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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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Brilliant_brown [7]

Answer:

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4 0
3 years ago
G(a) = a + 2. Find f(-7).
Mrrafil [7]

Answer:

-5= g(a)

Step-by-step explanation:

assuming this is a typo and you meant to say g(-7).

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4 0
3 years ago
The perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is 2l + 2w=16, where l re
cricket20 [7]
2l + 2w = 16   
2(l+ w)  = 16    Divide both sides by 2
l + w =  16/2

l + w  =  8

So for example the length l could be 5 and the width could be 3.
Length could be 5.
8 0
3 years ago
Read 2 more answers
rectangle ABCD is graphed in the cordinate plane. The following are the verticies of the rectangle; A(-6,-4),B(-4,-4),C(-4,-2),
Sholpan [36]

Answer:

Therefore Perimeter of Rectangle ABCD is 4 units

Step-by-step explanation:

Given:

ABCD is a Rectangle.

A(-6,-4),

B(-4,-4),

C(-4,-2), and

D (-6,-2).

To Find :

Perimeter of Rectangle = ?

Solution:

Perimeter of Rectangle is given as

\textrm{Perimeter of Rectangle}=2(Length+Width)

Length = AB

Width = BC

Now By Distance Formula  we have'

l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}

Substituting the values we get

l(AB) = \sqrt{((-4-(-6))^{2}+(-4-(-4))^{2} )}

l(AB) = \sqrt{((2)^{2}+(0)^{2} )}=2\ unit

Similarly

l(BC) = \sqrt{((-4-(-4))^{2}+(-2-(-4))^{2} )}

l(BC) = \sqrt{((0)^{2}+(2)^{2} )}=2\ unit

Therefore now

Length = AB = 2 unit

Width = BC = 2 unit

Substituting the values  in Perimeter we get

\textrm{Perimeter of Rectangle}=2(2+2)=2(4)=8\ unit

Therefore Perimeter of Rectangle ABCD is 4 units

8 0
3 years ago
last month Stephanie spent $57 on 4 allergy shots and 1 office visit .This month she spent $9 after 1 office visit and a refund
Sergeu [11.5K]

Visit $25 allergy shot $8

4a + 1v =57

-2a +1v= 9

I will multiply the second by -1 to cancel v variable (elimination method)

4a +1v =57

2a -1v = - 9

add both

6a. = 48

a= 8

4a= 32

32 + v = 57

v= 25

32+25 = 57

-16 +25=9

6 0
3 years ago
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