A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 12 feet from the dock, the length of the rope form the boat to the dock is 3 feet longer than twice the height of the dock above the water.

To Find :

The height of the dock.

Solution :

This will make a right angle triangle as given in link below .

Now , applying Pythagoras theorem :

$(2h+3)^2=h^2+12^2\\\\4h^2+9h+9=h^2+144\\\\h^2+4h-45=0\\\\(h-5)(h+9)=0$

Now , h = 5 or h = -9 .

Now , height cannot be negative .

So , height of the dock is 5 ft .

Hence , this is the required solution .

8 0

3 years ago

What is the solution to this system of linear equations?<br><br> x + y = 4<br><br> x − y = 6

Amiraneli [1.4K]

X+y = 4, therefore y = 4-x when you rearrange the equation.
You can subsitute this in: x-(4-x) = 6
-4+x = 6-x
x=10-x
2x = 10
x = 5
Substitute x into the previous equation:
5+y = 4
y = 4-5
y = -1

5 0

3 years ago

Read 2 more answers

to get to work truman waited 11 minutes for the bus, then travled 21.78 miles on the bus at a speed of 33 miles per hour how muc

alexgriva [62]

We have 11 as our base value, meaning that we add 11 to something, so we have 11+<something>. To find that something, we want to know how long it takes to go 21.78 miles at 33 miles per hour. To get this, we want to turn miles per hour into minutes per mile and multiply that by 21.78 miles to get our answer. Therefore, we cross them out as shown in the equation to get $\frac{21.78 miles}{1} * \frac{1 hour}{33 miles} * \frac{60 minutes}{1 hour}$

6 0

3 years ago