The density curve must satisfy two important conditions.
These two conditions are:
1- The total area under the density curve MUST BE equal to 1.
(Area total = 1)
2- Every point that is on the curve must have a vertical height that is equal to or greater than zero
(vertical height for each point ≥ zero)<span>
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To solve the exercirses which are shown in the figure attached, you must follow the proccedure below:
7) (x)=x³-6x²+8x
(x)=x(x³-6x²+8)
(x)=(x-4)(x-2)x
The lenght is: x
The height is= (x-4)
8) √(2x+8)-6=4
1. You need to clear the variable "x". Then:
√(2x+8)=4+6
√(2x+8)=10
(√2x+8)²=10²
2x+8=100
2x=100-8
x=92/2
x=46
9) l4x+3l=9+2x
1. To solve the left member, you must evaluate two cases: it could be positive,or negative. Then:
2. Negative:
l4x+3l=9+2x
-4x-3=9+2x
-4x-2x=9+3
-6x=12
x=12/-6
x=-2
3. Positive:
l4x+3l=9+2x
4x+3=9+2x
4x-2x=9-3
2x=6
x=6/2
x=3
Ok, so the quadratic coefient is 1, so great
take 1/2 of the linear coefient and square it
10/2=5, (5)^2=25
add that to both sides
x^2+10x+25=7+25
factor perfect square trionomial
(x+5)^2=32
squaer root both sides
x+5=+/-4√2
minus 5
x=-5+/-4√2
x=-5+4√2 and -5-4√2
37k (cost of the materials for each kite) plus 28k (the labor for each kite) plus 6,000=x (the total cost). With this equation you can plug in any number of kites so...
37k+28k+6,000=x Combine like terms...
65k+6,000=x Plug in k...
65(170)+6,000=x Multiply...
11,050+6,000=x Add...
x=17,050
