Let n = the number of points
(x-1) + ... (x-x)
The last term will always be 0, when you reach that, stop.
ex. 1pt: 1-1=0
2pt: (2-1) + (2-2) = 1
3pt: (3-1) + (3-2) + (3-3) = 3
Answer:
51.26 ft
Step-by-step explanation:
First find the area of the triangle:
a=1/2 base times height
a=(1/2)(6)(4)
a=12 ft
Now find the area of the circles:
a= pi times radius squared
a= pi times 2.5 squared
a=19.63 ft
19.63 + 12 = 31.63 ft
first off, let's convert the mixed fraction to improper fraction and then proceed, let's notice that by PEMDAS or order of operations, the multiplication is done first, and then any sums.
![\stackrel{mixed}{1\frac{7}{8}}\implies \cfrac{1\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{15}{8}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{3}{4}~~ + ~~\cfrac{15}{8} \div \cfrac{1}{2}\implies -\cfrac{3}{4}~~ + ~~\cfrac{15}{8} \cdot \cfrac{2}{1}\implies -\cfrac{3}{4}~~ + ~~\cfrac{15}{4} \\\\\\ \cfrac{-3+15}{4}\implies \cfrac{12}{4}\implies 3](https://tex.z-dn.net/?f=%5Cstackrel%7Bmixed%7D%7B1%5Cfrac%7B7%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B1%5Ccdot%208%2B7%7D%7B8%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B15%7D%7B8%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20-%5Ccfrac%7B3%7D%7B4%7D~~%20%2B%20~~%5Ccfrac%7B15%7D%7B8%7D%20%5Cdiv%20%5Ccfrac%7B1%7D%7B2%7D%5Cimplies%20-%5Ccfrac%7B3%7D%7B4%7D~~%20%2B%20~~%5Ccfrac%7B15%7D%7B8%7D%20%5Ccdot%20%5Ccfrac%7B2%7D%7B1%7D%5Cimplies%20-%5Ccfrac%7B3%7D%7B4%7D~~%20%2B%20~~%5Ccfrac%7B15%7D%7B4%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B-3%2B15%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B12%7D%7B4%7D%5Cimplies%203)
9514 1404 393
Answer:
22.5
Step-by-step explanation:
The average rate of change on the interval [a, b] is the ratio ...
(f(b) -f(x))/(b -a)
For your function and interval, it is ...
(f(0.5) -f(0))/(0.5 -0)
Since f(0) = 0, this reduces to ...
average rate of change = 2·f(0.5) = 2(5(0.5)² +20(0.5)) = 2(5/4 +10)
average rate of change = 22.5
Answer: 
Step-by-step explanation:
Given : The height of the rectangle = 
The width of the rectangle = 
Formula : Area = height x width
Therefore , the area of triangle in terms of polynomial will be :
![6k^3\times( 2k^2+4k+5)\\\\= 6k^3(2k^2)+6k^3(4k)+6k^3(5)\ \ [\text{Using Distributive property}]\\\\=12k^{3+2}+24k^{3+1}+30k^3\ \ [\text{Using exponents rule}:\ a^n\times a^m=a^{n+m}]\\\\=12k^5+24k^4+30k^3](https://tex.z-dn.net/?f=6k%5E3%5Ctimes%28%202k%5E2%2B4k%2B5%29%5C%5C%5C%5C%3D%206k%5E3%282k%5E2%29%2B6k%5E3%284k%29%2B6k%5E3%285%29%5C%20%5C%20%5B%5Ctext%7BUsing%20Distributive%20property%7D%5D%5C%5C%5C%5C%3D12k%5E%7B3%2B2%7D%2B24k%5E%7B3%2B1%7D%2B30k%5E3%5C%20%5C%20%5B%5Ctext%7BUsing%20exponents%20rule%7D%3A%5C%20a%5En%5Ctimes%20a%5Em%3Da%5E%7Bn%2Bm%7D%5D%5C%5C%5C%5C%3D12k%5E5%2B24k%5E4%2B30k%5E3)
Hence, the area of the entire rectangle =