This is annoying
the perimiter is 34 units
the width is 6.5 units
ok.
perimiter=2(Length+Width)
P=2(L+W)
solve for L
distribute
P=2L+2W
minus 2W
P-2W=2L
divide by 2
given that P=34 units and W=6.5 units
the equation would be
or
<u>Part a)</u> if a page is reduced to 80%, what percent enlargement is needed to return it to its original size?
Let
x---------> the percent enlargement
we know that
the original size is the 100%
so
x*80%=100%
x=(100%/80%)
x=1.25--------> 1.25=(125/100)=125%
therefore
<u>the answer Part a) is</u>
the percent enlargement is 125%
<u>Part b)</u> Estimate the number of times in succession that a page must be copied to make the final copy less than 15% of the size of the original
we know that
A photocopy machine can reduce copies to 80% of their original size
so
Copy N 1
0.80*100%=80%
Copy N 2
0.80*80%=64%
Copy N 3
0.80*64%=51.2%
Copy N 4
0.80*51.2%=40.96%
Copy N 5
0.80*40.96%=32.77%
Copy N 6
0.80*32.77%=26.21%
Copy N 7
0.80*26.21%=20.97%
Copy N 8
0.80*20.97%=16.78%
Copy N 9
0.80*16.78%=13.42%-------------> 13.42% < 15%
therefore
<u>the answer Part b) is</u>
the number of times in succession is 9
For us to be able to answer this question the number of the items that Micah is buying.
....and any important information concerning this problem.
Answer:
For this case, the first thing we must do is define variables:
x: number of hammers
y: number of wrenches
We write the system of inequations:
10x + 6y <= 120
x + y> = 14
Step-by-step explanation:
The function is written as:
f(x) = log(-20x + 12√x)
To find the maximum value, differentiate the equation in terms of x, then equate it to zero. The solution is as follows.
The formula for differentiation would be:
d(log u)/dx = du/u ln(10)
Thus,
d/dx = (-20 + 6/√x)/(-20x + 12√x)(ln 10) = 0
-20 + 6/√x = 0
6/√x = 20
x = (6/20)² = 9/100
Thus,
f(x) = log(-20(9/100)+ 12√(9/100)) = 0.2553
<em>The maximum value of the function is 0.2553.</em>
