At 0 degrees Celsius, the heat loss H ( in kilocalories per square meter per hour) from a person's body can be modeled by H= 33(10sqrtv-v + 10.45) where c is the wind speed ( in meters per second)
a. find dH/DV and interpet its meaning.
b. find the rate of change of H when v=2 and v=5

Answers

Answer 1

Answer:

Step-by-step explanation:

a. To find [tex]\frac{dH}{dV}[/tex], we need to take the derivative of H with respect to v:

[tex]\frac{dH}{dV}[/tex] = 33 [10(1/2)[tex]v^{(-1/2)}[/tex] - 1]

The derivative represents the rate of change of heat loss with respect to wind speed. It tells us how much the heat loss changes for a small change in wind speed.

b. To find the rate of change of H when v = 2 and v = 5, we plug in these values into the expression we found in part (a):

When v = 2:

[tex]\frac{dH}{dV}[/tex] = 33 [10([tex]\frac{1}{2}[/tex])[tex](2)^{(-1/2)}[/tex]- 1] = -19.49 kilocalories/([tex]m^{2}[/tex] hour)

When v = 5:

[tex]\frac{dH}{dV}[/tex] = 33 [10([tex]\frac{1}{2}[/tex])[tex]5^{(-1/2)}[/tex] - 1] = -25.61 kilocalories/(([tex]m^{2}[/tex]hour)

So the rate of change of heat loss decreases as wind speed increases. At v = 2 m/s, the heat loss decreases by approximately 19.49 kilocalories per square meter per hour for every additional meter per second increase in wind speed.

While at v = 5 m/s, the heat loss decreases by approximately 25.61 kilocalories per square meter per hour for every additional meter per second increase in wind speed.

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Related Questions

how many bit strings of length 9 have exactly two 1'S or two 0'S( this is one question, so you should have one answer)

Answers

Answer:

72.

Step-by-step explanation:

Number of strings with exactly 2 1's

= 9C2

= 9*8/2*1

= 36.

Same for  2 0s

= 36.

How would I do these questions?


A parabola has x- ints of -1 and 2 and passes through (4,10). Find its equation.

A parabola has x-ints of -2 and 3 and y int of -3. Find its equation.

A parabola has x-ints of 1/2 and 2 and passes through the point (1,3). Find its equation.


Any help will be greatly appreciated. I don't know the format of writing it out, so try to explain it easily so I can understand it. Thank you!

Answers

Answer:

Step-by-step explanation:

hello :

1)

the equation is : f(x)= a(x+1)(x-2)  because : x- ints of -1 and 2  means :

f(-1)=0 and f(2)=0

calculate : a   given f(4)=10

so :  a(4+1)(4-2)=10

10a =10   so : a = 1

the equation is : f(x)= (x+1)(x-2)

2) and 3) same method but   * y int of -3* meanes : f(0)= - 3

first sequence: 3 8 13 18 23 second sequence: -2 4 10 16 . find the TWO numbers that are in both number sequences.​

Answers

[tex]a(n) = 3 + 5n[/tex]

[tex]b(n) = - 2 + 6n[/tex]

[tex]a(n) = b(n) \\ 3 + 5n = - 2 + 6n \\ 5 = n \\ n = 5 \: (6th \: term)[/tex]

[tex]a(5) \: or \: b(5) = 3 + 5(5) = 28[/tex]

NEED HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

A

Step-by-step explanation:

The function has vertical asymptotes at x=7 and x=-3, so the denominator needs to have factors (x-7) and (x+3).

This eliminates all the options except for A.

The function f(x) = 200 × (1.098)x represents a village's population while it is growing at the rate of 9.8% per year.
Create a table to show the village's population at 0, 2, 4, 6, 8, and 10 years from now.
Use your table to create a graph that represents the village's population growth.
When the population doubles from its current size, the village will need to dig a new water well. To the nearest half of a year, about how long before it is time for the village to dig the new well?

Answers

The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.

How to graph a function?

For a function f(x) = y, the steps to draw a graph for the given function are as follows:

Consider certain values of x Substitute x values in the given function to obtain y valuesPlot the x and y values in the graphJoin the points to know the variation.

Calculation:

It is given that,

f(x) = 200 × [tex](1.098)^x[/tex]

Village's population growing rate = 9.8%

Creating a table for x and f(x) values:

x: 0   2   4   6   8   10

f(x = 0) = f(0) = 200 × [tex](1.098)^0[/tex] = 200

f(x = 2) = f(2) = 200 × [tex](1.098)^2[/tex] = 241

f(x = 4) = f(4) = 200 × [tex](1.098)^4[/tex] = 291

f(x = 6) = f(6) = 200 × [tex](1.098)^6[/tex] = 350

f(x = 8) = f(8) = 200 × [tex](1.098)^8[/tex] = 423

f(x = 10) = f(10) = 200 × [tex](1.098)^1^0[/tex] = 509

So,

(x, f(x)): (0, 200)  (2, 241)  (4, 291)  (6, 350)  (8, 423)  (10, 509)

Plotting these points in the graph and joining the points, the graph is shown below.

Finding the time for the village to dig a new well:

It is given that the population doubled from its current size, the village will need to dig new water well.

The current size of the village = 200

If it doubles for a certain time 't' = 400

So,

400 = 200 × [tex](1.098)^t[/tex]

⇒ [tex](1.098)^t[/tex] = 2

⇒ log[tex](1.098)^t[/tex] = log 2

⇒ t log(1.098) = 0.301

⇒ t × 0.04 = 0.301

∴ t = 7.525 years

Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.

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what is the mode of 250 100 75 200 150 100?

Answers

[tex]\textbf{Heya !}[/tex]

the mode is the number that occurs the most

All numbers here occur once, except [tex]\sf{100}[/tex].

so 100 is the mode.

`hope it was helpful to u ~

Mr. Mendez awards extra credit on quizzes to his students with quiz grades that exceed the class mean. Given that 107 students take the same quiz, what is the largest number of students who can be awarded extra credit

Answers

Answer:

106

Step-by-step explanation:

If 1 student gets a 1, and 106 get a 100, then the mean will be 99.99, and 106 students will get the extra credit.

Olga has a drawer of socks with four red pears, two gray pears, and a black hairs. she also has a bag of hair bands with 10 red, six gray, and 24 black hair bands if she selects randomly what is the probability that olga will select a red pair of socks and a red hairband

Answers

The probability that olga will select a red pair of socks and a red hairband is 14/47

Probability defines the likelihood of an event occurring. There are many situations in real life where we may need to predict the outcome of an event. We may or may not be certain of the outcome of the event. In such cases, we say that there is a probability that the event will or will not occur. Probability in general has great applications in games, in business for probabilistic predictions, and also probability has extensive applications in this new field of artificial intelligence.

The probability of an event can be calculated using the probability formula simply by dividing the number of favorable outcomes by the total number of possible outcomes. The value of the probability of an event occurring can lie between 0 and 1 because the number of favorable outcomes can never exceed the total number of outcomes. Also, a favorable number of results cannot be negative

For an experiment that has "n" number of outcomes, the number of favorable outcomes can be denoted by x. The formula for calculating the probability of an event is as follows.

Probability (event) = favorable outcomes/total outcomes = x/n

Olga has a drawer of socks with four red pears, two gray pears, and a black hairs. she also has a bag of hair bands with 10 red, six gray, and 24 black hair bands

Therefore total number of items are = 4 + 2 + 1 + 10 + 6 + 24 = 47

Probability that olga will select a red pair of socks and a red hairband is 4/47 + 10/47

= 14/47

Hence the probability that olga will select a red pair of socks and a red hairband is 14/47

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5. A fair coin is flipped 10 times. (a) What is the probability that there are an equal number of heads and tails

Answers

Answer:

you have a 50/50 chance to get equal number of heads & tails

HELP‼️‼️‼️‼️‼️‼️

1. If 8x + 4y = 44, what is the value of 6x + 3y?

Answers

Answer:

33.

Step-by-step explanation:

8x + 4y = 44

4(2x + y) = 44

2x + y =  44/4 = 11.

6x + 3y

= 3(2x + y)

= 3 * 11

= 33.

Find the surface.area of the composite.figure...
11 in.
3 in.
6 in.
3 in.
H
8 in.
SA =
3 in.
6 in.
11 in.
[?] in.2
If you'd like,
you can use a
calculator.
Enter

Answers

Answer is 521 in^2
Surface area can be found by multiplying
L x W of 3 sides x 2 for a total of 6 sides
For the large rectangle
6x8 = 48 x 2 = 96
6x11 = 66 x 2 = 132
8x11 = 88 x 2 = 176
_____
total 404

For the smaller rectangle
3x3 = 9 x 2 = 18
3x11 = 33 x 2 = 66
3x11 = 33 x 2 = 66
_______
Total 150

Now add both figures together
= 554
Now take away any connecting surface faces
We have the face of the small rectangle on the large rectangle
3x11 = 33
554-33= 521
Your total surface area is 521

Match each polynomial with its correct, most specific classification.
3x^2yz
2x^2+3xy-6y^2
3pq^2-3p
2xy+3x^2-2y^2-4x^2

Answers

The polynomials are classified as follows:

3x²yz: Monomial.2x² + 3xy - 6y²: Trinomial.3pq² - 3p: Binomial.2xy + 3x² - 2y² - 4x²: Polynomial.

How are the polynomials classified?

Depends on the number of terms, as follows:

3x²yz: Monomial, as it has one term.2x² + 3xy - 6y²: Trinomial, as it has three terms.3pq² - 3p: Binomial, as it has two terms.2xy + 3x² - 2y² - 4x²: Polynomial, as it has four terms.

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Sean tried to drink as fast as he could. He drank the slushy at a constant rate. There were originally 275 milliliters of slushy in the cup. After 13 seconds, 210 milliliters of slushy remained. (Please help and explain.)

How fast did Sean drink?

How long did it take Sean to drink all the slushy?

Answers

a. Sean drank at a rate of 5 milliliters per second.

b. It took Sean 55 s to drink all the slushy.

a. How to find the rate at which Sean drank?

Since Sean darnak at a constant rate and originally there were 275 milliliters of slushy in the cup. After 13 seconds, 210 milliliters of slushy remained.

The rate at which Sean drank, r = Change in volume of slushy/time for change

= (275 mL - 210 mL)/13 s

= 65 mL/13 s

= 5 mL/s

So, Sean drank at a rate of 5 milliliters per second.

b. How long did it take Sean to drink all the slushy?

The time it takes Sean to drink all the slushy is given by

T = V/r where

V = total volume of slushy = 275 milliliters and r = rate of drinking by Sean = 5 mL/s

So, T = V/r

= 275 mL/5 mL/s

= 55 s

So, it took Sean 55 s to drink all the slushy.

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URGENT!!! Write a compound interest function to model the following situation. Then, find the balance after the given number of years.

Answers

Answer:

The answer to our question is A = 16,100(1.001)12t; $17,510

Step-by-step explanation:

I hope this helps and have a good day!

If a truck traveled 75 miles in 3 hours, how many miles would the truck have traveled per minute?

Answers

The truck travelled 0.42 miles per minute

How to determine the miles per minute?

The given parameters are:

Distance = 75 miles

Time = 3 hours

Convert time to minutes

Time = 3 * 60 minutes

Time = 180 minutes

The speed is calculated as:

Speed = Distance/Time

This gives

Speed = 75 miles/180 minutes

Evaluate

Speed = 0.42 miles per minutes

Hence, the truck travelled 0.42 miles per minute

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the force, F newtons (N) between two particles is inversely proportional to the square of the distance, d m, between them. When the particles are 2m apart,
the force between them is 10 N. Find
1- the force between the particles when they are 5m apart,
2- the distance between the particles when the force between them is 25 N.

Answers

The force is 1.6N and the distance between them is 1.3 meters

The force between them

An inverse variation from force to the square of distance is represented s:

k = Fd^2

Where k represents the variation constant

When F = 10, d = 2.

So, we have:

k = 10 * 2^2

k = 40

Substitute k = 40 in k = Fd^2

Fd^2 = 40

When d = 5, we have:

F * 5^2 = 40

This gives

25F = 40

Divide by 25

F = 1.6

Hence, the force is 1.6N

The distance between them

In (a), we have:

Fd^2 = 40

When F = 25, we have:

25 * d^2 = 40

This gives

25d^2 = 40

Divide by 25

d^2 = 1.6

Take the square root of both sides

d = 1.3

Hence, the distance between them is 1.3 meters

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Can someone help please

Answers

Answer:

x=7 y=3

Step-by-step explanation:

-x+6y=11

2x-3y=5

-2x+12y=22

2x-3y=5

Add both equations

-2x+2x-3y+12=22+5

9y=27

y=3

plug y back in

-x+18=11

-x=-7

x=7

What is the value of the expression below when w = 9 and x = 5?


10w + 4x ​

Answers

Answer:

110

Step-by-step explanation:

10w + 4x

10 (9) + 4 (5)

90 + 20

110

The answer is 110.

Hope it helps!

Have a nice day:)

In a year of 365 days Paul skipped school for the months of January and February.
He had summer vacations for the months June to August. How many days of the
year (excluding Sundays) did he attend school?

Answers

The days of the year (excluding Sundays) paul attends school is 183 days

Calendar

Total days in a year = 365

Months Paul skipped school = January, February, June, July August

= 31 + 28 + 30 + 31 + 31

= 151 days

Days he attend school excluding Sunday = Total days in a year - (Months Paul skipped school + Sundays)

= 365 - (151 + 31)

= 365 - 182

= 183 days

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Find the sum.
14 + 42 + 70 + ... + (28n − 14)

Answers

Answer:

14n^2.

Step-by-step explanation:

This is Arithmetic with first term a =  14 and common difference d =  28.

Sum of n terms = n/2[2a + (n-1)d]

= n/2(28 +( n -1)28]

= n/2(28 + 28n - 28)

= 14n^2

Answer:

14n²

Step-by-step explanation:

14 = 14 *1

42 = 14 *3

70 = 14 *5

28n -14 = 14*2n - 14 = 14*(2n -1)

14 + 42 + 70 + ........+(28n -14) = 14*1  + 14*3  + 14*5 + ....... + 14*(2n - 1)

                                               = 14 * (1 + 3 + 5 + ......+ (2n-1) )

                                               = 14 * n²

                                               = 14n²

1 + 3 + 5 + .... +(2n -1)  ->  sum of first 'n' odd numbers.

Formula for finding sum of first 'n' odd numbers  = n²

If the rr is equal to 25%, what is the value of the money multiplier (simple deposit multiplier)? if $35,000 in cash is taken from under your mattress and deposited into a bank, predict the impact on the money supply in the economy.

Answers

The money supply in the economy is  $1025302.6

Bank loans or invests its excess reserves to earn greater hobby. A one-dollar boom inside the financial base reasons the money deliver to boom through more than one dollar. The growth inside the money supply is the cash multiplier.

The money multiplier is the primary can used to calculate what a change in reserves could do to the money supply. The method for the cash multiplier is 1/r where r is the reserve ratio. once one has calculated the money multiplier, they might then multiply that through the exchange in reserves.

The money multiplier is critical in macroeconomics because it determines the cash supply, which affects interest charges. it is also critical in banking because it impacts economic coverage and the steadiness of the banking region.

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the value of dimes in a vending machine is $1.70 more than what it contains in quarters.if there are 199 coins in all how many dimes and quarters are there

Answers

Using a system of equations, it is found that there are 147 dimes and 52 quarters in the machine.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Variable x: Number of dimes.Variable y: Number of quarters.

There are 199 coins, hence:

x + y = 199 -> y = 199 - x.

The value of dimes(each is worth $0.1) is $1.7 more than the sum of the quarters(each is worth $0.25), hence:

0.1x - 0.25y = 1.7.

Since y = 199 - x:

0.1x - 0.25(199 - x) = 1.7.

0.35x = 51.45

x = 51.45/0.35

x = 147

y = 199 - 147 = 52

There are 147 dimes and 52 quarters in the machine.

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In which number is the value of the underlined digit ten times the value of the bold digit

Answers

Step-by-step explanation:

I don't see any numbers, so I just give you an example :

11

every position in a number is worth 10 times the value of the position to its very right.

so, in e.g. 11

the left 1 is worth 10 times the value of the right 1.

the ratio of peters money to henrys money is 4 : 3 there at first. after perter spent 12 dollars they had an equal amount of money each. How much money id peter have at first

Answers

Using a system of equations, it is found that Peter had $48 at first.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Variable x: Peter's money.Variable y: Henry's money.

The ratio of peters money to henrys money is 4 : 3, hence:

[tex]\frac{x}{y} = \frac{4}{3}[/tex]

After Peter spent $12, they had the same amount, hence:

y = x - 12.

Then, replacing in the ratio:

[tex]\frac{x}{y} = \frac{4}{3}[/tex]

[tex]\frac{x}{x - 12} = \frac{4}{3}[/tex]

4(x - 12) = 3x

x = 48.

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Solve 3[-x + (2 x +1)]=x-1

Answers

Question :

Solve 3 [-x + (2x + 1) ] = x - 1

Solution :

3 [-x + 2x + 1] = x - 1

3 [x + 1] = x - 1

3 × [x + 1] = x - 1

3x + 3 = x - 1

3x - x + 3 = -1

2x + 3 = -1

2x = -1 - 3

2x = -4

x = -4 / 2

x = -2

Simplifying

3[-1x + (2x + 1)] = x + -1

Reorder the terms:

3[-1x + (1 + 2x)] = x + -1

Remove parentheses around (1 + 2x)

3[-1x + 1 + 2x] = x + -1

Reorder the terms:

3[1 + -1x + 2x] = x + -1

Combine like terms: -1x + 2x = 1x

3[1 + 1x] = x + -1[1 * 3 + 1x * 3] = x + -1[3 + 3x] = x + -1

Reorder the terms:

3 + 3x = -1 + x

Solving

3 + 3x = -1 + x

Solving for the variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

3 + 3x + -1x = -1 + x + -1x

Combine like terms: 3x + -1x = 2x

3 + 2x = -1 + x + -1x

Combine like terms: x + -1x = 0

3 + 2x = -1 + 03 + 2x = -1

Add '-3' to each side of the equation.

3 + -3 + 2x = -1 + -3

Combine like terms: 3 + -3 = 0

0 + 2x = -1 + -32x = -1 + -3

Combine like terms: -1 + -3 = -4

2x = -4

Divide each side by '2'.

x = -2

Simplifying

x = -2

Someone help me please

Answers

Answer: 12

Step-by-step explanation:

Let's say that the length needed to be found is x
As the two lengths of both triangles are parallel to one another, we can use the equation to find x
6/x = (6+4)/20

6/x = 1/2

x = 12

I SHOULD ALREADY KNOW THIS

Answers

[tex]t \geqslant 35[/tex]

Since there are at least 35 tic tacs, there has to be 35 tic tacs or more in the box.
Here is the solution for the question

Describe a relationship that can be modeled by the function represented by the graph, and explain how the function models the relationship. Identify and interpret the key features of the function in the context of the situation you described in part A.

Answers

The graph is a decreasing exponential graph.

How to illustrate the information?

Part A: The given graph is decreasing the exponential graph since the graph is decreasing rapidly as the value of x is increasing the value of y is decreasing very rapidly.

Part B: The graph shown here is maybe the case of any electric appliance which is of cheap quality. The time when it is brought then its performance and its life is awesome after that its life is decreasing rapidly.

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Mrs. Pollo was making pizza. She used 3/8 of a cup of olives to make 1 pizza. At this rate, what amount of olives would she use on 1/2 of a pizza?

Answers

Answer is 3/16 cup
She used 3/8 cup of olives on one pizza
She is going to use 1/2 of 3/8 cup for 1/2 pizza
1/2 of 3/8 = x
Multiply (1/2)(3/8) =
3/16 cup of olives

3/16 cup haveeee toooo maakeeeee ittttt lonnnnngggggeeerrrr

Find the arc length if the measure of the central angle is 80° and the radius
is 8 inches.

Answers

Answer:

[tex]\frac{32\pi }{9}[/tex] or [tex]11.17[/tex]

Step-by-step explanation:

The formula for arc length is [tex]2\pi r( \frac{x}{360} )[/tex] where "r" stands for radius and "x" stands for your angle

[tex]2\pi 8(\frac{80}{360} )[/tex]

[tex]=16\pi (\frac{80}{360} )[/tex]

[tex]=16\pi (\frac{2}{9})[/tex]

[tex]=\frac{32\pi }{9}[/tex]

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