Answer:
x=37 CD=20
Step-by-step explanation:
We know this becuase the two triangles are congruent.
Step-by-step explanation:
Step-by-step explanation:
Distance = rate × time
If B is the rate of the boat, and C is the rate of the current, then we can write two equations:
18 = (B + C) × 3
18 = (B − C) × 9
Simplifying the equations:
6 = B + C
2 = B − C
Add the equations together to eliminate C:
8 = 2B
B = 4
Plug into either equation to find C:
C = 2
The boat's rate is 4 mph, and the current's rate is 2 mph.
Ok, I'm going to start off saying there is probably an easier way of doing this that's right in front of my face, but I can't see it so I'm going to use Heron's formula, which is A=√[s(s-a)(s-b)(s-c)] where A is the area, s is the semiperimeter (half of the perimeter), and a, b, and c are the side lengths.
Substitute the known values into the formula:
x√10=√{[(x+x+1+2x-1)/2][({x+x+1+2x-1}/2)-x][({x+x+1+2x-1}/2)-(x+1)][({x+x+1+2x-1}/2)-(2x-1)]}
Simplify:
<span>x√10=√{[4x/2][(4x/2)-x][(4x/2)-(x+1)][(4x/2)-(2x-1)]}</span>
<span>x√10=√[2x(2x-x)(2x-x-1)(2x-2x+1)]</span>
<span>x√10=√[2x(x)(x-1)(1)]</span>
<span>x√10=√[2x²(x-1)]</span>
<span>x√10=√(2x³-2x²)</span>
<span>10x²=2x³-2x²</span>
<span>2x³-12x²=0</span>
<span>2x²(x-6)=0</span>
<span>2x²=0 or x-6=0</span>
<span>x=0 or x=6</span>
<span>Therefore, x=6 (you can't have a length of 0).</span>
Answer:
1230.88
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = (3.14) * (7)^2 * 8
V = 3.14 * 49*8
V =1230.88