The distance a freely falling body covers in the nth second is given by S(n)=d(n)-d(n-1). Show s(n) in terms of g, in simplified form.

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]s=ut+\frac{1}{2}gt^2\\if ~the~body~falls~freely,~then~at~t=0,d=0\\s_{n}=d_n=\frac{1}{2}gn^2\\S_{n-1}=\frac{1}{2}g(n-1)^2\\distance~covered ~in~nth~second\\S(n)=d(n)-d(n-1)=\frac{1}{2}gn^2-\frac{1}{2}g(n-1)^2=\fracg[n^2-(n-1)^2]\\=\frac{1}{2}g{(n+n-1)(n-n+1)]\\=\frac{1}{2}g(2n-1)[/tex]


Related Questions

In 2003, the price of a certain automobile was approximately $30,600 with a depreciation of $1,440 per year. After how many years will the car's value be $19,080?

a) Write an equation to model the problem. Let t represent the number of years after 2003. For example, the year 2005 would be represented by t = 2.
Answer:
b)Solve the equation to find the answer to the question above. (Note: Include the units, in this case years.)
Answer:

Answers

Answer:

  a) v(t) = 30600 -1440t

  b) 8 years

Step-by-step explanation:

You want an equation that models the value of a car that is initially $30,600 and falls at the rate of $1440 per year. Then you want the number of years it takes for the value to fall to $19,080.

a) Equation

Since the rate at which the value falls is a constant, we can use a linear equation for the model. Its form will be ...

  value = initial value - (depreciation per year) × years

  v(t) = 30,600 -1440t

b) Time

The time it takes for the value to fall to 19080 can be found by solving for t:

  19080 = 30600 -1440t

  1440t = 30600 -19080 = 11520

  t = 11520/1440 = 8

After 8 years the car's value will be $19,080.

DUE SOON PLEASE HELP! WHAT ANGLES SHOW THAT LINE 1 AND 2 ARE PARALLEL AND WHY!

Answers

Answer:

Both e and h and a and c

Step-by-step explanation:

e and h are corresponding angles on a transversal. Lines are parallel when the corresponding angles of a transversal have the some degree of measure

Same goes for a and c

e and g are not because g doesn't correspond to e because g is in 2 transversals.

the high temperature for the week were 50, 52, 71, 54, and 51. what is the mean of the temperatures without the outlier?

Answers

Answer: 55.6 or 55.60

Step-by-step explanation: Okay, so we have to add up all the numbers and divide by how many numbers there are, so we would add 50 + 52 + 71 (Including this outlier) + 54 + 51, to get 278. Now, since there are 5 numbers in the data set, we would divide 278 by 6, and you should get 55.6 or 55.60 (They are the same thing)

What value(s) of b will cause 27x2 + bx + 3 = 0 to have one real solution? Select all that apply.A. b = −18. B. b = −9. C. b = 9. D. b = 18.

Answers

The value of b is 18 that will cause equation 27x² + bx + 3 = 0 to have real solution.

What is a quadratic equation?

A quadratic equation is an equation of second order. Quad implies the square power, it is also called equation of degree 2.

The standard form of a quadratic equation is ax² + bx + c = 0.

Where a, b and c are constants.

The given equation is,

27x² + bx + 3 = 0.

Compare the given equation from the standard quadratic equation

ax² + bx + c = 0

Compare both the equations,

a = 27, b = b , c = 3

To find the real solution of the quadratic equation,

Substitute discriminant of the equation equal to zero.

D = 0

b² - 4ac = 0

b²  - 4 x 27 x 3 = 0

b²  = 4 x 81

b  = 2 x 9

b = 18.

The required value of b for the given equation is 18.

To know more about Quadratic equation on:

https://brainly.com/question/17177510

#SPJ1

10. The figures below are similar.
State the ratio of similarity and then use it
to find the value of x. (2 points)

Answers

Answer:

x = 16.5

Step-by-step explanation:

the ratio of similarity is the ratio of corresponding sides, that is

ratio = [tex]\frac{18}{12}[/tex] = [tex]\frac{15}{10}[/tex] = 1.5

Then

[tex]\frac{x}{11}[/tex] = 1.5 ( multiply both sides by 11 to clear the fraction )

x = 16.5

Sybush
5 Resuelve como en el ejemplo.
TH
.-6+8-10 + 13 = +2 -10 + 13 = -8 + 13 = +5
b) 5-9+7-6
d) -8 + 12-9-2
a) 10-3-5 + 11
c) −2+2+7+8

Answers

The Answers for the four parts are

a)  5-9+7-6=-3

b) -8 + 12-9-2=-7

c) 10-3-5 + 11 =13

d)  −2+2+7+8= 15

What are Integers?

Integers come in three types:

Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)

Given:

a)  5-9+7-6

= -4 +7-6

= 3-6

=-3

So, the value of 5-9+7-6 is (-3).

b) -8 + 12-9-2

= 4-9-2

= -5-2

=-7

So, the value of -8 + 12-9-2 is (-7).

c) 10-3-5 + 11

= 7-5+11

= 2+11

=13

So, the value of  10-3-5 + 11 is (13).

d)  −2+2+7+8

= 0+7+8

= 7+8

= 15

So, the value of −2+2+7+8 is (15).

Learn more about Integers here:

https://brainly.com/question/15276410

#SPJ1

The Translation of the Attached Question:

Solve as in the example

What is the length of X Y? 5 units 4 units 3 units 2 units

Answers

The length of XY in the given figure is 3 units.

What does congruent mean?

same in size and form

Congruent refers to things that are exactly the same size and form. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

What is an example of congruent?

Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another.

In the above question,

According to the congruency criteria

HI=XY

Hence, Value of XY is 3 units.

To know more about congruency, click the following link:-

https://brainly.com/question/2938476

#SPJ1

is an altitude in triangle WXZ.

Triangle W X Z is shown. An altitude is drawn from point W to point Y on side Z X, forming a right angle. Angles Z W Y and W X Y are congruent.

If ΔYWZ ~ ΔYXW, what is true about AngleXWZ?

AngleXWZ is an obtuse angle.
AngleXWZ is a right angle.
AngleXWZ is congruent to AngleWXY.
AngleXWZ is congruent to AngleXZW.

Answers

Angle XWZ is a right angle if line WY is an altitude in triangle WXZ.

Define angle.

In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The Latin word "angulus," which means "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. A geometrical shape called an angle is created by connecting two rays at their termini. In most cases, an angle is expressed in degrees. In geometry, there are several different kinds of angles.

Given,

Triangle W X Z is shown. On side ZX, an altitude is drawn at a right angle from point W to point Y. The angles ZWY and WXY are congruent.

ΔYWZ ~ ΔYXW

Angle XWZ is a right angle is true about Angle XWZ.

To learn more about the angle, visit:

https://brainly.com/question/9448891

#SPJ1

Answer:Angle XWZ is a right angle if line WY is an altitude in triangle WXZ.

Step-by-step explanation:

Got it right on edge

A cryptographer uses a combination of two functions to develop the initial "key” in a sequence of coded numbers. The functions are:

f(x) = log5(x) – 8

g(x) = x3 + 3

Which is h(x) = f(x) – g(x)?

h(x) = log5(x) – x3 – 5
h(x) = log5(x3) – 3
h(x) = log5(x) – x3 + 11
h(x) = log5(x) – x3 – 11

Answers

The value of the function h(x) = f(x) – g(x) will be h(x) = log5(x) – x³ – 11. The correct option is D.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a cryptographer uses a combination of two functions to develop the initial "key” in a sequence of coded numbers. The functions are:

f(x) = log5(x) – 8

g(x) = x³ + 3

The value of the function h(x) = f(x) - g(x) is,

h(x) = f(x) - g(x)

h(x) = log5(x) – 8 - x³ - 3

h(x) = log5(x) – 8 - x³ - 11

To know more about an expression follow

https://brainly.com/question/28350832

#SPJ1

Answer:

D. h(x) = log5(x) – x3 – 11

Step-by-step explanation:

could anyone help this is so confusing

Answers

Step-by-step explanation:

I and somebody else answered this already. how often did you post this ?

A table of values of a linear function is shown below. Find the output when the input is n . Type your answer in the space provided.
Input 1 2 3 4 n
output -1 3 7 11

PLEASE ANYONE I NEED HELP ASAP THANK YOU!!

Answers

Answer:

input: n

output: 15

Step-by-step explanation:

What is a linear function?

A linear function is an equation that increases by a constant, additive amount.A linear function looks like a straight line when graphed.

To find the output that corresponds to n, we can:

make a table of values to find the constant, additive amount of this linear functionuse said constant, additive amount to find the output that corresponds to n

Remember:

"input" = x-values"output" = y-values

Let X and Y be independent and identically distributed exponential random variables with rate λ.
Let U = X/Y and let V = XY . Find the joint desnity for (U, V ). Also find the marginal densities fU (u)
and fV (v).

Answers

The joint density for (U, V) is given by:

f(u,v) = fX/Y,XY(u,v) = fX(v/u) * fY(v/u) * |(v/u)|

                = λ^2 * v * e^(-λv/u) * |(v/u)|

The marginal density for U is given by:

fU(u) = ∫f(u,v)dv

        = ∫λ^2 * v * e^(-λv/u) * |(v/u)|dv

        = λ^2 * u * ∫ve^(-λv/u)dv

        = λ^2 * u * (-(u/λ)^2 * e^(-λv/u))|v=0 to v=∞

        = λ^2 * u * (-(u/λ)^2)

        = λ^3 * u^2

The marginal density for V is given by:

fV(v) = ∫f(u,v)du

       = ∫λ^2 * v * e^(-λv/u) * |(v/u)|du

       = λ * v * ∫e^(-λv/u) * |(v/u)|du

       = λ * v * (∫e^(-λv/u)du)|v=0 to v=∞

       = λ * v * (-(u/λ) * e^(-λv/u))|u=0 to u=∞

       = λ * v * (-1)

       = λ * v

Therefore, the joint density for (U, V) is

f(u,v) = λ^2 * v * e^(-λv/u) * |(v/u)|du.

Learn more about Marginal Density here:

https://brainly.com/question/15109814

#SPJ4

Write the ratio 0.1 to 0.2 as a simplified fraction

Answers

1/10: 1/5
the simplified fraction of 0.1 is 1/10
the simplified fraction of 0.2 is 1/5

m/JHI =(2x+7)° and m/GHI = (8x - 2)° and m/JHG= 65°. Find m/JHI and m/GHI

Answers

The value of  m/JHI and m/GHI is  angle 19 and 46.

What is  angle ?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

[tex]\begin{aligned}2 x+7+8 x-2 & =65 \\10 x+5 & =65 \\10 x & =60 \\x & =6\end{aligned}[/tex]

m/JHI =(2x+7) = (2* 6+7)=12+7=19.

m/GHI = (8x - 2)° = (8*6-2)=48-2=46

To learn more about angle  visit:https://brainly.com/question/28451077

#SPJ1

Write the tangent equation to solve for angle f

Answers

Answer:

Tan(f) = 24/7

Step-by-step explanation:

Tan is opposite over adjacent.

The opposite of angle F is 24 and the adjacent is 7.

solve the equation 1 half 4s + 2 = 10. on a numberline thanks.

Answers

To solve this equation, we need to isolate the variable s on one side of the equation. To do this, we can subtract 1 half from both sides of the equation, which gives us: 1 half 4s + 2 - 1 half = 10 - 1 half

Next, we can combine the like terms on the left side of the equation by adding 1 half and 2 together, which gives us: 1 half 4s + 2 + 1 half = 10 - 1 half
1 half 4s = 10 - 1 half - 2

Now we can isolate the variable s by dividing both sides of the equation by 1 half, which gives us: 1 half 4s = 10 - 1 half - 2
4s = 10 - 1 half - 2
4s = 9 half - 2
4s = 19 half - 4
s = 19 half - 4 / 4
s = 19 half - 1

To plot this solution on a number line, we can start by drawing a line and marking the numbers from 0 to 10 at equal intervals. Then, we can find the point that corresponds to 19 half - 1 and mark it on the number line. This point will be the solution to the equation.

6. How much will you pay for 14.8 gallons of diesel fuel at $1.39 per gallon?
Round to the nearest cent

Answers

Answer:

$20.5

Step-by-step explanation:

A triangle has one angle that measures 25 degrees, one angle that measures 104 degrees, and one angle that measures
51 degrees.
What kind of triangle is it?
OA. equilateral triangle
OB. right triangle
OC. acute triangle
OD. obtuse triangle

Answers

Answer:

D) Obtuse triangle

Step-by-step explanation:

Obtuse triangles have an angle greater than 90 degrees, and this triangle has an angle of 105.

The product of x and 10 is greater then or equal to 23

Answers

Answer:

x ≥ 2.3

Step-by-step explanation:

Product means multiplication

10x ≥ 23  Divide both sides by 10

x ≥ 2.3

The answer will be : X is equal to 23

A school bought 105 boxes of chocolate cookies and 22 boxes of vanilla cookies
for a fundraiser. Each box contained 12 cookies.
The school then repacked the cookies into smaller packs of 8 to sell.
How many small packs were there? How many cookies were left over?

Answers

Answer:190 small packs and 4 cookies left over

Step-by-step explanation:

Add the boxes of cookies together 105+22=127

Multiply each box by 12

127 x 12=1524

Because we need to put them into smaller packs of 8 cookies

we need to divide by 8

1524÷8=190 small boxes

This is a total of 190 x 8=1520 cookies there are 4 cookies left over

Differentiate the function with respect to x. Answer is B. I need the step. Thank you

Answers

Answer:

y(x) = integral(6 c^2 - 20 x^3)/(5 x^2 + 3) dx = -2 x^2 + 1/5 log(5 i x + sqrt(15)) (-i sqrt(15) c^2 + 6) + 1/5 log(-5 i x + sqrt(15)) (i sqrt(15) c^2 + 6) + k_1, where k_1 is an arbitrary constant.

Step-by-step explanation:

Rewrite the equation to -((6 c^2 - 20 x^3) dx)/(3 + 5 x^2) + dy = 0 and solve

Solve (dy(x))/(dx) = (6 c^2 - 20 x^3)/(5 x^2 + 3):

Integrate both sides with respect to x:

Answer: y(x) = integral(6 c^2 - 20 x^3)/(5 x^2 + 3) dx = -2 x^2 + 1/5 log(5 i x + sqrt(15)) (-i sqrt(15) c^2 + 6) + 1/5 log(-5 i x + sqrt(15)) (i sqrt(15) c^2 + 6) + k_1, where k_1 is an arbitrary constant.

4. Suppose y varies directly with x. If y = 6 when x = -2, find x when y = 15.

Answers

Answer:

x is -7.5 or -14/2 or -7½

Step-by-step explanation:

- Supposing y varies directly with x

[tex] { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} [/tex]

[k is a constant of proportionality (k ≠ 0)]

- When y is 6, x is -2

[tex] \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}[/tex]

- Therefore, the equation is;

[tex]{ \boxed{ \tt{y = - 2x}}}[/tex]

- What is x when y is 15

[tex]{ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}[/tex]

The value of x is -5

The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:

                                        k = y/x

                                        k = 6/-2

                                        k = -3

Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation

                                15 = -3x

Then solve x,

                       x = [tex]\frac{-15}{3}[/tex]

                        x = -5

Therefore, when y = 15, x = -5.

Learn how to solve equation:

brainly.com/question/26260688

Heather plans to make monthly payments of $800 for next 25 years and into it an annuity offering and annual interest rate of 4.8% how much money will she have in 25 years round to the nearest hundred

Answers

Answer:

formula

= Pmt [(1 + i/n)^nt - 1] / (i/n)

answer in picture hihi ^_^

Step-by-step explanation:

heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ  -{ elyna s }-

Here is an inequality: 7 x+6<3 x+2.
Select all values that are solutions.
(Select all that apply.)
x=1
x=0
x=-1
x=-2
x=-8

Answers

By solving a linear inequation, it can be calculated that

The values that are solutions are

x= -2 and x= -8

What is linear inequation?

Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤

A one degree inequation is known as linear inequation.

Here the inequation is  7x + 6 < 3x + 2

7x + 6 < 3x + 2

7x - 3x < 2 - 6

4x < - 4

x < [tex]-\frac{4}{4}[/tex]

x < -1

So the values that are solutions of the inequation are

x=-2 and x=-8

To learn more about linear inequation, refer to the link-

https://brainly.com/question/24372553

#SPJ1

The relative frequency distribution describes the number of observations that fall within each class. O proportion of observations that fall within each class. O number of observations that are within or below each of the classes. O proportion of observations that are within or below each of the classes. O none of these is correct.

Answers

True statement is number of observations that are within or below each of the classes.

Describe relative frequency.

A relative frequency describes how frequently a particular kind of event happens among all observations. It is a kind of frequency that employs fractions, percentages, and proportions. The ratio of the total number of events occurring in a scenario to the number of times an event occurs is known as relative frequency. Relative Frequency = Subgroup Frequency/Total Frequency is the formula for relative frequency. A relative frequency count is a way to count how many times an event happens compared to all the other events. It can be described as a percentage. It is frequently represented as a percentage as well.

Given

The relative frequency distribution describes the number of observations that fall within each class.

Statement which is true is,

Number of observations that are within or below each of the classes.

To learn more about relative frequency, visit:

https://brainly.com/question/29739263

#SPJ4

If 5/33 is expressed in decimal form, what digit is in the 92nd place to the right of the decimal point?

Answers

Answer: 5

Step-by-step explanation:

If you plug 5/33 into a calculator (or just solve with long division), you'll find that it makes 0.151515... (with 15 repeating forever.)

In every EVEN decimal place there's a 5, but in every ODD decimal place there's a 1. (The first decimal place is 1, the second is 5, etc.)

Since 92 is an even number, there is a 5 in the 92nd decimal place.

What is the missing number, what property did you use? 0=–––×3×4

Answers

Answer:

0, zero product property

Step-by-step explanation:

the top of an electric pole is s supported by a wire of 26 ft long on the ground level. how far is tightened spot from the foot of the pole if its height is 24 ft?​

Answers

Answer:

The tightened spot is 10 feet away from the foot of the pole.

Step-by-step explanation:

1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.

2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.

What is the Pythagoras' Theorem?

[tex](C)^2 = (A)^2 + (B)^2[/tex]An equation to find a 3rd side lengthC = hypotenuseA = one legB = another leg

3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.

Let B= the distance from the tightened spot to the foot of the pole.

[tex](C)^2 = (A)^2 + (B)^2[/tex]

[tex]26^2 = 24^2 + B^2[/tex]

[tex]676 = 576 + B^2[/tex]

[tex]100 = B^2[/tex]

[tex]\sqrt{100} = \sqrt{(B)^2}[/tex]

[tex]10 = B[/tex]

∴ The tightened spot is 10 feet away from the foot of the pole.

Diagram:

Jim has to choose between two gym membership plans. Plan A: $50 monthly membership fee and $10 per visit. Plan B: $25 one time membership fee and $15 per visit. How many visits must Jim make to make Plan A the cheaper option?

How many visits for them to cost the same?

Answers

The number of visits Jim must make to make Plan A the cheaper option is 6 and 5 visits will cost the same.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Suppose n number of visits will make plan A cheaper than B.

The total cost of A <  total cost of B

50 + 10n < 25 + 15n

15n - 10n > 50 - 25

5n > 25

n > 5

n = 6

At n = 5

Total cost of A = 50 + 10 x 5 = $100

Total cost of B = 25 + 15 x 5 = $100

Hence "Jim needs to visit 6 times, and 5 visits will cost the same, for Plan A to be more affordable".

For more about the equation,

https://brainly.com/question/10413253

#SPJ1

Fill in the blanks 30 = 27 __ ___x 9 = 54 81 / ___ = 92 = ___ / “” 58 x ___ = 32 “” 72 / ___ = 8 “” 7* __ = 49

Answers

Answer:

30 = 27 __ 3 x 9 = 54

81 / __9 = 9

2 = __4 / 8

58 x __6 = 32

72 / __8 = 9

7* __7 = 49

Step-by-step explanation:

Other Questions
Law that promote or favors the use organic farming in agriculture At SA Please help me please At his birthday party, Aiden collected 15% of the candy that fell out of the piata. If Aiden collected 6 pieces of candy, how many pieces of candy fell out of the piata? A scientist used 786 milliliters of a liquid for an experiment. How many liters of the liquid did the scientist use for this experiment?A. 786,000 L B. 7.86 L C. 0.786 L D. 0.0786 L Please Help! Brainliest!Convert the following to milligrams: 5.6 x 10-4 kilograms. Show your work on a separate sheet of paper and attachwith your assignment. what charge does nitrogen have 3710) The area of a rectangular park is 5 square miles. The length of the park is mile. What is thewidth of the park?21A 40 miles3C. 5 miles24B. 35 miles4D. 3 miles HELP DUE in 10 MINS!DC =?? Find the sum and express it in simplest form.(-54-46) 1-24 + 76 S)Enter the correct ansveOOH1 What is a best practice to follow when sending instant messages at work?A. Message your coworkers whenever it's convenient for you.B. Whenever possible, use abbreviations to save time.C.Use instant messages for personal conversations, such as making dinner plans.D.Keep your messages brief and work-related because the recipients may be busy. what is the range of the following relation? Find the surface area of the rectangular prism be sure to include the correct unit in your answer help me plzzzzzzzzzzzzzz A student invested 1300 in account that pays 4% annual compound interest. He will not make any additional deposits or withdraws. How much will he have in the account at the end of five years? Match the following vocabulary words. 1.ciliary musclesA transparent liquid which is located between the cornea and iris. 2.optic nerveMuscles attached to the lens to change its shape 3.coneA photoreceptor cell which functions best in bright light. It detects color. 4.vitreous humorThe transparent portion of the sclera at the front of the eye 5.retinaA special part of the choroid layer composed of colorful tissue 6.rodThe nerve connecting the eye to the brain 7.aqueous humorSpecialized cells located in the retina that receive light images 8.scleraA delicate light-sensitive membrane covering the inside of the eyeball 9.irisA photoreceptor cell which is sensitive to dim light, but detects no color10.corneaA fibrous material surrounding the eye to give it shape11.photoreceptorA transparent jellylike substance filling the eyeball 21 divided 3 +(8 - 2 divided 2) Help will give brainly The image shows the magnetic field lines around a magnet.Which statements are true for this magnet?- the right pole is the south pole - the left pole is the south pole - the left pole is the north pole - the right pole is the north pole Choose all that apply how have social categories, roles, and practices have changed since 1900? . There are 18 students in the Math Club. Of the 18 students 1/6 have red hair, 4/6 have brown hair and the rest have blonde hair. How many students have blonde hair