<span>the measure of ∠APD is </span>30 degrees
We know that 12² = 144 and 13² = 169 , then :
12² < 152 < 13²
Step-by-step explanation:
x+9-7
x+2?????????????
First, solve f(x)=4x-3x^2=0,
or
x(4-3x)=0
=>
x=0, x=4/3
The area enclosed by the parabola over the x-axis is therefore
A=integral f(x)dx from 0 to 4/3=[2x^2-x^3] from 0 to 4/3 = 32/27
Let the line intersect the parabola at a point (a,f(a)) such that the area bounded by the line, the parabola and the x-axis is half of A, or A/2, then the area consists of a triangle and a section below the parabola, the area is therefore
a*f(a)/2 + integral f(x)dx from a to 4/3 = A/2 = 16/27
=>
2a^2-3a^3/2+a^3-2a^2+32/27=16/27
=>
(1/2)a^3=16/27
a=(32/27)^(1/3)
=(2/3)(4^(1/3))
=1.058267368...
Slope of line is therefore
m=y/x=f(a)/a=4-2(4^(1/3))
=0.825197896... (approx.)
72 ft.
there are 6 faces
2 faces are 3 by 6 which equals 36 because 3×6=18 and 18 ×2=36
2 faces are 3 by 2 which equals 12 because 3×2=6 and 6×2=12
2 faces are 6 by 2 which equals 24 because 6×2=12 and 12×2=24
and 36+12+24=72