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3 years ago

Find the angle θ between u = <7, –2> and v = <–1, 2>.

Mathematics

2 answers:

AlekseyPX3 years ago

8 0

Answer:

132.5°

Step-by-step explanation:

u•v = |u| |v| cos(theta)

(7×-1) + (-2×2) = sqrt(53) × sqrt(5) cos(theta)

-7-4 = sqrt(265) cos(theta)

cos(theta) = -11/sqrt(265)

theta = 132.510447078

Dmitry_Shevchenko [17]3 years ago

7 0

The angle between two vectors is:

CosФ = u - v / Magnitude(u) x magnitude(v)

Magnitude of u = SQRT(7^2 + -2^2) = SQRT(49 +4) = SQRT(53)

Magnitude of v = SQRT(-1^2 +2^2) = SQRT(1 +4) = SQRT(5)

u x v = (7 x -1) + (-2 x 2) = -7 + -4 = -11

cosФ = -11 / sqrt(53) x sqrt(5)

cosФ = -11sqrt265) / 265

Ф =cos^-1(-11sqrt265) / 265)

Ф=132.51 degrees.

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Circle O, with center (x, y) passes through the points A(0, 0), B(-3, 0), and C(1, 2). Find the coordinates of the center of the

KonstantinChe [14]

Answer:

The center of the circle is

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Step-by-step explanation:

Let the equation of the circle be

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The points lying the circle must satisfy the equation of this circle.

A(0,0)

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B(-3,0)

$(-3)^2+0^2+2a(-3)+2b(0)+c=0$

$\implies 9+0-6a+0+c=0$

$\implies -6a+c=-9$

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C(1,2)

$1^2+2^2+2a(1)+2b(2)+c=0$

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Put the value of 'a' and 'c' to find 'b'

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3 years ago

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3 years ago

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Answer:

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2 years ago

3. Here is a diagram of a softball field:

Crank

a. Length of the fence around the field = perimeter of quarter circle = 892.7 ft.

b. The area of the outfield is about 39,584 sq. ft..

<h3>What is the Perimeter of a Quarter Circle?</h3>

Perimeter of circle = 2πr

Perimeter of a quarter circle = 2r + 1/4(2πr).

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= 2r + 1/4(2πr).

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Plug in the value

The length of the fence around the field = 2(250) + 1/4(2 × π × 250)

= 892.7 ft.

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= 1/4(πR²) - πr²

R = radius of the full field = 250 ft

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Plug in the values

Size of the outfield = 1/4(π × 250²) - π × 55²

= 49,087 - 9,503

= 39,584 sq. ft.

Learn more about perimeter of quarter circle on:

brainly.com/question/15976233

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