When we Simplify [(x^2)^3 × 5x] / [6x^2 × 15x^3], the result obtained is (1/18)x^2
<h3>Data obtained from the question</h3>
- [(x^2)^3 × 5x] / [6x^2 × 15x^3]
- Simplification =?
<h3>How to simplify [(x^2)^3 × 5x] / [6x^2 × 15x^3]</h3>
[(x^2)^3 × 5x] / [6x^2 × 15x^3]
Recall
(M^a)^b = M^ab
Thus,
(x^2)^3 = x^6
- [(x^2)^3 × 5x] / [6x^2 × 15x^3] = [x^6 × 5x] / [6x^2 × 15x^3]
Recall
M^a × M^b = M^(a+b)
Thus,
x^6 × 5x = 5x^(6 + 1) = 5x^7
6x^2 × 15x^3] = (6×15)x^(2 + 3) = 90x^5
- [x^6 × 5x] / [6x^2 × 15x^3] = 5x^7 / 90x^5
Recall
M^a ÷ M^b = M^(a - b)
Thus,
5x^7 ÷ 90x^5 = (5÷90)x^(7 - 5) = (1/18)x^2
Therefore,
- [(x^2)^3 × 5x] / [6x^2 × 15x^3] = (1/18)x^2
Learn more about algebra:
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Answer:
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Answer:
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Step-by-step explanation:
From given condition
equation of line is given as,
x*cos(α)+y*sin(α)=p
& as tanα= 5/12 so from Pythagoras theorem
sinα= 5/13
cosα= 12/13
⇒12x+5y=39
<h2>
⇒12x+5y−39=0</h2>
We want to cut pieces of length:
from 35 metal rods each 40in long, and we want to know how many we can cut.
In order to answer the question, we must compute the number of pieces that we can cut from each metal rod, and then multiply the result by the number of metal rods. Let's do that!
1) From each metal rod we can cut:
2) We have 35 metal rods, so the total number of pieces of 6 1/4 in that we can cut is:
Answer
We can cut 210 pieces from the 35 metal rods.
Remark: we see that by cutting the pieces we will have a waste of metal from each rod.
