An egg that has been falling for x seconds has dropped at an average speed of 16x feet per second. If the egg is dropped from th

e top of a building, its total distance traveled is the product of the average rate times the time. Write a simplified expression to show the distance the egg has traveled after x seconds

Mathematics

1 answer:

ivanzaharov [21]4 years ago

5 0

$average \: rate \: of \: fall = 16x \: feet \: per \: second \\ duration \: of \: fall \: (time) = x \: seconds \\ distance \: of \: fall = 16x \: feet \: per \: second \times x \: seconds \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =x(16x) \: feet \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 16 {x}^{2} \: feet \\ \: the \: egg \: traveled \: 16 {x}^{2} \: feet \: in \: x \: seconds.$

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16 plus 5 times a number is more than the number minus 8. Write an inequality and solve it

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n > -6 is the inequality for 16 plus 5 times a number is more than the number minus 8

<em><u>Solution:</u></em>

Given statement is:

16 plus 5 times a number is more than the number minus 8

We have to write a inequality

From given statement,

16 plus 5 times a number is more than the number minus 8

Let the number be "n"

Therefore,

16 plus 5 times "n" is more than "n" minus 8

Here, "plus" means addition and "minus" means subtraction and "times" means multiplication

Thus the statement is translated into inequality as:

$16 + 5n >n-8$

Simplify the inequality

$16 + 5n >n-8\\\\\mathrm{Subtract\:}16\mathrm{\:from\:both\:sides}\\\\16 + 5n -16 > n - 8 -16\\\\5n >n-24\\\\\mathrm{Subtract\:}n\mathrm{\:from\:both\:sides}\\\\5n-n>n-24-n\\\\\mathrm{Simplify}\\\\4n>-24\\\\\mathrm{Divide\:both\:sides\:by\:}4\\\\\frac{4n}{4}>\frac{-24}{4}\\\\n>-6$