3 boxes times 40 = 120 + 3 = 143
or 3 boxes times 43 = 129
Step-by-step explanation:
LHS = Left Hand Side ; RHS = Right Hand Side
a) RHS = 1/ tan x
= 1/ (Sin x/Cos x)
= Cos x/Sin x
= LHS
b) LHS = Sin^2 x / tan^2 x
= Sin^2 x / (Sin^2 x/Cos^2 x)
=( Sin^2 x * Cos^2 x) / (Sin^2 x)
= Cos^2 x
= 1 - Sin^2 x (Because sin^2 x + cos^2 x = 1)
= RHS
c) RHS = Sin^3 x / tan x + Cos^3 x
= Sin^3 x / (Sinx/Cosx) + Cos^3 x
= (Sin^3 x * Cos x)/Sin x + Cos^3 x
= Sin^2 x * Cos x + Cos^3 x
= Cos x (Sin^2 x + Cos^2 x)
= Cos x *(1) {Because, Sin^2 x + Cos^2 x = 1}
= Cos x
= LHS
Answer: 10
Step-by-step explanation:
Use Pythagorean theorem!
a^2+b^2=c^2
6^2+8^2=c^2
64+36=c^2
100=c^2
Take the square root of 100 and you get c=10
Answer:Area of the lawn is 1725 ft^2
Step-by-step explanation:
The yard is in the shape of a trapezoid. The area of the lawn can be determined by finding the area of the trapezoid. The formula for determining the area of a trapezoid is expressed as
Area of trapezoid =
1/2(a + b)h
Where
a is the length of one of the parallel sides of the trapezoid
b is the length of the other parallel side of the trapezoid.
h is the perpendicular height of the the trapezoid.
From the diagram,
a = 50 feet
b = 65 feet
h = 30 feet
Area of the lawn = 1/2(50 + 65)× 30
= 1/2 × 115 × 30 = 1725 ft^2