I need help with an Algebra question. The question is in the picture. Thank you <3
1 answer:
The domain is the set of allowed inputs, in this case t values. The smallest t value allowed is t = 0. The largest is t = 165. So that's why the domain is 
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The range is
since H = 0 is the smallest output of the function and H = 40,000 is the largest output. Like the domain, the range is the set of possible outputs of a function.
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The range is
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You're looking for the volume of the prism. The dead giveaway there is that you're looking for "cubic" measurement. Cubic measures are indicators that the volume is being determined, just like "square feet" or inches, etc indicates area is being determined. The volume for this prism is found by multiplying the length times the width times the height. In decimal form, 45×30×40=54,000. But that is in cubic inches and we want cubic feet. So we will use dimensional analysis to convert that. Setting up the DA looks like this, keeping in mind that there are 12 cubic inches in 1 cubic foot: 
. The label of cubic inches cancels out leaving us with cubic feet, and doing the division there gives us 54,000/(12*12*12) which is 31.25 cubic feet.