namely is just the difference of 3/10 - 1/4, since the denominators are 10 and 4, the LCD will then be 20.
Someone knows how to do this?
1 answer:
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Answer:
f(x) = 1.5x - 0.5x
Step-by-step explanation:
The function of the pattern represented by the pentagonal numbers is the sum of three triangular numbers.
The triangular number general formula
x (x + 1) / 2
For example,
The sequence
1, 3, 6, 10
*
* * *
* * * * * *
* , * *, * * *, * * * *
_____________________________
The pentagonal numbers
The sequence:
1, 5, 12, 22, 35
As shown in the picture can be divided into three triangles
Triangle 2
x (x + 1) / 2
Triangle 1 and 3 (they are triangles one unit smaller than 2)
n (n + 1) / 2
n= x-1
Replacing n
(x-1) ((x-1) + 1) / 2
(x-1) (x) / 2
(x-1) x / 2
______________
Function represents the pattern
Triangle 2 + (Triangle 1 + Triangle 3)
Triangle 1 = Triangle 3
So then,
Triangle 2 + 2* Triangle 1
x (x +1) /2 + 2* (x -1) x/2
Rearranging
0.5 x (x +1) + x(x -1)
0.5x^2 + 0.5x + x^2 -x
(0.5 x^2 + x^2) + (0.5x -x )
1.5 x^2 - 0.5 x
______
Answer:look at attachments
Step-by-step explanation:
Got 100% on Plato
Answer:
1,107 cc
Step-by-step explanation:
The 10 intervals of the scanning are
[0,1.5), [1.5,3), [3,4.5), [4.5,6), [6,7.5), [7.5,9), [9,10.5), [10.5,12), [12,13.5), [13.5,15)
The ideal thing would be to estimate the volume with the Midpoint Rule should be take n=10.
As we must use n=5, we divide the interval [0,15] in five intervals of length 15/5 = 3
[0,3], [3,6], [6,9], [9,12], [12,15] and take their midpoints
1.5, 4.5, 7.5, 10.5, and 13.5.
Now we estimate the volume V of 5 cylinders of height h=3 and area of the base A equals to the area given for the scanning where that midpoints fall
Cylinder 1
Midpoint=1.5, interval of scanning 2nd
A = 18, V= height*area of the base = 18*3 =54 cc
Cylinder 2
Midpoint=4.5, interval of scanning 4th
A = 78, V= height*area of the base = 78*3 =234 cc
Cylinder 3
Midpoint=7.5, interval of scanning 6th
A = 106, V= height*area of the base = 106*3 =318 cc
Cylinder 4
Midpoint=10.5, interval of scanning 8th
A = 129, V= height*area of the base = 129*3 =387 cc
Cylinder 5
Midpoint=13.5, interval of scanning 10th
A = 38, V= height*area of the base = 38*3 =114 cc
And the <em>estimate volume </em>is
54+234+318+387+114=1,107