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2 years ago

In a circle an arc length 10 is intercepted by a central angle of 2/3 radius

1 answer:

5 0

We have been given that in a circle an arc length 10 is intercepted by a central angle of 2/3. We are supposed to find the radius of the circle.

We will use arc-length formula to solve our given problem.

$l=r\theta$ , where,

$l$ = Arc length,

$r$ = Radius,

$\theta$ = Central angle corresponding to arc length.

Upon substituting our given values in arc-length formula, we will get:

$10=r\cdot \frac{2}{3}$

$10\cdot \frac{3}{2}=r\cdot \frac{2}{3}\cdot \frac{3}{2}$

$5\cdot \frac{3}{1}=r$

$15=r$

Therefore, the radius of the given circle would be 15 units.

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Find the line through (3, 1, −2) that intersects and is perpendicular to the line x = −1 + t, y = −2 + t, z = −1 + t. (HINT: If

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Answer:

( xo , yo , zo ) = ( 1 , 0 , 1 )

Step-by-step explanation:

Given:-

- A line passing through point (3, 1, −2) intersects and is perpendicular to line with coordinates:

x = −1 + t, y = −2 + t, z = −1 + t .... t = arbitrary parameter.

Find:-

The coordinates for point of intersection.

Solution:-

- The line that passes through point (3, 1, −2) = ( a, b , c ) and an a arbitrary point on the given line have the following direction vector d2 :

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x2 = a - ( x ) = 3 - ( -1 + t ) = 4 - t

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d2 = ( 4 - t , 3 - t , -1 - t )

- The direction vector d1 of the given line is:

d1 = ( x1 , y1 , z1 )

x1 = 1

y1 = 1

z1 = 1

d1 = ( 1 , 1 , 1 )

- The dot product of two orthogonal vectors is always equal to zero:

d1.d2 = 0

( 4 - t , 3 - t , -1 - t ) . ( 1 , 1 , 1 ) = 0

- Solve for parameter (t):

(4 - t) + (3 - t) + (-1 - t) = 0

6 -3t = 0

t = 2

- The coordinates of the point of intersections can be evaluated by substituting the value of "t" into the given equation of line:

xo ( t = 2) = - 1 + 2 = 1

yo ( t = 2) = - 2 + 2 = 0

zo ( t = 2) = - 1 + 2 = 1

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( xo , yo , zo ) = ( 1 , 0 , 1 )

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2 years ago

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If 28 tiles is placed in 7 rows then each row has 4 tiles.

<u>Step-by-step explanation:</u>

The total number of tiles given =28.

The number of rows = 7.

The number of tiles in each row is given by diving the total number of tiles given by the number of rows.

No of tiles in each row= $\frac{total number of tiles}{number of rows}$ .

No of tiles in each row = $\frac{28}{7}$ .

No of tiles in each row = 4.

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3 years ago

Suppose you know that Mr. and Mrs. Vincent have at most eight children. One day you happen to meet two girls who were the Vincen

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Step-by-step explanation:

Data provided in the question:

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now,

let the number of children be 'n'

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thus,

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2x(x-1) = n(n-1)

now

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therefore,

The number of children are 4 out of which 3 are girls

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