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olya-2409 [2.1K]
3 years ago
6

What is the length of AB if A and B have coordinates of A (-3,7) and B (7,3)​

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
7 0

Answer:

AB = √116 ≈ 10.77

Step-by-step explanation:

Use the formula that calculate the distance between two points:

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

L means length

For the x and y, substitute a coordinate value that you will label as set 1 or 2.

For example:

A (-3, 7) will be set 1. x₁ = -3    y₁ = 7

B (7 , 3) will be set 2. x₂ = 7   y₂ = 3

Substitute the points into the formula to find the length AB. Simplify.

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

AB = \sqrt{(7 - (-3))^{2}+(3 - 7)^{2}}   Solve inside the brackets first

AB = \sqrt{(10)^{2}+(-4)^{2}}      Square each term under the root

AB = \sqrt{100+16}    Add under the root

AB = \sqrt{116}     Final exact answer is radical (root) form

AB = 10.77      Final approximate or rounded answer to 2 decimals

The length of AB is the squareroot of 116, or about 10.77 units.

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Consider a geometric sequence with a first term of 4 and a fourth term of -2.916.
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Answer:

a) Find the common ratio of this sequence.

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b) Find the sum to infinity of this sequence.

Answer: 2.2

Step-by-step explanation:

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where

a is the first term

r is the common ratio and

n is the nth term

_________________________________

given

a = 4

4th term = -2.196

let

common ratio of this sequence. be r

4\ th \ term = ar^n-1\\-2.196 = 4r^{4-1} \\-2.196/4 = r^{3} \\r = \sqrt[3]{-0.549} \\r = -0.82

a) Find the common ratio of this sequence.

answer: -0.82

sum of infinity of geometric sequence is given by = a/(1-r)

thus,

sum to infinity of this sequence = 4/(1-(-0.82) = 4/1.82 = 2.2

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago
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