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GB-17-04-001 · Direct proportion to a power

yy is directly proportional to x2x^2. When x = 6, y = 144.

(a) Find a formula for y in terms of x.

(b) Find y when x = 21.

Part (a) Direct and Inverse Proportion (Direct Square) Booklet p. 23
Method
1) Replace ∝ with = k (y = kx²)
2) Sub in given pair (x, y)
3) Solve to find k
4) Write general formula and sub in new x
Worked Example (GB-17-04-001 · Part (a))
Find a formula for y in terms of x.
1)
y=kx2y=kx^2
2)
144=k(6)2⇒k=14436=4144=k(6)^2\Rightarrow k=\frac{144}{36}=4
3)
y=4x2y=4x^2
Ans = y=4x2y=4x^2
Part (b) Direct and Inverse Proportion (Direct Square) Booklet p. 23
Method
1) Replace ∝ with = k (y = kx²)
2) Sub in given pair (x, y)
3) Solve to find k
4) Write general formula and sub in new x
Worked Example (GB-17-04-001 · Part (b))
Find y when x = 21.
1)
y=kx2y=kx^2
2)
144=k(6)2⇒k=14436=4144=k(6)^2\Rightarrow k=\frac{144}{36}=4
3)
y=4x2y=4x^2
4)
y=4(21)2=1764y=4(21)^2=1764
Ans = 1764