Math
total surface area = 2 ends + (front and back) + (top and bottom) = 2(2x3) + 2(2x4) + 2(3x4) = 12 + 16 + 24 = 52 Whatever is lxwlh ??
Maths
cos 4x = 1 - 2sin^2 (2x) = 1 - 2(sin 2x)(sin 2x) = 1 - 2(2sinxcosx)(2sinxcosx) = 1 - 8(sinxcosx)^2 or = 1 - 8(sin^2 x)(cos^2 x) as required
math
my arithmetic error 144 - 81 = 63 , not 108 so height = √63 = 3√7 = 7.937 area = (1/2)(18)(3√7) = 71.435
math
let each of the equal sides be x then the base is (3/2)x x+x+3x/2= 42 times 2 4x + 3x = 84 7x = 84 x = 12 sides are 12, 12, and a base of 18 we need the height for area calculation: make a sketch showing the height, let it be h I see: h^2 + 9^2 = 12^2 h^2 = 108 h = √108 ...
Maths A Year 12
what is 32500(1.15)^4 ?
Maths A
I will assume that "with monthly rests" means compounded monthly (never heard that it expressed that way) i = .054/12 = .0045 amount = 20000(1.0045)^36 = 23508.66
algebra
testing for x = ±2, ± 4 and ±13, I found f(4) = 0 , so x=4 is a zero, and x-4 is a factor x^3-8x^2+29x-52 = (x-4)(x^2 - 4x + 13) = 0 solving x^2 - 4x + 13 = 0 by completing the square (in this case faster than the formula) x^2 - 4x + 4 = -13+4 (x-2)^2 = -9...
Calculus
f(5) = 125 - 35 + 5 = 95 f(5+h) = (5+h)^3 - 7(5+h) + 5 = h^3 + 15h^2 +68h + 95 --- (I'll let you check that derivative = Lim ( f(h+5) - f(5) )/h as h ---> 0 = lim ( h^3 + 15 h^2 + 68h = 95 - 95)/h = lim h^2 + 15h + 68 , as h --> 0 = 68 so equation of tangent at (5,95...
math
time = 8 + 125/365 = 8 + .345466 = 8.345466 let the present value be x x e^(.0835(8.345466)) = 225500 x = $112361.83
math
A , C, and F are linear, thus defined for all x's B) x^2 + y^2 = 1 is a circle , thus not a function, which is only defined for -1 ≤ x ≤ +1 E) a quadratic function, defined for all x's D) not sure what you meant here if it is y = √(10-2x) then it woul...
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