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ella [17]
3 years ago
6

The volume is 15 ft cubed. The area of the base is 6 ft squared. What is the height in feet

Mathematics
1 answer:
kkurt [141]3 years ago
5 0

Answer:

h = 2.5\,ft

Step-by-step explanation:

Let consider that object is regular prism. The height in feet is obtained by dividing the volume by the area of the base:

h = \frac{15\,ft^{3}}{6\,ft^{2}}

h = 2.5\,ft

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\tan \: A =  \frac{4}{5}  \\  \\  \cot \: A =   \frac{1}{ \tan \: A }  =  \frac{1}{ \frac{4}{5} }  =  \frac{5}{4}  \\  \\ csc\: A = \sqrt{1  +   {cot}^{2}\: A}     \\  =  \sqrt{1 +   { \bigg( \frac{5}{4}  \bigg)}^{2}  } \\  = \sqrt{1 +  \frac{25}{16} }   \\  = \sqrt{\frac{16 + 25}{16} }   \\  =   \sqrt{\frac{41}{16}}  \\  =  \frac{ \sqrt{41} }{4}  \\  =  \frac{6.40312424}{4}  \\  = 1.60078106 \\  \therefore \: csc \: A =1.6

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3 years ago
The sum of the ages of Mr Lin and his son Ethan is 38 years. In three years' time, Mr Lin will be three times as old as his son.
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