4 inches I believe would be the answer
V = x · y²
2 x + y = 3
y = 3 - 2 x
V = x · ( 3 - 2 x )² = x · ( 9 - 12 x + 4 x² ) = 9 x - 12 x² + 4 x³
V ` = 9 - 24 x + 12 x² = 3 ( 4 x² - 8 x + 3 ) = 3 ( 4 x² - 6 x - 2 x + 3 ) =
= 3 [ 2 x ( 2 x - 3 ) - ( 2 x - 3 ) ] = 3 ( 2 x - 3 ) ( 2 x - 1 )
The largest volume is when: V ` = 0, so:
2 x - 3 = 0
2 x = 3
x = 1.5 ( which is incorrect, because : y = 0 )
or: 2 x - 1 = 0
2 x = 1
x = 0.5, y = 3 - 2 · 0.5 = 3 - 1 = 2
V max = 0.5 · 2² = 0.5 · 4 = 2 ft³
Answer:
Step-by-step explanation:
To write a linear inequalities we use the same guidelines as linear equations. They are written in the form, and or with any other inequality signs.
One line has y-intercept 2 and slope is -5/1 (down 5 and over 1).
This means the equation is
.
Test a point not on the line to determine the direction of the inequality sign.
(0,0)
This is true but not the equation becasue (0,0) is not shaded.
The other line has y-intercept -4 and slope 3/1 (up 3 and over 1).
This means the equation is
.
Test a point not on the line to determine the direction of the inequality sign.
(0,0)
This is false and the equation since (0,0) is not in the shaded portion.
True.................................
Using an exponential function, it is found that it takes 5.42 years for the car to halve in value.
<h3>What is an exponential function?</h3>
A decaying exponential function is modeled by:
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem, the car depreciates 12% a year in value, hence r = 0.12 and the equation is given by:
.
It halves in value at t years, for which A(t) = 0.5A(0), hence:
t = 5.42.
It takes 5.42 years for the car to halve in value.
More can be learned about exponential functions at brainly.com/question/25537936
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