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
BARSIC [14]
3 years ago
8

Represent real-world situations a rectangular piece of sheet metal is rolled and riveted to form a circular tube that is open at

both ends, as shown. the sheet metal has a perimeter of 36 inches. each of the two sides of the rectangle that form the two ends of the tube has a length of x inches, and the tube has a circumference of x - 1 inches because an overlap of 1 inch is needed for the rivets. write a volume function for the tube in terms of x. then, to the nearest tenth, find the value of x that maximizes the volume of the tube. answer
Mathematics
1 answer:
Citrus2011 [14]3 years ago
3 0
<span>12.3 Volume function: v(x) = ((18-x)(x-1)^2)/(4pi) Since the perimeter of the piece of sheet metal is 36, the height of the tube created will be 36/2 - x = 18-x. The volume of the tube will be the area of the cross section multiplied by the height. The area of the cross section will be pi r^2 and r will be (x-1)/(2pi). So the volume of the tube is v(x) = (18-x)pi((x-1)/(2pi))^2 v(x) = (18-x)pi((x-1)^2/(4pi^2)) v(x) = ((18-x)(x-1)^2)/(4pi) The maximum volume will happen when the value of the first derivative is zero. So calculate the first derivative: v'(x) = (x-1)(3x - 37) / (4pi) Convert to quadratic equation. (3x^2 - 40x + 37)/(4pi) = 0 3/(4pi)x^2 - (10/pi)x + 37/(4pi) = 0 Now calculate the roots using the quadratic formula with a = 3/(4pi), b = -10/pi, and c = 37/(4pi) The roots occur at x = 1 and x = 12 1/3. There are the points where the slope of the volume equation is zero. The root of 1 happens just as the volume of the tube is 0. So the root of 12 1/3 is the value you want where the volume of the tube is maximized. So the answer to the nearest tenth is 12.3</span>
You might be interested in
Write y = -2x + 1 in standard form​
Amiraneli [1.4K]

Answer:

2 x + y = 1

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
A boat took 5 h to travel 60 km up a river, against the current. The return trip took 3 h. Find the speed of the boat in still w
Dafna11 [192]

Answer:

Correct answer: V₁ boat = 16 km/h and V₂ current = 4 km/h

Step-by-step explanation:

If we take speed (velocity) of the boat as V₁ and speed of the current V₂

Let us form equations:

Traveling down the current  V₁ + V₂ = 60/3 = 20 km/h

Traveling against the current  V₁ - V₂ = 60/5 = 12 km/h

V₁ - V₂ = 12

V₁ + V₂ = 20

If we add up the left and right sides of the equations we get:

2 V₁ = 32  =>    V₁ = 32/2 = 16 km/h

from the second equation we get:

V₂ = 20 - V₁ = 20 - 16 = 4 km/h

V₂ = 4 km/h

God is with you!!!

8 0
3 years ago
5) Find the value of the term in the arithmetic sequence. (an = a1 + (n - 1)d) 11,
kvasek [131]

Answer:

139, I am sorry if I'm wrong

Step-by-step explanation:

a1=11; d=19-11=8

a17=11+(17-1)*8=11+128=139

6 0
3 years ago
Drag the tiles to the boxes to form correct pairs. Match each function to the equation of the tangent line to its graph at x = 2
Ede4ka [16]

Step-by-step explanation:

the picture includes the answer and work

I plugged in 2 for x

the equations that got the same answer, I put together

3 0
3 years ago
While driving on the highway, Dave averages 60 miles per hour. In the city, he averages 30 miles per hour. On a trip to his gran
Tasya [4]
Dave arrived to his grandmother's hours in7.75 hours.
7 0
3 years ago
Read 2 more answers
Other questions:
  • When constructing parallel an perpendicular lines, how are the steps similar
    5·1 answer
  • Sally’s parents deposited $15,000 into a college savings account on her third birthday. The account had an interest rate of 9.6%
    8·2 answers
  • A man completes 10 laps of a circular track with a radius of 4.5 metres (when rounded to one decimal place). Find the minimum an
    11·1 answer
  • At Ken's boutique, 33 customers wore a size small, and 51 customers wore a different size.
    5·2 answers
  • The 3 × 3 matrix P satisfies the matrix equation P^2 = P.
    9·1 answer
  • In the example problem, 0.000000005 = 5 x 109.<br><br> What is the standard form of 10-??
    5·1 answer
  • What is -11/19 minus 35/16 + -1/6
    11·2 answers
  • HELP ME ANSWER IT PLZ ASAP<br> 6(6x−1)=5(5x+4)−2x
    12·2 answers
  • Five friends including Marlon, purchased two boxes of pizzas. They equally shared the pizza among themselves. How much pizza did
    14·1 answer
  • 14 The straight line, L, has the equation y = 5 - 2x
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!