A painting is shaped like a golden rectangle. It's length is 24 cm. What is the paintings width to the nearest tenth of a cm?
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Answer:
Step-by-step explanation:
Volume of the box = x³ +11x² + 20x – 32 I think the ' is a typo for ³
the width is x-1 and the height is x+8
Find an expression for the length
Vol = LWH solve L
Vol / (WH) = L so
L = (x³ +11x² + 20x – 32) / (x-1) (x+8)
so it would help to factor the numerator
(x³ +11x² + 20x – 32) I'm willing to bet (x-1) and (x+8) are factors
but I will plot the equation to find the three roots
(x³ +11x² + 20x – 32) = (x-1) (x+8) (x+4)
L = (x³ +11x² + 20x – 32) / (x-1) (x+8)
= (x-1) (x+8) (x+4) / (x-1) (x+8) the (x-1) and (x+8) cancel out leaving
L = (x + 4)
so, let's first change the bounds from 1 to 9, so we'll be dropping the indices by 1, in order to do the variable "n".
however, let's use a variable hmmm say "k", where "k" is the value of "n" beginning at 1, thus k = n - 1.
however, if k = n - 1, then k + 1 = n. So let's use those fellows then,