Rashad is considering two designs for a garden. In Design 1 he would use fencing to surround a square plot of land that has an a
rea of 1,296 square feet. In Design 2 he would divide a plot of land into two rectangular sections, each 15 feet by 36 feet, and surround the plot with fencing, as well as place fencing along the dividing line of the two sections.
Which plan would cost less in fencing? Explain.
A. Design 1, because it requires 12 fewer feet of fencing than Design 2
B. Design 1, because it requires 24 fewer feet of fencing than Design 2
C. Design 2, because it requires 12 fewer feet of fencing than Design 1
D. Design 2, because it requires 24 fewer feet of fencing than Design 1
The ANSWER IS B all of the answer i found online were wrong when I was doing the quiz ...being a helping hand
Which plan would cost less in fencing? Explain.
A. Design 1, because it requires 12 fewer feet of fencing than Design 2
B. Design 1, because it requires 24 fewer feet of fencing than Design 2
C. Design 2, because it requires 12 fewer feet of fencing than Design 1
D. Design 2, because it requires 24 fewer feet of fencing than Design 1
The ANSWER IS B all of the answer i found online were wrong when I was doing the quiz ...being a helping hand
1 answer:
We know that
see the attached figure to better understand the problem
design 1
the perimeter of a square=4*b
where
b is the length side
area of a square=b²
area=1296 ft²
so
1296=b²
b=√1296----> b=36 ft
the perimeter of a square (design 1)=4*b----> 4*36-----> 144 ft
design 2
the perimeter of design 2=15*4+36*3----> 168 ft
design 1 require 144 ft of fence
design 2 require 168 ft of fence
design 2 > design 1
design 2-design 1=168 ft-144 ft------> 24 ft
therefore
the answer is the option
<span>B. Design 1, because it requires 24 fewer feet of fencing than Design 2</span>
see the attached figure to better understand the problem
design 1
the perimeter of a square=4*b
where
b is the length side
area of a square=b²
area=1296 ft²
so
1296=b²
b=√1296----> b=36 ft
the perimeter of a square (design 1)=4*b----> 4*36-----> 144 ft
design 2
the perimeter of design 2=15*4+36*3----> 168 ft
design 1 require 144 ft of fence
design 2 require 168 ft of fence
design 2 > design 1
design 2-design 1=168 ft-144 ft------> 24 ft
therefore
the answer is the option
<span>B. Design 1, because it requires 24 fewer feet of fencing than Design 2</span>
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Answer:
Part 1)
See Below.
Part 2)
Step-by-step explanation:
Part 1)
The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:
We want to verify that the expression:
Is the linear approximation for the function:
At <em>x</em> = 0.
So, find f'(x). We can use the chain rule:
Simplify. Hence:
Then the slope of the linear approximation at <em>x</em> = 0 will be:
And the value of the function at <em>x</em> = 0 is:
Thus, the linear approximation will be:
Hence verified.
Part B)
We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.
In other words:
By definition:
Therefore:
We can solve this by using a graphing calculator. Please refer to the graph shown below.
We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.
In interval notation:
