Y Varies directly as X and inversely as Z. Y=100 when X=5 and Z=10 Find Y when X=3 and Z=60

y = 10

Step-by-step explanation:

based on the question if y  varries directly as x

mathematically

y ∝ x

also, y varries inversly as z can be mathematically expressed as

y ∝ 1/z

combining the two expressions

y ∝ x ∝ 1/z

i. e

y = kx/z where k is the constant of proportionality

make  k the subject of formulae

yz = kx

Divide both sides by x

k =yz/x

when y=100 , x = 5 z =10

k = 100 × 10/5

k = 200

to find y when x = 3 and z = 60

k =yz/x

200 =60y/3

cross multiply

60y = 200 × 3

60y = 600

divide both sides by 60

y = 10

(D)

Step-by-step explanation:

The given equation is:

Cubing on both the sides, we get

therefore, the solutions are:

and

Substitute x=6 in the given equation, we have

which is true, thus x=6 is a true solution.

Put x=-2 in the given equation, we have

which is true, thus x=-2 is a true solution.

Therefore, Both x = –2 and x = 6 are true solutions.