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

3 sisters are each 2 years apart in age. The youngest sister is Emily the middle sister Samantha and the older sister is Lauren

Jet001 [13]

Emily is 12, Samantha is 14, and Lauren is 16. Basically all you do to solve this problem is add numbers that are two apart until you find something.

Ex. 2+4+6=12 4+6+8=18 so on and so forth.

3 0

3 years ago

Read 2 more answers

Profit, P(x), is the difference between revenue, R(x), and cost, C(x), so P(x) = R(x) - CC). Which

aleksklad [387]

Answer:

Step-by-step explanation:

Profit, P(x), is the difference between revenue, R(x), and cost, C(x)

R(x) = 2x^4 - 3x^3 + 2x - 1

C(x) = x^4 -x^2 + 2x + 3

Substituting into the equation

P(x) = R(x) - C(x)

= (2x^4 - 3x^3 + 2x - 1) - (x^4 -x^2 + 2x + 3)

= x^4 - 3x^3 + x^2 - 4

The answer is the lower left option.

7 0

3 years ago

Read 2 more answers

if a piece of string which is 368cm long must be cut into 8 equal pieces how long will each piece be (answer in mm)​

if a piece of string which is 368cm long must be cut into 8 equal pieces how long will each piece be (answer in mm)