1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mademuasel [1]
3 years ago
9

A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat,

which is 6 feet below the level of the pulley.
If the rope is pulled through the pulley at a rate of 18 ft/min, at what rate will the boat be approaching the dock when 90 ft of rope is out?
Mathematics
1 answer:
anyanavicka [17]3 years ago
8 0
The answer is x' = 16.07 ft/min and here is the procedure to get this one: 
<span>y = 8 ft, the distance the boat is below the pulley. 
x =the distance from the bottom of the dock to the front of the boat. 
c= the amount of rope out. 
c is the hypotenuse of a right triangle formed between the height of the dock and the distance from the dock t the boat. 

y = constant, while x and c are all changing with time, so: 

[x(t)]² + y² = [c(t)]² 

Dropping the (t) notation and differentiating implicitly with respect to time, 

x² + 64 = c² 
2xx' = 2cc' 
xx' = cc' 
From the problem statement, 
c = 90 ft 
c' = 16 ft/min 
We know that when c = 90 ft, y = 8 ft, so we can solve for x at this time. 
x² + 64 = 8100 
x = 89.64 ft 
x' = cc'/x 
= (90 ft)(16 ft/min)/89.64 ft 
x' = 16.07 ft/min</span>
You might be interested in
Add.
VladimirAG [237]
The answer to this question is 14 3/4
5 0
2 years ago
would Annabelle be able to pay off the loan with the lower montly payment in 5 years by setting aside $200 each month​
NISA [10]

Answer:

no

Step-by-step explanation:

3 0
3 years ago
Perform the indicated operation <br> 5(3x^3)^3-2(3x^3)
Pie
<span>5(3x^3)^3-2(3x^3)
=</span><span>5(3^3 x^9) - 6x^3
= 135x^9 - 6x^3
= 3x^3 (45x^6 - 2)</span>
5 0
3 years ago
For the polynomial below, find F(-3)<br><br> F(-3)= -4x^2+3x-1
Elodia [21]
f(-3)=-4\cdot(-3)^2+3\cdot(-3)-1=-4\cdot9-9-1=-36-10=-46
4 0
3 years ago
Number 13 is what I need done
Nadusha1986 [10]
Instead of using an = sign we use \leq becuase its less than or equal to 100 dollars.

The equation of the line is y=10x+7

sub in 100 for y and the inequallity sign

10x+7\leq100

solve so x is isolated

10x\leq93
x\leq9.3

technically the answer is 9 because you cant buy a fraction of a CD
5 0
3 years ago
Other questions:
  • Find g(1) if g(x) = x^2 + 1.<br><br> 2<br> 3<br> 4<br><br> Answer is NOT 3.
    11·2 answers
  • How do I do this problem?
    15·1 answer
  • Trevor paints 1/6 of the fence surrounding his farm each day. How many days will it take him to paint 3/4 of the fence?
    5·1 answer
  • You flip a fair coin.
    12·1 answer
  • HELLLPPPPPPP
    13·1 answer
  • ashley is on a road trip. so far she has traveled 28.61% of the trip which is 101 miles. how many miles is the entire trip?
    6·1 answer
  • TIME REMAINING
    7·1 answer
  • Find: 11 3 ÷ 2 3 The quotient is 5 and .
    12·2 answers
  • Simplify the expression.<br> 3.4m + 9 - 2.4m =blank
    9·1 answer
  • A square pyramid has a slant height of 15 cm. A side length of the base is 20 cm. What is the surface area of the pyramid? Enter
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!