Answer:
please see detailed answers below
Explanation:
16) (b^x) / (b^y) = b^5 (call this equation 1)
(b^(x+2)) / b^(2y) = b^4. (call this equation 2)
divide first equation by second:
(b^5) / (b^4) = b^1
(b^x) / (b^y) ÷ (b^(x+2)) / b^(2y)
= (b^x) / (b^y) X b^(2y) / (b^(x+2))
= [b^(x + 2y)] / [b^(x + 2 + y)] = b^1.
b^[(x + 2y) - (x + 2 + y)] = b^1
b^(y - 2) = b^1
so y - 2 = 1, y = 3.
back to equation 1:
(b^x) / (b^y) = b^5
(b^x) / (b^3) = b^5
b^x = b(3+5) = b^8
so x = 8.
the answer was found by using the laws of indices [a^m + a^n = a^(m+n).
a^m ÷ a^n = a^(m - n)]
18) 10^30 ÷ 10^18 = 10^(30 - 18) = 10^12.
British system is 10^12 larger than American system.
19) Volume of sphere = (4/3) X π X r ³
small sphere: volume = (4/3) X π X (1/2) ³ = π/6 ft³
middle sphere: volume = (4/3) X π X (3/4) ³ = (9π)/16 ft³
large sphere: volume = (4/3) X π X (3/2) ³ = (9π)/2 ft³