Problem 1 :
Solve for w in the formula for area of a rectangle :
A = l ⋅ w
Problem 2 :
Solve for c in the formula for Einstein’s Theory of Relativity :
E = mc2
Problem 3 :
Solve for h in the formula for the surface area of a right cylinder :
S = 2∏r(h + r)
Problem 4 :
Solve for r in the formula for volume of sphere :
V = 4/3 ⋅ ∏r3
Problem 5 :
Solve for w in the formula for perimeter of the rectangle :
P = 2(l + w)
Problem 6 :
Solve for a :
Q = 3a + 5ac
Problem 7 :
Solve for b1 :
A = 1/2 ⋅ h(b1 + b2)
Problem 8 :
Solve for b :
a2 + b2 = c2
Problem 1 :
Solve for w in the formula for area of a rectangle :
A = l ⋅ w
Solution :
A = l ⋅ w
Divide each side by l.
A / l = w
Problem 2 :
Solve for c in the formula for Einstein’s Theory of Relativity :
E = mc2
Solution :
E = mc2
Divide each side by m.
E / m = c2
Take square root on each side.
√(E/m) = √c2
√(E/m) = c
Problem 3 :
Solve for h in the formula for the surface area of a right cylinder :
S = 2πr(h + r)
Solution :
S = 2πr(h + r)
Use distributive property of multiplication over addition.
S = 2πrh + 2πr2
Subtract 2∏r2 from each side.
S - 2πr2 = 2πrh
Divide each side by 2∏r.
(S - 2πr2) / 2πr = h
Problem 4 :
Solve for r in the formula for volume of sphere :
V = 4/3 ⋅ πr3
Solution :
V = 4/3 ⋅ πr3
Multiply each side by 3/4.
3V/4 = πr3
Divide each side by ∏.
3V/4π = r3
Take cube root on each side.
3√(3V/4π) = 3√r3
3√(3V/4π) = r
Problem 5 :
Solve for w in the formula for perimeter of the rectangle :
P = 2(l + w)
Solution :
P = 2(l + w)
Use distributive property of multiplication over addition.
P = 2l + 2w
Subtract 2l from each side.
P - 2l = 2w
Divide each side by 2.
(P - 2l) / 2 = w
Problem 6 :
Solve for a :
Q = 3a + 5ac
Solution :
Q = 3a + 5ac
Factor a out of 3a + 5ac.
Q = a(3 + 5c)
Divide each side by (3 + 5c).
Q / (3 + 5c) = a
Problem 7 :
Solve for b1 :
A = 1/2 ⋅ h(b1 + b2)
Solution :
A = 1/2 ⋅ h(b1 + b2)
Multiply each side by 2/h.
2A/h = b1 + b2
Subtract b2 from each side.
2A/h - b2 = b1
Problem 8 :
Solve for b :
a2 + b2 = c2
Solution :
a2 + b2 = c2
Subtract a2 from each side.
b2 = c2 - a2
Take square root on each side.
√b2 = √(c2 - a2)
b = √(c2 - a2)
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