More Homework help?

Question

Use the following equations to construt an equation for w that involves only the variables a and b.

xw = yt

x/a = b

a^3y = b

a^2 = tb .........your answers help me understand the concept. Thank you so much!

Answer 1

In the 2nd equation, x = ab

3rd eqn: y = b/a^3

4th eqn: divide by t to get a^2/b = t

Substituting all this into the 1st eqn, we get

abw = (b/a^3)(a^2/b)

Simplify right side:

abw = (ba^2)/(ba^3)

abw = 1/a

Divide by ab:

w = 1/(a^2b)

Answer 2

In the first solve for w by dividing by x on both sides and you get w = yt/x
In the second equation solve for x by multiplying a on both sides and you get x = ba
In the third equation you solve for y by dividing a^3 on both sides and you get y = b/a^3
In the forth equation solve for t by dividing both sides by b and you get t = a^2/b
Lastly you substitute x, y, and t into the first equation and you get w = (b/a^3)(a^2/b)/(ba)

Answer 3

xw=yt

so w=(yt)/x

x/a=b so x=ab

so w=(yt)/ab

a^3 y=b so y=b/(a^3)

so w=((b/(a^3)t)/(ab)

a^2=tb so t=(a^2)/b

yt = (b/a^3)(a^2/b) b over b crosses out and (a^2/a^3) = 1/a

So (1/a)/ab=(1/a)(1/(ab)=1/(a^2b)

Answer 4

w = yt/x

x = ab
y = b/a³
t = a²/b

w = (a²/b)(b/a³) / ab
w = (1/a) / ab
w = b