Answer: 4 inches
Step-by-step explanation:
Let the width of the pool in the drawing be represented by x.
Since scale drawing of a pool has scale of 1 in :4 ft and the actual pool is 16 ft wide, this can be represented in an equation as:
1/4 = x/16
Cross multiply
4 × x = 1 × 16
4x = 16
x = 16/4
x = 4
Therefore, the pool representation in the drawing is 4 inches
Answer:
<em>p = ± q / 5r + 8; Option D</em>
Step-by-step explanation:
We are given the following equation; q^2 / p^2 - 16p + 64 = 25r^2;
q^2 / p^2 - 16p + 64 = 25r^2 ⇒ Let us factor p^2 - 16p + 64, as such,
p^2 - 16p + 64,
( p )^2 - 2 * ( p ) * ( 8 ) + ( 8 )^2,
( p - 8 )^2 ⇒ Now let us substitute this into the equation q^2 / p^2 - 16p + 64 = 25r^2 in replacement of p^2 - 16p + 64,
q^2 / ( p - 8 )^2 = 25r^2 ⇒ multiply either side by ( p - 8 )^2,
q^2 = 25r^2 * ( ( p - 8 )^2 ) ⇒ divide either side by 25r^2,
q^2 / 25r^2 = ( p - 8 )^2 ⇒ Now apply square root on either side,
| p - 8 | = √( q^2 / 25r^2 ) ⇒ Simplify,
| p - 8 | = q / 5r,
| p | = q / 5r + 8,
<em>Answer; p = ± q / 5r + 8; Option D</em>
Answer:
The radius of the circle is 9 units.
Step-by-step explanation:
To calculate the area of the circle we need to find it's radius, since we have the area of the sector and it's angle, therefore we can calculate the radius by using the following formula:
sector area = (central angle)*pi*r²/360
27pi = 120*pi*r²/360
27pi = pi*r²/3
27 = r²/3
r² = 81
r = sqrt(81) = 9
The radius of the circle is 9 units.
