One number is eight more than twice another. If their sum is decreased by nine, the result is fourteen. Find the numbers

1 answer:

6 0

$x-\ first \ number\\
y-\ second\ number\\\\
x-8=2y\\
x+y-9=14\\\\
x=2y+8\\
x+y=23\\\\
2y+8+y=23\\
3y+8=23\ \ \ |subtract\ 8\\
3y=15\ \ \ |divide\ by\ 3\\
y=5\\\\x=18$ Answer here

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An open box is to be constructed so that the length of the base is 3 times larger than the width of the base. If the cost to con

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Step-by-step explanation:

Let assume that the volume = 88 cubic feet

Then:

$L = 3w --- (1)volume = l \times w \times h \\ \\ 88 = (3w) \times w \times h \\ \\ 3w^2 h= 88 \\ \\ h = \dfrac{88}{3w^2}--- (2) \\ \\$

The construction cost now is:

$C = 4(l \times w) + 2 ( w \times h) + 2(l \times h) \\ \\ C = 4(3w^2) + 2(w \times \dfrac{88}{3w^2}) + 2(3w \times \dfrac{88}{3w^2}) \\\\ C = 12w^2 + \dfrac{176}{3w} + \dfrac{176}{w}$

Now, to determine the minimum cost:

$\dfrac{dC}{dw}= 0 \\ \\ \implies 24 w - \dfrac{176}{3w^2}- \dfrac{176}{w^2}=0 \\ \\ 24 w ^3 = \dfrac{176}{w^2}(\dfrac{1}{3}+1) \\ \\ 24 w ^3 = \dfrac{176(4)}{3} \\ \\ w^3 = \dfrac{88}{3(3)}$