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
Nimfa-mama [501]
3 years ago
5

A rope is wound round s drum of diameter 21cm is attached to a bucket that is resting at the bottom of a well in depth 9.89 m. F

ind the number of turns required to bring up the bucket such that the bottom of the bucket is suspended just above the mouth of the well
Mathematics
1 answer:
Misha Larkins [42]3 years ago
5 0

Answer:

15

Step-by-step explanation:

Depth of well = No. of turns × length of one turn

Given:   Depth of well = 9.89m = 989cm          [1m = 100cm]

Let number of turns be x

Length of one turn = 2πr or π×diameter

Now , 989=x×π×21

989=x×(22/7)×21

x=989×7/(22×21)

x=14.98 ≈15 turns    

[Number of turn never be in decimals]

Hence number of  15 complete turns of the handle required to bring up the bucket

You might be interested in
....................................................................
Eva8 [605]
The answer is negative twenty five. By the way, if that is you in the picture, you are beautiful.
5 0
3 years ago
You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along
sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}

Then, the time (speed divided by distance) is:

t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1

To optimize this function we have to derive and equal to zero:

\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\  \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\

x

As d_b=x, the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0
3 years ago
Christina is making a salad for a dinner party with 1.78 pounds of lettuce and 4.36 pounds of tomatoes.
gizmo_the_mogwai [7]

Answer:

A) 2.58 pounds

Step-by-step explanation:

To solve you would have to subtract the pounds of tomatoes from the pounds of lettuce. The equation would look like this,

4.36 - 1.78 = 2.58

Hope that helps and have a great day!

6 0
3 years ago
Solve the system of equations. 6x – 3y = 3 –2x + 6y = 14
Oxana [17]

Answer:

x=2; y=3

Step-by-step explanation:

You first add 3y to both sides. Divide both sides by 6. Then subsitute to get your answer.

6 0
3 years ago
Read 2 more answers
What is the following sum? 2(^3√16x^3y)+4(^3√54x^6y^5)
victus00 [196]
Option A: 4x(^3√2y)+12x^2y(^3√2y^2)
6 0
3 years ago
Read 2 more answers
Other questions:
  • Increasing W-4 allowances will ________ the net pay in your paycheck and ______ your total tax burden.
    9·1 answer
  • What is fraction 5/33 in a decimal form
    11·2 answers
  • Which is greater? 0.7 or -1?
    14·2 answers
  • 5-13)<br> -10-15<br> what’s the equation for the line that passes through points (5,-3) and (-10,15)
    14·1 answer
  • Find the center of the circle: x2 + 2x - 3 + y2 = 5.
    7·1 answer
  • Name the property demonstrated by the following equation: (5 + 4) + 6 = 5 + (4 + 6).
    7·2 answers
  • Ouglas made 122 dollars by washing cars to buy holiday presents. He decided to spend m dollars on a present for his mom and then
    11·1 answer
  • Solve the proportion
    5·1 answer
  • John paid $50 for renting a cycle for 5 hours. Which graph shows the relationship between the cost of renting a cycle for differ
    11·2 answers
  • Greg deposited $4000 into an account with a 9.8% annual interest rate, compounded semiannually. Assuming that no withdrawals are
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!