The energy cost of a speed burst as a function of the body weight of a dolphin is given by E = 43. 5w-0. 61, where w is the weight of the dolphin (in kg) and E is the energy expenditure (in kcal/kg/km). Suppose that the weight of a 400-kg dolphin is increasing at a rate of 8 kg/day. Find the rate at which the energy expenditure is changing with respect to time. A) -0. 0017 kcal/kg/km/day B) -20. 5166 kcal/kg/km/day C) -0. 0137 kcal/kg/km/day D) -5. 491 kcal/kg/km/day

Answers

Answer 1

The rate at which the energy expenditure is changing with respect to time is -0.0137 kcal/kg/km/day.

To find the rate at which the energy expenditure is changing with respect to time, we need to use the chain rule of differentiation.

Given the equation E = 43.5w^(-0.61), where E represents energy expenditure and w represents the weight of the dolphin in kg, we want to find dE/dt, the rate of change of energy expenditure with respect to time.

First, we express w as a function of time t. We are given that the weight of the dolphin is increasing at a rate of 8 kg/day, so we can write w = 400 + 8t.

Now, we differentiate E with respect to t:

dE/dt = dE/dw * dw/dt

To find dE/dw, we differentiate E with respect to w:

dE/dw = -0.61 * 43.5 * w^(-0.61 - 1) = -26.5735 * w^(-1.61)

Substituting w = 400 + 8t:

dE/dw = -26.5735 * (400 + 8t)^(-1.61)

Next, we find dw/dt:

dw/dt = 8

Finally, we can calculate dE/dt:

dE/dt = -26.5735 * (400 + 8t)^(-1.61) * 8

Evaluating this expression at t = 0 (initial time), we get:

dE/dt = -26.5735 * (400 + 8 * 0)^(-1.61) * 8 = -26.5735 * 400^(-1.61) * 8

Simplifying the expression yields:

dE/dt ≈ -0.0137 kcal/kg/km/day

Therefore, the rate at which the energy expenditure is changing with respect to time is approximately -0.0137 kcal/kg/km/day.

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Related Questions

In triangle ABC, m∠A = 68° and m∠B = 9°. What is the measure of ∠C?

Answers

Answer:

103 degrees

Step-by-step explanation:

The sum of the measures of all triangles is 180 degrees.  The two angles given total 77 degrees.  Subtracting 77 from 180 leaves 103 degrees for the 3rd angle

A meteorologist found that the rainfall in Campbell during the first half of the month was 3/10 of an inch. At the end of the month, he found that the total rainfall for the month was 1/2 of an inch. How much did it rain in the second half of the month?

Answers

Answer: 1/5

Step-by-step explanation:

Let the amount of rainfall in the second half of the month be represented by x.

From the information given in the question, the equation formed will be:

3/10 + x = 1/2

x = 1/2 - 3/10

x = 5/10 - 3/10

x = 2/10

x = 1/5

Therefore, the answer is 1/5

15x - 6xy
Helppppppppppo

Answers

Answer:

3x(5-2y)

Step-by-step explanation:

Answer:

3x(5-2y)

Step-by-step explanation:

15x-6xy=3x(5-2y)

I NEED HELP AND YOU GUYS ARE SMART ANDBI NEED THE HELP NOW PLEASE

What does a 100% increase mean?

Example: I am a store owner I purchased t-shirts each for $5, I sell them each for $10.

Answers

Answer:

it means your adding it again lets use your example.

Step-by-step explanation:

Your increasing by 100% because 100% of 5 is 5 so your just addding 5+5 which is 10.

If you want another example tell me

Hope this helps : D

Answer: It means that the quantity has doubled he re is an example if you do not quite get it: An increase of 100% in a quantity means that the final amount is 200% of the initial amount (100% of initial + 100% of increase = 200% of initial.

Step-by-step explanation:

please help me out lolll

Answers

Step-by-step explanation:

[tex] \sin(30) = \frac{35}{x} \\ x \sin(30) = 35 \\ x = \frac{35}{ \sin(30) } \\ x = 70[/tex]

the person above me is correct!! I just checked

Back Next
Check
Question 1
Indicate the answer choice that best completes the statement or answers the que
Solve s 3. Graph the solution on a number line.
Ву
+ +
0 1 2 3 4 5 6 7 8 9
-1
Oa
十一
0 1 2 3 4 5 6 7 8 9
Ob.
+
0 1 2 3 4 5 6 7 8 9
Ос.
0 1 2 3 4 5 6 7 8 9
Od

Answers

Answer:

C

Step-by-step explanation:

✔️First, solve for r:

r/2 ≤ 3

Multiply both sides by 2

r/2 × 2 ≤ 3 × 2

r ≤ 6

This implies that possible value of r is equal to 6 or less than 6.

Graphing this on a number line, the line with a shaded circle, indicating that 6 is included, starts at 6 and points to the left.

This indicates that value of r ranges from 6 and below.

The graph is C.

the total for dinner was $55 before a discount and tax there was a 10% discount and 7% sales tax
use the tiles to create and expression that could be used to find the total

55xblank x blank

use :0.10 0.9 1.07 0.07 to make the equation ​

Answers

Answer:

( 55 x .10 ) x .07

Find the area of the semicircle.​

Answers

Answer:

39.25 centimeters squared is the area of the semicircle


Boden's account has a principal of $300 and a simple
interest rate of 3.6%. Complete the number line. How much
money will be in the account after 4 years, assuming
Boden does not add or take out any money?
years
2
3
and the missing year value is 1
In the double number line, the missing interest value is
(Type integers or decimals.)
Enter your answer in the edit fields and then click Check Answer.
Check Answer
Clear All
1
part
remaining
lof 11
Back
Next →

Answers

Answer:

808

Step-by-step explanation:

cause that's the answer

Mrs. Thomas used similar rectangles to make a design. Which statement about the rectangles in the design must be true?

Answers

Answer:

what are the statements

Step-by-step explanation:

the answer please?????????

Answers

Answer:

Answer A- "The system of equations has one solution." :)

Step-by-step explanation:

Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. ... If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.

Hope this helps! <3

Three friends want to take a bus trip to the Grand Canyon. The entire trip costs $1,025 per person, plus $383 per person for the meal plan.

Answers

Answer:

4224 dollars

Step-by-step explanation:

1025 times 3 is 3075. 383 times 3 is 1149. 3075+1149 is 4224.

Pls help me, I have to find the area.

Answers

Answer:

a) 136

Step-by-step explanation:

(20x2x2)+(14x4)=136

. Chris read 25 books in 135 days. At this rate, in how many days will he read another 5 books? Another 10 books?

Answers

Answer:

5 books - 27 days

10 - 54 days

15 books - 81 days

Step-by-step explanation:

First, you need to find how many days it takes to read one book, to do this, simply divide 135 by 25 (135/5=5.4). Then, you multiply that number by the amount of books it wants to know how long it would take him to read (5 and 15 since it asks "another 10". It could also be 54 if it was asking how many for 10 books not including the 5 he would have read). 5*5.4=27, 10*5.4=54, and 15*5.4=81.

Sheila is flying a kite with a string that makes a 59-degree angle with
the sand. If the height of the kite above the ground is 97 feet, how
long is the string? (Please use the exact ratio to calculate the missing
side and round your answer to the nearest hundredth.)

Answers

Answer:

113.16 feet

Step-by-step explanation:

Representing the given details appropriately with a right angle triangle. Let the length of the string for the kite be represented by x. Applying required trigonometric function, we have:

Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin [tex]59^{o}[/tex] = [tex]\frac{97}{x}[/tex]

x = [tex]\frac{97}{Sin59^{o} }[/tex]

  = [tex]\frac{97}{0.8572}[/tex]

  = 113.1591

x = 113.16 feet

Thus, the string for the kite is 113.16 feet long.

The ages, in years, of a group of students are given in the box. Work out the mode.11 11 12 13 13 14 15 15 15 15

Answers

Answer:  Mode = 15

Explanation:

The mode is the most frequent value. We see that "15" shows up a total of 4 times, which is the most of the the unique values {11, 12, 13, 14, 15}.

How do I round 31732.441804 to the nearest dollar?

Answers

Answer and Step-by-step explanation:

To round to the nearest dollar, you are essentially rounding to the nearest whole number.

This involves looking at the tenths place.

31732.441804

The bolded 4 is in the tenths place (after the decimal), and determines if the number to the left of it rounds up or stay the same.

Since 4 is not greater than or equal to 5, it makes the number stay 2.

So, we get the answer to be $31732.

#teamtrees #WAP (Water And Plant)

ummm i think it might be the last number after the decimal if it’s over 5 it’s the next number

Can the terms susc as "less than" and "more than" be used in a real situation? Can you give an example or examples?

Answers

Answer:

Yes

Step-by-step explanation:

She had more than me

I would help her but she has less than me

State if the three numbers can be the measures of the sides of a triangle.

17, 19,7

A) yes
B) no

Answers

they measured can be sides of triangle

Figs come in 2.4 lb bags. Apples come in 7.2 lb bags. How many times as many pounds are the apple bags as the fig bags?

Answers

The answer is 3 times.

What is the solution of the system of equations?
y=x+2
y = 3x
F. (3,-1) G.(-3, 1) H. (1,3)I. (1, -3)

Answers

Answer:

the right answer is H.(1,3)

Mariah's teacher tells her that this expression can be written as log k, where k is an integer.

3 log 3x – log 9x^4 + log x

What is the value of K?

The value of k is?

Answers

Answer: 3

Step-by-step explanation:

Deion left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Deion is xx minutes after he left his house, until he got back home.
\text{How many blocks is it from Deion's house to the bank?}
How many blocks is it from Deion’s house to the bank?

Answers

Answer:

I dont know if this is still helpful but the answer is 14 blocks

Step-by-step explanation:

The regular price of a camera is 180.00 the camera is on sale for 25% off the regular price. What is the sales price of the camera in dollars and cents

Answers

Answer:

$135

Step-by-step explanation:

180 decrease 25% =

180 × (1 - 25%) = 180 × (1 - 0.25) = 135

What is the slope of this graph ?​

Answers

Answer:

linear slope paragraph

Answer:

the slope is 58

Step-by-step explanation:

hope this helps :)

NEED HELP MATH HOMEWORK ASAP plz help

Answers

The second and third options are the correct answers

how to solve for mamath

Answers

Answer:

2

Step-by-step explanation:

Answer:

X= 20

Step-by-step explanation:

To find x you need to know what are the dimensions

48 divided by 12 = 4

5 x 4 = 20

x = 20

hope this helps

Are 12/7 and 36/21 proportional

Answers

Answer:

Step-by-step explanation:

Cross multiply:

12 * 21 = 7 * 36

Simplifying

12 * 21 = 7 * 36

Multiply 12 * 21

252 = 7 * 36

Multiply 7 * 36

252 = 252

Add '-252' to each side of the equation.

252 + -252 = 252 + -252

Combine like terms: 252 + -252 = 0

0 = 252 + -252

Combine like terms: 252 + -252 = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

(hope this helps can i plz have brainlist :D hehe)

From the calculations below, 12/7 and 36/21 are proportional, therefore, the statement is true.

The first fraction given is 12/7.

The second fraction given is 36/21.

In order to check, we can multiply both the numerator and the denominator by 3. This will be;

= (12 × 3) / (7 × 3)

= 36 / 21

Therefore, it has been solved that 12/7 and 36/21 are proportional.

Read related link on:

https://brainly.com/question/18759132

CORRECT ANSWER GETS BRANLIEST, IF I SUBMIT MY TEST AND ITS INCORRECT U WILL BE REPORTED <3



Which equation has solutions at (3, 4)?
A. y=5x+2
B. y=2x-1
C. y=5x-2
D. y=2x+1

Answers

Answer:

none of them do

Step-by-step explanation:

i checked with a graphing calculator

Find the measure of the missing angle.

Answers

A box indicates a 90° angle.

So to find m<a, we can setup the equation 41 + a = 90.

Now subtract 41 from both sides to get a = 49.

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