Given y is inversely proportion to x?

Question

a. let y = 0.4 when x=2.5. Find y when x=4

b. The number of hours, h that it takes m men to assemble x machines varies directly as the numbers of machines and inversely as the number of men. If fore men can assemble 12 machines in four hours, how many men are needed to assemble 36 machines in eight hours.

Answer 1

a. Given that y = 0.4 & x = 2.5 and
y is inversely proportional to x.

First we put it into an equation:

y = k / x; solving for k = proportionality constant
k = xy
k = 2.5 (0.4)
k = 1

Now if x = 4; y is equal to:

y = k / x; x=4
y = 1 / 4

b. We must first turn the statement into equation with the given that:
h = no. of hours
x = no. of machines &
m = no. of men

h = k (x/m); solving for proportionality constant "k"
k = hm/x
k = 4 (4) / 12
k = 16 / 12
k = 1 4/12
k = 1 ⅓

So to assemble 36 machines in eight hours:
h = k (x/m)
m = k (x/h)
m = 1 ⅓ (36/8)
m = 1 ⅓ ( 4½)
m = (4/3) (9/2)
m = 36/6
m = 6

so 6 men are needed to finish 36 machines in 8 hours

Answer 2

i believe the problems you posted deals with proportionality constants...............
a.) y=k/x because y is inversely proportional to x
0.4=k/2.5
so your proportionality constant, k=2.5*.04
k=1
now to find y when x = 4:
y = k/x
y = 1/4
y= 0.25


b.) h= kx/m ..as hours varies directly as machines and inversely as the number of men
if four men can assemble 12 machines in four hours:
4=k(12/4)
4 = k (3)
therefore your proportionality constant, k= 4/3
now to find how many men are needed to make 36 machines in eight hours:
h=k(x/m)
8=(4/3)(36/m)
8=(4*36)/3m
8=144/3m
8=48/m
m=48/8
m=6
so you need 6 men to work 8 hours to make 36 machines

Answer 3

a) y=m/x, so m = y*x=0.4*2.5

then y=m/x=0.4*2.5/4=0.25

b) h=a*x/m, so 4=a*12/4, then a= 16/12=1.3

then 8=1.3*36/m, so m= 6 men

Answer 4

a.
y2/y1 = x1/x2
y2 = 0.4*2.5/4 = 0.25

b.
h2/h1 = n2*m1/n1m2
n2 = h2*n1*m2/(h1*m1)
n2 = 8*4*36/(4*12) = 24 men