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Given:
l = length of the rectangle
w = width of the rectangle
P = 4 ft, constant perimeter
Because the given perimeter is constant,
2(w + l) = 4
w + l = 2
w = 2 - l (1)
Part A.
The area is
A = w*l
= (2 - l)*l
A = 2l - l²
This is a quadratic function or a parabola.
Part B.
Write the parabola in standard form.
A = -[l² - 2l]
= -[ (l -1)² - 1]
= -(l -1)² + 1
This is a parabola with vertex at (1, 1). Because the leading coefficient is negative the curve is downward, as shown below.
The maximum value occurs at the vertex, so the maximum value of A = 1.
From equation (1), obtain
w = 2 - l = 2 - 1 = 1.
The maximum value of the area occurs when w=1 and l=1 (a square).
Answer:
The area is maximum when l=1 and w=1.
The geometric argument is based on the vertex of the parabola denoting maximum area.
l = length of the rectangle
w = width of the rectangle
P = 4 ft, constant perimeter
Because the given perimeter is constant,
2(w + l) = 4
w + l = 2
w = 2 - l (1)
Part A.
The area is
A = w*l
= (2 - l)*l
A = 2l - l²
This is a quadratic function or a parabola.
Part B.
Write the parabola in standard form.
A = -[l² - 2l]
= -[ (l -1)² - 1]
= -(l -1)² + 1
This is a parabola with vertex at (1, 1). Because the leading coefficient is negative the curve is downward, as shown below.
The maximum value occurs at the vertex, so the maximum value of A = 1.
From equation (1), obtain
w = 2 - l = 2 - 1 = 1.
The maximum value of the area occurs when w=1 and l=1 (a square).
Answer:
The area is maximum when l=1 and w=1.
The geometric argument is based on the vertex of the parabola denoting maximum area.
Yes it is true that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars because null hypothesis is rejected.
Given among 2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticut trucks, 45 had only rear license plates.
let be the probability that commercial cars have rear license plates and
be the probability that connected trucks have rear license plates.
Cars Trucks Total
Total 2049 334 2383
x 239 45 284
p 0.1166 0.1347 0.1191
α=0.05
Hypothesis will be :
It is a left tailed test at 0.05 significance.
Standard errors of p=
=
=
=0.0066
Test statistic Z=p difference/standard error
=(0.1166-0.1347)/0.0066
=-0.0181/0.0061
=-2.967
p value=0.001505<5%
Since p is less than 5% we reject null hypothesis.
We cannot calculate standard deviation so we cannot calculate confidence interval.
Hence there is statistical evidence at 5% significance level to support that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
Learn more about z test at brainly.com/question/14453510
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