2m+3v=23
4m+8v=56
-2(2m+3v=23)
-4m-6v=-46
4m+8v=56
2v=10
v=5
plug in v
2m+15=23
2m=8
m=4
movies=$4
video games=$8
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.)
Answer:
120
Step-by-step explanation:
the formula of a box is L x W x H
so since the length is 6 and the width is 4 and the height is 5 you multiply
6x4x5=120
Tan 2x = 2 tan x / (1-tan^2x)
hence, tan 2x = 1
2x = pi
x = pi/2.