Answer:
Step-by-step explanation:
ummmmmmmmmmm sorry
Answer:
You will need 220 mL of the 60% solution and 80 mL of pure alcohol.
Step-by-step explanation:
Let 'x' be the amount of 50% alcohol solution and y the amount of pure alcohol.
Therefore:
(0.5x + y)/300 = 0.65 ⇒ 0.5x + y = 190
x + y = 300
Solving the sistem of equations:
x = 220 and y = 080
Therefore, You will need
220 mL of the 60% solution
and 80 mL of pure alcohol.
Greatest common factor (or denominator) is 6,
least common multiple is 180
hmm
(note:
I spent like 30 mins trying to use a math only of finding the values
but it didn't work so I did a force brute and elimination method
explained below)
so
a and b must be multiples of 6
so list all the multiples of 6
wait
180=6*30
and 30's factors are 1,2,3,5,6,10,15,30 so only list the numbers that
are the result of multiplying 6 and any of those numbers in that list
(so we can have the lcm of 180)
so
6*1=6
6*2=12
6*3=18
6*5=30
6*6=36
6*10=60
6*15=90
6*30=180
these are our possible candidates for the 2 numbers
now we must find the pair that has a GCD of only 6
doing the math is long and tedious so do it yourself (trial and error)
we see that our choices that fulfill both requirements (GCD of 6 and LCM of 180) are
90&12
60&18
30&36
sum them to find the least one
90+12=102
60+18=78
30+36=66
the least possible sum is 66
Answer:
Time machine one = 3.56
Time machine two = 4.56
Step-by-step explanation:
Let machine 2 do the job in x hours
Let machine 1 do the job in x - 1 hours.
The general formula for this problem is
Time = A*B/(A + B)
Givens
Time = 2 hours
B = x hours alone
A = x - 1 hours alone.
#################
x *( x - 1)
======= = 2
(x + x - 1)
(x^2 - x)/(2x - 1) = 2
x^2 - x = 2(2x - 1)
x^2 - x = 4x - 2
x^2 - 5x + 2 = 0
a = 1
b = - 5
c = 2
This gives 2 roots
x = 4.56
x = 0.43
The second root will not work because when 1 is subtracted from 0.43 the time give will be minus, which won't work.
Time for machine 2 is 4.56
The time for machine 1 is 3.56
Check
(A * B)/(A + B) = 2
A = 4.56
B = 3.56
Time = 4.56*3.56/(4.56 + 3.56)
Time = 16.2336/(8.12)
Time = 1.9992
The rounding error in the check comes from the rounding error in the times.
Answer:
-1/2
Step-by-step explanation:
y2-y1 = -5-0 =-5
x2-x1 = 8-(-2)=10
-5/10= -1/2