Can you help me in my math work
1 answer:
The LCM of 18 and 24 using the prime-factorization method is <u>72</u>.
The LCM of 27, 81, and 54, using the division method is <u>162</u>.
In the first question, we are asked to find the LCM of the given numbers using the prime factorization method.
(i) 18, 24.
Prime factorization gives:
18 = 2*3², and 24 = 2³*3.
The LCM is the product of the highest power of each prime factor.
Thus, LCM = 2³*3² = 8*9 = 72.
Thus, the LCM of 18 and 24 using the prime-factorization method is <u>72</u>.
Doing similarly for other sub-parts, The LCM of:
(ii) 16, 40 is 80.
(iii) 30, 36 is 180.
(iv) 28, 44 is 308.
(v) 20, 32 is 160.
(vi) 20, 135 is 540.
(vii) 45, 75 is 225.
(viii) 36, 84 is 252.
(ix) 12, 18, 24 is 72.
(x) 25, 35, 45 is 1575.
(xi) 9, 15, 21 is 315.
(xii) 25, 50, 75 is 150.
In the second question, we are asked to find the LCM of the given numbers, using the division method.
(i) 27, 81, 54.
The division method gives:
The LCM is the product of all the numbers used for division.
LCM = 2*3*3*3*3*1 = 162.
Thus, the LCM of 27, 81, and 54, using the division method is <u>162</u>.
Doing similarly for other sub-parts, The LCM of:
(ii) 18, 45, 63 is 630.
(iii) 35, 55, 100 is 7700.
(iv) 210, 140, 315 is 1260.
(v) 112, 120, 150 is 8400.
(vi) 144, 180, 300 is 3600.
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Answer
Josh's textbook reached the ground first
Josh's textbook reached the ground first by a difference of
Step-by-step explanation:
Before we proceed let us re write correctly the height equation which in correct form reads:
Eqn(1).
Where:
: is the height range as a function of time
: is the initial velocity
: is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:
Eqn(2).
Now let us use the given information and set up our equations for Ben and Josh.
<u>Ben:</u>
We know that
Thus Eqn. (2) becomes:
Eqn.(3)
<u>Josh:</u>
We know that
Thus Eqn. (2) becomes:
Eqn. (4).
<em><u>Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at </u></em><em><u>. Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one. </u></em>
Thus we have for Ben, Eqn. (3) gives:
Using the quadratic expression to find the roots of the quadratic we have:
Since time can only be positive we reject the solution and we keep that Ben's book took
seconds to reach the ground.
Similarly solving for Josh we obtain
Thus again we reject the negative and keep the positive solution, so Josh's book took seconds to reach the ground.
Then we can find the difference between Ben and Josh times as
So to answer the original question:
<em>Whose textbook reaches the ground first and by how many seconds?</em>
- Josh's textbook reached the ground first
- Josh's textbook reached the ground first by a difference of