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antiseptic1488 [7]
3 years ago
12

The magnitude and direction of two vectors are shown in the diagram. What is the magnitude of their sum? ​

Mathematics
2 answers:
Kisachek [45]3 years ago
7 0

Answer: 2√5

Step-by-step explanation:

Use the Sine Law of triangles: In triangle with sides of length 1,2,3 that are opposite to angles 1,2,3 we have

1/sin1=2/sin2=3/sin3.

VLD [36.1K]3 years ago
5 0

Separate the vectors into their <em>x</em>- and <em>y</em>-components. Let <em>u</em> be the vector on the right and <em>v</em> the vector on the left, so that

<em>u</em> = 4 cos(45°) <em>x</em> + 4 sin(45°) <em>y</em>

<em>v</em> = 2 cos(135°) <em>x</em> + 2 sin(135°) <em>y</em>

where <em>x</em> and <em>y</em> denote the unit vectors in the <em>x</em> and <em>y</em> directions.

Then the sum is

<em>u</em> + <em>v</em> = (4 cos(45°) + 2 cos(135°)) <em>x</em> + (4 sin(45°) + 2 sin(135°)) <em>y</em>

and its magnitude is

||<em>u</em> + <em>v</em>|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)

… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))

… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))

… = √(16 + 16 cos(135° - 45°) + 4)

… = √(20 + 16 cos(90°))

… = √20 = 2√5

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aivan3 [116]

The synthetic division's representation of the dividend is 2x3 + 10x2 + x + 5.

Given that

An L shape is created when two lines intersect vertically and horizontally.

The shape has entries in two rows.

Entries in row 1 are 2, 10, 1, and 5.

Blank, -10, and 0 are the entries in row 2.

A simplified method of dividing a polynomial with another polynomial equation of degree one is known as synthetic division.

On the exterior, to the left of the form, is entry number 5.

The entry stands for the divisor's zero.

If the variable is x, then this entry to the variable is;

2x³+10x²+x+5

The dividend is thus represented by synthetic division as

2x³+10x²+x+5

The Question is incomplete And complete question is given below!!

What dividend is represented by the synthetic division below? A vertical line and horizontal line combine to make a L shape. There are two rows of entries within the shape. Row 1 has entries 2, 10, 1, 5. Row 2 has entries blank, negative 10, 0, negative 5. Entry negative 5 is on the outside to the left of the shape, and a third row of entries is outside and below the shape. Row 3 has entries 2, 0, 1, 0. Negative 10 x squared minus 5 2 x cubed 10 x squared x 5 2 x squared 1 2 x cubed x.

Learn more about Synthetic division here

brainly.com/question/27979968

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Step-by-step explanation:

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