Question

If t is directly proportional to s under cube and t = 4 when s = 64. Find

1. the value of t when s = 125
2. the value of s when I = 2.​

Answer 1

1. t = 5
2. s = 8

Explanation:

`t \:\alpha\: \sqrt[3]{s} \\t = k\sqrt[3]{s} \:..........(1)\\\\t = 4, s = 64\\\\Substitute \:the \:values\:into \: equation\: 1\\4 = k\sqrt[3]{64} \\4 = 4k\\Divide \:both\:sides\:of\:the\:equation\:by\:4\\(4)/(4)= (4k)/(4) \\k = 1\\Substitute k \:for\:1 \:in\:equation\:1\\t = 1\sqrt[3]{s} \\t = \sqrt[3]{s} \:= Formula\:connecting\:t\:and\:s`

1.

`t = ? , s=125\\\\t = \sqrt[3]{s} \\\\t = \sqrt[3]{125} \\\\t = 5`

2.

`s = ? , t= 2\\\\t = \sqrt[3]{s} \\\\2 = \sqrt[3]{s} \\Cube\:both\:sides\:of\:the\:equation\\2^3 = \sqrt[3]{s} ^3\\\\8 =s\\s =8`