Let's solve your equation step-by-step.<span><span><span>−18</span>−<span>6k</span></span>=<span>6<span>(<span>1+<span>3k</span></span>)
</span></span></span>Step 1: Simplify both sides of the equation.
<span><span><span>−18</span>−<span>6k</span></span>=<span>6<span>(<span>1+<span>3k</span></span>)
</span></span></span><span>Simplify: (Show steps)</span><span><span><span>−<span>6k</span></span>−18</span>=<span><span>18k</span>+6
</span></span>Step 2: Subtract 18k from both sides.<span><span><span><span>−<span>6k</span></span>−18</span>−<span>18k</span></span>=<span><span><span>18k</span>+6</span>−<span>18k</span></span></span><span><span><span>−<span>24k</span></span>−18</span>=6
</span>Step 3: Add 18 to both sides.<span><span><span><span>−<span>24k</span></span>−18</span>+18</span>=<span>6+18</span></span><span><span>−<span>24k</span></span>=24
</span>Step 4: Divide both sides by -24.<span><span><span>−<span>24k</span></span><span>−24</span></span>=<span>24<span>−24</span></span></span><span>k=<span>−1
</span></span>Answer:<span>k=<span>−<span>1</span></span></span>
If we let
x as the distance traveled by the boat
y as the distance between the boat and the lighthouse.
Then, we have:
tan 18°33' = 200 / (x + y)
and
tan 51°33' = 200 / y
Solving for y in the second equation:
y = 200 / tan 51°33'
Rearranging the first equation and substituting y
x = 200 / tan 18°33' - 200 / tan 55°33'
x = 458.81 ft
Therefore, the boat traveled 458.81 ft before it stopped.
Answer:
(b) Radius of the sphere = 5 units.
Step-by-step explanation:
Here, given:
The volume of the sphere = 
cubic units ... (1)
Also, radius of the sphere = x units
Now, VOLUME OF SPHERE = 
So, volume of a sphere with radius x = 
But volume of sphere is given by (1).
Hence, radius of the sphere = 5 units.
