Step 1
<u>Find the Greatest Common Factor (GCF)</u>
the prime factorization of each number is equal to
The GCF is 17
That means that the maximum number of packets is 17 and the maximum number of the items possible in each packet is
Number of pencils=527/17=31 pencils in each packet
Number of erasers=646/17=38 erasers in each packet
Number of sharpeners=748/17=44 sharpeners in each packet
1/2 of the books are science books because once you convert the other two books you get 2/6 +1/6= 1/2 so the science books will be the other half.
Part A:
To determine the values of the times to which the height of the two cannon balls are the same, we equate the given functions.
H(t) = g(t)
Substitute the expressions for each.
-16t² + 48t + 12 = 10 + 15.2t
Transpose all the terms to the left-hand side of the equation.
-16t² + (48 - 15.2)t + (12 - 10) = 0
Simplifying,
-16t² + 32.8t + 2 = 0
The values of t from the equation are 2.11 seconds and -0.059 seconds
Part B:
In the context of the problem, only 2.11 seconds is acceptable. This is because the second value of t which is equal to -0.059 seconds is not possible since there is no negative value for time.
It would be 4x < h < 10x
the difference between 3x - 7x =4
and the sum would be 3x + 7x =10
