Answer:
(-4, -3), (4, -1), (8, 0), (12, 1)
Step-by-step explanation:
The x- and corresponding y-values are listed in the table. Put each pair in parentheses, <em>x-value first</em>. (That is an <em>ordered pair</em>.)
(x, y) = (-4, -3) . . . . from the first table entry
(x, y) = (4, -1) . . . . from the second table entry
(x, y) = (8, 0) . . . . from the third table entry
(x, y) = (12, 1) . . . . from the last table entry
Given:
height = 6m
chord = 20 m
We need to find the radius of the circle.
20 m = 2 √ [ 6m( 2 x radius - 6 m ) ]
20 m / 2 = 2 √<span>[ 6m( 2 x radius - 6 m ) ] / 2 </span>
10 m = √<span> [ 6m( 2 x radius - 6 m ) ] </span>
(10 m)² = √[ 6m( 2 x radius - 6 m ) ] ²
100 m²<span> = 6 m( 2 x radius - 6 m ) </span>
100 m²<span> = 12 m x radius - 36 sq m </span>
100 m² + 36 m² = 12 m x radius - 36 m² + 36 m²
136 m²<span> = 12 m x radius </span>
136 m²<span> / 12 m = 12 m x radius / 12 m </span>
<span>11.333 m = radius
</span>
the area beneath an arc:
<span>Area = r</span>²<span> x arc cosine [ ( r - h ) / r ] - ( r - h ) x </span>√<span>( 2 x r x h - h</span>²<span> ).
</span>
<span>r</span>²<span> = (11.333 m)</span>²<span> = 128.444 m</span>²<span> </span>
<span>r - h= 11.333 m - 6 m = 5.333 m </span>
<span>r * h = 11.333 m x 6 m = 68 m</span>²
<span>Area = 128.444 m</span>²<span> x arc cosine [ 5.333 m / 11.333 m ] - 5.333 m x </span>√<span>[ 2 x 68 m</span>²<span> - 36 m</span>²<span> ] </span>
<span>Area = 128.444 m</span>²<span> x arc cosine [ 0.4706 ] - 5.333 m x </span>√<span> [ 100m</span>²<span> ] </span>
<span>Area = 128.444 m</span>²<span> x 1.0808 radians - 5.333 m x 10 m </span>
<span>Area = 138.828 m</span>²<span> - 53.333 m</span>²<span> </span>
<span>Area = 85.4 m</span>²
Answer:
x =20
Step-by-step explanation:
We can use similar triangles and proportions to solve. Take the smaller triangle side on top and the larger triangle side on the bottom.
11 10
---------- = --------------
11+121 10 +5x+10
Combine like terms
11 10
---------- = --------------
132 5x+20
Using cross products
11*(5x+20) = 10*132
55x+220 = 1320
Subtract 220 from each side
55x+220-220 = 1320-220
55x = 1100
Divide by 55
55x/55= 1100/55
x =20
