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Flauer [41]
3 years ago
11

A ribbon is cut into n parts. The length of each part increases such that they form a geometric progression. SPM Given the lengt

h of the fourth part of the ribbon is 9 times the length of the second part of the ribbon.
(a) Calculate the common ratio.

(b) If the total length of the ribbon is 1 476.2 m and the length of the first part is 5 cm, calculate

(i) the value of n,

(ii) the length, in cm, of the last part of the ribbon. panjang,
​
Mathematics
1 answer:
emmainna [20.7K]3 years ago
5 0

Answer:

Step-by-step explanation:

Let\ say\ r \ the \common\ ratio:\\a)a_4=r^2*a_2=9*a_2\Longrightarrow\ r=3\ (not\ -3\ since\ parts\ are\ positive)\\\\b)\\\displaystyle \sum_{i=1}^{n} a_i =a_1+a_2+a_3+...+a_n\\\\=a_1+a_1*r+a_1*r^2+a_1*r^3+...+a_1*r^{n-1}\\\\=a_1*(1+r+r^2+...+r^{n-1})\\\\=a_1*\dfrac{r^n-1}{r-1} \\\\147620=5*\frac{(3^n-1)}{3-1} \\\\3^n-1=\frac{2*147620}{5} \\\\3^n=59049 \\\\n*ln(3)=ln(59049)\\\\n=\dfrac{ln(59049)}{ln(3)} \\\\n=10\\\\a_n=5*3^{10-1}=5*19683=98415(cm)

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Answer:

  x = 2, y = -2, AB = 142

Step-by-step explanation:

The fact that X is the midpoint gives you two relations:

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Since you have two unknowns, this number of equations is sufficient to find their values. Substituting the given expressions in the above equations, you have ...

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Simplifying the first of these can make simplifying the second one easier.

  24x +40 -3y +21 -22x = 5x +y +23 -4x +48

  2x -3y +61 = x +y +71 . . . . . . we can use this simplification

  x -4y = 10 . . . . . . . . . . . . . . . . subtract x+y+61

Now, we can simplify the second equation to ...

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  3x -2y +132 = 2x -5y +128 . . . . . simplify the left side

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