answer.
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
kirill
2 days ago
11

The fuel cost per hour for running a ship is approximately one half the cube of the speed (measured in knots) plus additional fi

xed costs of $216 per hour. Find the most economical speed to run the ship for a 500 M (nautical mile) trip. Note: Assume that there are no major disturbances, such as heavy tides or stormy seas
Mathematics
1 answer:
Zina [3.9K]2 days ago
7 0

Answer:

6 knots

Step-by-step explanation:

Let the velocity be v knots

thus, the time required to traverse 500 M is given by 500 / v hours

Fuel consumption per hour is equal to 216 plus half the cube of the speed (v^3).

Let F denote the fuel consumption for the journey

= [500/v][216 + 0.5v^3]

= 500[216/v + 0.5v^2]

The derivative of F with respect to v is: dF/dv = 500[ - 216/v^2 + v]

The second derivative, d^2F/d^2v = 500[432/v^3 + 1], indicates positivity.

Setting dF/dv to zero helps find the minimum.

500[ -216/v^2 + v] = 0

or v = 216/v^2

or v^3 = 216

By solving, we arrive at v = [216]^(1/3) = 6 knots

You might be interested in
What’s the x value of PR=9x-31 and QR=43?
AnnZ [3900]

Reducing

9x + -31 = 43

Rearranging the components:

-31 + 9x = 43

Finding the solution

-31 + 9x = 43

Isolating the variable 'x'.

Shift all terms with x to one side,

Add '31' to both sides of the equation.

0 + 31 + 9x = 43 + 31

Summing up similar items:

-31 + 31 = 0

0 + 9x = 43 + 31

9x = 43 + 31

Summing similar items:

43 + 31 = 74

9x = 74

Split each side by '9'

x = 8.222222222

Simplifying

x = 8.222222222

6 0
17 days ago
Read 2 more answers
f(x) = 7x g(x) = 7x + 6 Which statement about f(x) and its translation, g(x), is true? The domain of g(x) is {x | x > 6}, and
Leona [4187]
The asymptote of g(x) represents the asymptote of f(x) shifted six units upwards.
7 0
8 days ago
Read 2 more answers
The organizers of a talent show have budgeted $1800 to buy souvenir clothing to sell at the event. They can buy shirts for $10 e
babunello [3666]

Let s denote the count of shirts and h the count of hats.

According to the provided information, the talent show organizers have a budget of $1800 to purchase merchandise clothing for sale at the event. The price for shirts is $10 each, while hats are priced at $8.

The expense for s shirts is given by 10s, and the cost for h hats is described by 8h. The combined cost for s shirts and h hats must not surpass 1800, which can be expressed as:

10s+8h\leq 1800

Additionally, they plan to acquire at least five times more shirts than hats. This implies that the quantity of shirts should be at least five times that of hats. This can be represented as:

s\geq 5h

Therefore, the second inequality should be s\geq 5h making option C the correct answer.

6 0
8 days ago
If m∠1= (7x –19)°, and m∠2 = (x + 5)°, find m∠2.
babunello [3666]

Given :

∠m1 = ( 7x - 19 )°.

∠m2 = ( x + 5 )°.

To Find :

The value of x .

Solution :

As the relationship between angle ∠m1 and ∠m2 isn't specified,

let's presuppose that the sum of ∠m1 and ∠m2 equals 180°.

Thus,

(7x-19)+(x+5)=180^{\circ}\\\\8x-14=180\\\\8x=194\\\\x=24.25^{o}

Angle ∠m2 = (24.25 + 5 )° = 29.25°.

Consequently, ∠m2 is 29.25°.

Hence, this solution meets the requirements.

7 0
14 days ago
the volume of a sphere whose diameter is 18 centimeters is 246 324 648 972 π cubic centimeters. if its diameter were reduced by
Inessa [3926]
The sphere's radius is calculated as 18 divided by 2, giving 9 cm.

Using the formula for the volume of a sphere, we find it to be 4/3 πr^3, resulting in 4/3 x π x (9)^3 which equals 972 π cubic centimeters.

If we halve the diameter, the new volume can be calculated as: 4/3 x π x (9/2)^3 equals 4/3 x π x (9)^3 x (1/2)^3, simplifying down to 1/8 of 972.

Thus, the new volume will only be 1/8 of the original volume.
4 0
9 days ago
Other questions:
  • How much profit was generated by the sales of gold label and black label combined?
    8·2 answers
  • If BD = 7x – 10, BC = 4x – 29, and CD = 5x – 9, find each value.
    14·1 answer
  • Using cell references, enter a formula in cell B6 to calculate monthly payments for the loan described in this worksheet. The an
    14·1 answer
  • Ollie has installed security lights on the side of his house that are activated by a sensor. The sensor is located at point C di
    12·1 answer
  • What is the value of n? 9x27+2x31-28= n
    10·2 answers
  • Complete the table of inputs and outputs for the given function g(x)=3-8x.
    13·1 answer
  • You are given the coordinates of a triangle and
    10·2 answers
  • In a huge chess tournament, 66 games were played. Find out how many people were involved if it is known that each participant pl
    10·1 answer
  • Two parallel lines are crossed by a transversal. What is the value of x ?
    5·2 answers
  • 1. The cities of Dallas, Charleston, and Indianapolis form a triangle. The distance from Dallas to
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!