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3 years ago

What is the exact distance from (−1, 4) to (6, −2)?

2 answers:

Studentka2010 [4]3 years ago

8 0

Same as last time:

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(6--1)^2+(-2-4)^2

d^2=7^2+(-6)^2

d^2=49+36

d^2=85

d=√85 (85=5*7 and both 5 and 7 are prime so √85 cannot be simplified any further)

The exact distance is √85 units.

aniked [119]3 years ago

7 0

Answer:

The distance is √ 85 units

Step-by-step explanation:

To find the exact value, all we will simply do is to use the distance formula to solve;

D =√ (x₂ - x₁)² + (y₂ - y₁)²

From the question given;

The points given are (−1, 4) and (6, −2)

so; x₁ = -1 y₁ = 4 x₂ = 6 y₂ = -2

We can now proceed to substitute the formula into the equation

D = √ (x₂ - x₁)² + (y₂ - y₁)²

=√ (6 - -1)² + (-2 - 4)²

=√ (6+ 1)² + (-2 - 4)²

=√ (7)² + (-6)²

=√ 49 + 36

=√ 85

The distance is √ 85 units

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How to solve 76×327 step by step

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Here's a method that takes advantage of the values of these particular numbers.

... 76 = 80 - 4

... 76 × 327 = (80 -4)×327

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Repeated doubling will give us values that are 2, 4, and 8 times 327.

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... 2×654 = 4×327 = 654+654 = 1308 . . . . we'll use this later

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We want 80×327, so we can add a zero to the end of this last:

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Now, we can subtract 4×327 to get 76×327

... 80×327 - 4×327 = 26160 -1308 = 24852 = 76×327

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More conventionally, you would multiply every digit of one number by every digit of the other and add the products according to their respective place values.

327 × 076 = (3×0)×10000 + (3×7 +2×0)×1000 +(3×6 +7×0 +2×7)×100 +(2×6 +7×7)×10 +(7×6)×1

... = 0 +21,000 +3,200 + 610 +42

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Note the pattern of partial products here. This is a method taught to/by practitioners of Vedic mathematics, and can be done in your head. At most, you would write down the partial product sums 21, 32, 61, and 42 to keep from having to carry more than one number in your head at a time.

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