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

A company is developing a new high-performance wax for cross country ski racing. In order to justify the price marketing wants,

andrew11 [14]

Answer:

A)Yes they should market the wax, because it melts before 55 seconds

C) Null hypothesis: mean <55 vs. Alternative hypothesis :mean =55

D) the value is 51.33 seconds

Step-by-step explanation:

The selected samples for the champion are : 57.9, 62.9, 50.6, 50.5,48.2,47.2,50.2 and 43.1

The mean is ;

Sum =57.9 + 62.9 + 50.6 + 50.5+48.2+47.2+50.2+ 43.1 =410.6

Mean= 410.6/8 =51.33= mean

Assuming Significant =0.05 thus applying this level will give you 51.28-51.38

if specifically, the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion, then the null hypothesis is correct

Then;

Null hypothesis: mean <55

Alternative hypothesis :mean =55

7 0

2 years ago