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3 years ago

How do I solve these for example 3

Mathematics

1 answer:

Natasha2012 [34]3 years ago

8 0

As the three longitudinal lines are parallel:

angle 4 = 5 = 6 = 82 degree (corresponding angles) = 9 = 8 = 7 = 82 degrees (vertical angles)

and

angle 11 = 180-82= 98 degrees (linear pair)

so:

angle 10 = 11 = 12 = 98 degrees (corresponding angles) = 3 = 2 = 1 = 98 degrees (vertical angles)
.

hope you got it

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Simplify the following expression (x+y)²

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2 years ago

A person starts walking from home and walks: 4 miles east 3 miles southeast 3 miles south 4 miles southwest 3 miles east find to

Fantom [35]

A geometry program can show you the total displacement is about 10.14 miles.

_____
You can use a vector calculator to find the solution, too. Using bearing angles, the sum is
4∠90° + 3∠135° + 3∠180° + 4∠225° + 3∠90° ≈ 10.1390∠141.6354°

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If you want to do it by hand, you can recognize the sum will be
7 miles east + 3 miles south + 3 miles southeast + 4 miles southwest

Distances that are not in the direction of one of the coordinate axes can be translated to rectangular coordinates by
displacement*(cos(angle), sin(angle))
Angles can be measured in the conventional way—from the positive x-axis. A direction of southeast will be +315° or -45°. A direction of southwest will be +225° or -135°.

Then the sum of the displacements in rectangular coordinates is ...
= (7, -3) + 3*(cos(-45°), sin(-45°)) + 4*(cos(-135°), sin(-135°))
= (7, -3) + ((√2)/2)*((3, -3) + (-4, -4))
= (7, -3) + 0.707107*(-1, -7)
= (6.2929, -7.9497)
Then the Pythagorean theorem is used to find the direct distance from home to this displaced location.
d = √(6.2929² +(-7.9497)²) ≈ √102.7990
d ≈ 10.1390 . . . . miles

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3 years ago