what is the successor and the predecessor of - 16 - math - integers
what is the successor and the predecessor of - 16 ?
successor of 16 is 17
predecessor of 16 is 15
express as a sum of perfect square 16 a square + b square + 9 c square minus 4 a b minus 3 b c - 12 ca? we are given`16 cot x=12` .we are asked to find the following `(sin x-cos x)/(sin x+cos x)` we know that: `cot x= "base"/"perpendicular" ` → "base"=3 → "perpendicular"=4 → `"hypotenuse"= sqrt(("perpendicular")^2+("base")^2)` → `"hypotenuse"=sqrt(16+9)` →`"hypotenuse"=5` now we have `16 cot x=12` `cot x=12/16` `cot x=3/4`, we know sin x=`"perpendicular"/"hypotenuse" and cos x= "base"/"hypotenuse"` now we find `(sin x- cos x)/(sin z+cos x)` = `(4/5-3/5)/(4/5+3/5)` =`(1/5)/(7/5)` =`1/7` a - ii, b - iv, c - i, d - iii so finding the square root by vedic method, four digits are in the number, so the digits in it’s square root will be 2. the quotient is 46, so the square root is 46.hint –i. four digits in the number so two digits in the square root.ii. first square root digit = 4iii. 21 - = 5 = remainderiv. pair of digits 16 was descended before 5. so new dividend = 516.v. divisor = 4 2 = 8, i.e., double of square root digit.vi. 86 divides 516 by 6, so write 6 ahead digit 4 in the quotient.vii. 516 – 86 6 = 516 – 516 = 0remainder = 0, square root = quotient = 46. 65 ÷ ( – 13) = **-5** a=c and b=d
b=d and `anec`
`ab=1 " and "cdne1`
`cd=1" and "ab=ne1`
answer: a
solution: using `a.m.gtg.m,` we have   
 `a+(1)/(b)gt2sqrt((a)/(b))b+(1)/( c )gt2sqrt((b)/( c )),c+(1)/(d)gt2sqrt(( c )/(d))" and "d+(1)/(a)gt2sqrt((d)/(a))`   
 `implies(a+(1)/(b))(b+(1)/( c ))(c+(1)/(d))(d+(1)/(a))gt16`   
 but,`(a+(1)/(b))(b+(1)/( c ))(c+(1)/(d))(d+(1)/(a))=4xx1xx4xx1=16`   
 `:." "a=(1)/(b),b=(1)/( c ),c=(1)/(d)" and "d=(1)/(a)`   
 `implies" "a=(1)/(b)=2,b=(1)/( c )=(1)/(2),c=(1)/(d)=2" and "d=(1)/(a)=(1)/(2)`   
 `implies" "a=2,b=(1)/(2),c=2" and "d=(1)/(2)`   
 `implies" "a=c" and "b=d` finding the correct answer here is important, but perhaps equally important is finding it using the method of matrix reduction, since those are the instructions.the augmented matrix is4 -2 -5 -514 -1 -2 -364 -2 4 -24you'll have to forgive the poor formatting. this answer box doesn't have a proper math symbol editor.using elementary row operations, the reduced row echelon form of the augmented matrix is1 0 0 -60 1 0 60 0 1 3from which we conclude that the system has a unique solution (-6,6,3). Definition used:  

Congruence.  

Let m be an integer greater than 1. If xand yare integers, then x is congruent to y modulo m if x — y is divisible by m. It can be represented as \(\displaystyle{x}={y}{\left({b}\ mod\ {m}\right)}\). This relation is called as congruence modulo m.  

Calculation:   

Consider the values and congruence classes modulo m,  

\(\displaystyle{\left[{13}\right]}^{{{6}}}\) and m = 15.  

It is evident that [x]=[y] if \(\displaystyle{\left[{x}={y}{\left({b}\ mod\ {m}\right)}\right]}\). Since \(\displaystyle{13}=-{2}{\left({b} \ mod \ {15}\right)}\).  

Then,  

[13]=[-2]  

\(\displaystyle{\left[{13}\right]}^{{{6}}}={\left[-{2}\right]}^{{{6}}}\)  

\(\displaystyle={\left[{\left(-{2}\right)}^{{{6}}}\right]}\)  

=[64]  

Since, by the principal or congruence \(\displaystyle{64}={4}{\left({b}\ mod \ {15}\right)}\). Therefore, \(\displaystyle{\left[{13}\right]}^{{{6}}}={\left[{4}\right]}\) in \(\displaystyle{Z}\_{{{15}}}\).  

Therefore, the value of the expression is [4]. ok, in that case replace these two lines
 last = lastrow(destsh)
 shlast = lastrow(sh)

with
 last = destsh.range("a" & rows.count).end(xlup).row
 shlast = sh.range("a" & rows.count).end(xlup).row 1.6 x 10-11