression
H = √((550^2) / ((22/7)^2 * 49))
H = √((550 * 49 * 7^2) / (22^2))
H = √(269500 / 484)
H = √556.1983471
Therefore, the height of the cone is approximately 23.58 cm.
(2)
(a) Given equation: n^2 - 1/m = 4
Step 1: Add 1/m to both sides of the equation
n^2 = 4 + 1/m
Step 2: Take the square root of both sides of the equation (considering both positive and negative square roots)
n = ±√(4 + 1/m)
Therefore, n in terms of m is: n = ±√(4 + 1/m)
(b) Given m = 12
Step 1: Substitute the value m = 12 into the expression for n
n = ±√(4 + 1/12)
n = ±√(4 + 1/12)
n = ±√(4 + 1/12)
n = ±√(48 + 1)/12
n = ±√(49)/12
n = ±7/12
Therefore, when m = 12, n can be either 7/12 or -7/12.