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Law Incorporation [45]
3 years ago
13

Find the 8th term in the geometric sequence which has a first term of 10 and a common ratio of 1.75.

Mathematics
2 answers:
kobusy [5.1K]3 years ago
7 0
A(8) = A(1) * 1.75^(8-1) = 10 * 1.75^7 = 502.65
julsineya [31]3 years ago
4 0
A = 10
r = 1.75
n = 8

8th term = a×(r)^n-1
= 10 × (1.75)^8-1
= 10 × (1.75)^7
= 10 × 50.265
= 502.65
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The scale factor is 4/3, which is the mixed numeral of 1 1/3.

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-64=(2cos(pi/2)+2i sin(pi/2))^n..... n=??​
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anastassius [24]

The translation rule that maps point D ( 7 , − 3 ) onto point D ' ( 2 , 5 )

is (x , y) → (x - 5 , y + 8)

Step-by-step explanation:

Let us revise the translation

  • If the point (x , y) translated horizontally to the right by h units  then its image is (x + h , y)
  • If the point (x , y) translated horizontally to the left by h units  then its image is (x - h , y)
  • If the point (x , y) translated vertically up by k units  then its image is (x , y + k)
  • If the point (x , y) translated vertically down by k units  then its image is (x , y - k)

(x , y) → (x ± h , y ± k) the right arrow symbol used to show the

translation from a point to its image

Example:

∵ P (0 , 0) → P' (1 , 2)

∴ The rule is (x , y) → (x + 1 , y + 2)

Let us find the translation rule that maps point D ( 7 , − 3 ) onto

point D' (2 , 5)

∵ Point (x , y) = (7 , -3)

∵ Its image after translation (x + h , y + k) = (2 , 5)

∴ x + h = 2

∵ x = 7

∴ 7 + h = 2

- Subtract 7 from both sides

∴ h = -5

∵ y + k = 5

∵ y = -3

∴ -3 + k = 5

- Add 3 to both sides

∴ k = 8

∴ The rule of translation is (x , y) → (x - 5 , y + 8)

The translation rule that maps point D ( 7 , − 3 ) onto point D ' ( 2 , 5 )

is (x , y) → (x - 5 , y + 8)

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