SOLUTION: Help me answer this question please:
⌊1.25 + ⌊𝑥⌋⌋ = 12
I am completely unsure as I have no clue what that style of brakcets mean
Algebra.Com
Question 1106550: Help me answer this question please:
⌊1.25 + ⌊𝑥⌋⌋ = 12
I am completely unsure as I have no clue what that style of brakcets mean
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Those brackets indicate the "floor" function.
floor(x) = k where k is the greatest integer less than or equal to x; x is a real number, k is an integer.
—
The question is asking to find x such that the floor( floor(x) + 1.25 ) = 12
The inner-most floor (floor(x)) is an integer, so we can re-write this problem using integer n:
floor(n + 1.25) = 12
if n = 10 we get floor(10 + 1.25) = floor(11.25) = 11 too low
if n = 11 we get floor(11 + 1.25) = floor(12.25) = 12 ok
Since the inner-most floor (floor(x)) is taken first in order to get the 11 in 11+1.25, x can be any value in the range
——
Check:
x=11: floor(x) = floor(11) = 11 and floor(11+1.25) = floor(12.25) = 12 (ok)
x=12-s where 0 < s <= 1: floor(x) = floor(12-s) = floor(some number greater than or equal to 11, and less than 12) = 11 and floor(11+1.25) = floor(12.25) = 12 (ok)
You can also do negative checks by letting x=11-s and x=12 to see that those do not result in a final value of 12, to convince yourself the highlighted range captures all possible values of x.
—
One thing about the floor() function, you must be very careful about your less than or equal signs.
A related function is the ceiling() function.
RELATED QUESTIONS
Prove or disprove the statements below.
(a) For all positive real numbers x and y,... (answered by Edwin McCravy)
For every real number k, let ⌊k⌋ represent the "floor function", i.e.,... (answered by Edwin McCravy)
Let ⌊x ⌋ = the greatest integer that is less than or equal to x. For example (answered by robertb)
9(⌊4(x-5)+19⌋- ⌊3(2x-3)+1⌋). I need to simplify this problem. I... (answered by unlockmath)
I have no clue how to solve this problem would you please show me how?
Factor... (answered by stanbon)
The question states: factor completely or state the polynomial is prime...
9x^2+25... (answered by solver91311,jsmallt9)
I have no clue how to do this... Will you help me... (answered by elima)
1<3x+2<12... i have no clue how to solve this, someone help... (answered by jim_thompson5910)
Please help me solve this problem.....
I have tried and I don't think I understand and... (answered by richard1234)