The answer is:
The fabric will cost $4.58
D.$4.58
Why?Since it's a conversion exercise, we need to pay special attention to the conversion procedure.
From the statement we know that:
[tex]1ft=0.305m[/tex]
So, if she needs 10 feet of fabric, we need to convert it to meters, and then, calculate its cost.
We have that:
[tex]10*1ft=10*0.305m\\\\10ft=3.05m[/tex]
Now, we have that each meter of fabric cost $1.50, so, 3.05m of fabric will cost:
[tex]\frac{1m}{1.50(dollars)}=\frac{3.05m}{cost}\\\\cost=\frac{3.05m*1.50(dollars)}{1m}=4.575(dollars)=4.58(dollars)[/tex]
Hence, we have that the cost of the fabric will be $4.58.
The correct option is: D.$4.58
Have a nice day!
Answer:
Sarah will need $4.58 for the fabric. therefor, your answer will be...
D: $4.58
Jay and Hanna are selling programs at a Mariners game. Hanna sells 5 times more programs
than Jay does. The difference in sales between them is 204. How many programs did each
sell?
Answer:
51 and 255
Step-by-step explanation:
Let the number of programs sold by Jay be x.
Then programs sold by Hanna is 5x.
Also, the difference between them is 204.
5x - x =204
4x = 204
x = 204/4
x = 51
Therefore, Jay sold 51 programs and Hanna sold 5 x 51 = 255 programs.
Please mark Brainliest if this helps!
Jay sold 51 programs and Hanna sold 255 programs.
To determine how many programs Jay and Hanna sold, let's start by defining some variables.
Let [tex]J[/tex] be the number of programs Jay sold.
Since Hanna sells 5 times more programs than Jay, we can express her sales as [tex]5J[/tex].
We know the difference in their sales is 204 programs.
Therefore, we can write the equation:
[tex]5J - J = 204[/tex]
Simplify the equation:
[tex]4J = 204[/tex]
Next, solve for [tex]J[/tex] by dividing both sides by 4:
[tex]J = \frac{204}{4}[/tex]
[tex]J = 51[/tex]
So, Jay sold 51 programs.
Since Hanna sells 5 times more programs than Jay, we can calculate Hanna's sales as:
[tex]5 \times 51 = 255[/tex]
Find the volume of the composite solid
Answer:
[tex]\large\boxed{V=(157.5+27.648\pi)\ yd^3}[/tex]
Step-by-step explanation:
We have the rectangular prism and the cone.
The formula of a volume of
1) a rectangular prism
[tex]V=lwh[/tex]
l - length
w - width
h - height
2) a cone
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have:
1)
l = 7yd, w = 5yd, h = 4.5yd
Substitute:
[tex]V_R=(7)(5)(4.5)=157.5\ yd^3[/tex]
2)
r = 4.8yd, l = 6yd
l - slant height
Use the Pythagorean theorem to calculate H :
[tex]H^2+r^2=l^2[/tex]
Substitute:
[tex]H^2+4.8^2=6^2[/tex]
[tex]H^2+23.04=36[/tex] subtract 23.04 from both sides
[tex]H^2=12.96\to H=\sqrt{12.96}\\\\H=3.6\ yd[/tex]
Calculate the volume:
[tex]V_C=\dfrac{1}{3}\pi(4.8)^2(3.6)=\dfrac{82.944}{3}\pi=27.648\pi\ yd^3[/tex]
The volume of the composite solid:
[tex]V=V_R+V_C[/tex]
Substitute:
[tex]V=(157.5+27.648\pi)\ yd^3[/tex]
What is the slope of the line with equation 6x+3y=12?
Answer:
The slope m = -2Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation in the standard form:
[tex]6x+3y=12[/tex]
Convert to the slope intercept form:
[tex]6x+3y=12[/tex] subtract 6x from both sides
[tex]3y=-6x+12[/tex] divide both sides by 3
[tex]y=-2x+4[/tex]
slope: m = -2
y-intercept: b = 4
In △ABC,a=14, b=17, and c=22. Find m∠A
Answer:
m∠A = 39.5°
Step-by-step explanation:
* Lets revise how to find the measure of an angle by using the cosine rule
- In any triangle ABC
# ∠A is opposite to side a
# ∠B is opposite to side b
# ∠C is opposite to side c
- The cosine rule is:
# a² = b² + c² - 2bc × cos(A)
# b² = a² + c² - 2ac × cos(B)
# c² = a² + b² - 2ab × cos(C)
- To find the angles use this rule
# m∠A = [tex]cos^{-1}\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]
# m∠B = [tex]cos^{-1}\frac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]
# m∠C = [tex]cos^{-1}\frac{a^{2}+b^{2}-c^{2}}{2ab}[/tex]
* Lets solve the problem
∵ a = 14 , b = 17 , c = 22
∵ m∠A = [tex]cos^{-1}\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]
∴ m∠A = [tex]cos^{-1}\frac{17^{2}+22^{2}-14^{2}}{2(17)(22)}[/tex]
∴ m∠A = [tex]cos^{-1}\frac{289+484-196}{748}[/tex]
∴ m∠A = [tex]cos^{-1}\frac{577}{748}[/tex]
∴ m∠A = 39.5°
Answer:
∠A = 39.52°
Step-by-step explanation:
In Δ ABC,
a = 14, b = 17 and c = 22 then we have to find the measure of ∠A.
Since a² = b² + c² - 2.b.c.cosA [ From cosine law]
(14)² = (17)²+ (22)² - 2(17)(22)cosA
196 = 289 + 484 - (748)cosA
196 = 773 - (748)cosA
748(cosA) = 773 - 196 = 577
cosA = [tex]\frac{577}{748}=0.7714[/tex]
A = [tex]cos^{-1}(0.7714)[/tex]
A = 39.52°
WILL GIVE BRAINLEIST PLEASE HURRY SUPER EASY. A fall candle gift set has 4 vanilla candles and 6 pumpkin spice candles. Use v to represent the cost of each vanilla candle and p to represent the cost of each pumpkin candle. Write and simplify and expression that represents the total cost of 4 sets.
Answer:
total cost= 16v+24p
Step-by-step explanation:
One set 4v+6p
Multiply the. expression by 4 because we are buying 4 sets
4v+6p
*4. *4
16v+24p
Answer:
(4v + 6p)4 = n
Step-by-step explanation:
If 1 set is
4v + 6p,
Then multiply it by 4 to get the total cost of 4 sets. Since there is so price for 1 set, we could use n for the missing total cost.
When two equal forces are inclined at an angle 2a their resultant is twice as great as
when they are inclined at an angle 2B. Show that cosa = 2 cosß.
Step-by-step answer:
Referring to the attached diagram, the resultant of two forces each with magnitude F and inclined to each other at 2a equals
Ra = 2Fcos(a) ..............................(1)
Similarly, the resultant of two forces each with magnitude F and inclined to each other at 2b equals
Rb = 2Fcos(b)..............................(2)
We are given that
Ra = 2Rb ....................................(3)
Substitute (1) & (2) in (3) gives
2Fcos(a) = 2(2Fcos(b))
Expand
2Fcos(a) = 4Fcos(b)
Simplify
cos(a) = 2 cos(b) QED
Note: Please note that you might have a faster response if you posted this question in the physics or the (new) Engineering section.
Have a nice day!
given the function f(x) = 2^x, find the value of f−1(32). (1 point) f−1(32) = 0 f−1(32) = 1 f−1(32) = 5 f−1(32) = 16
Answer:
5
Step-by-step explanation:
The inverse of [tex]f(x)=2^x[/tex] is [tex]g(x)=\log_2(x)[/tex].
[tex]g(32)=\log_2(32)[/tex]
[tex]\log_2(32)=5[/tex] since [tex]2^5=32[/tex].
[tex]g(32)=\log_2(32)=5[/tex]
Note: In general, the inverse of [tex]f(x)=a^x[/tex] is [tex]g(x)=\log_a(x)[/tex].
what is the slope of the line represented by the equation f(t) =2t-6
Answer:
The slope is 2.
Step-by-step explanation:
The given line has equation: [tex]f(t)=2t-6[/tex].
This is a linear equation in [tex]t[/tex].
The slope is the coefficient of the independent variable [tex]t[/tex].
The coefficient of [tex]t[/tex] in [tex]f(t)=2t-6[/tex] is 2.
Therefore the slope is 2.
Alternatively, [tex]f(t)=2t-6[/tex] is of the form [tex]f(t)=mt+c[/tex], where [tex]m=2[/tex] is the slope.
Answer:
Step-by-step explanation:
The slope is 2 and the y intercept is -6
How do I solve substitution with picture ??
Answer:
no solution
Step-by-step explanation:
If you divide the first equation by 2 you get:
2x+2y=4 (first equation after dividing both sides by 2)
2x+2y=-4 (second equation)
This is setup for elimination.
Subtract the equations:
2x+2y=4
2x+2y=-4
--------------Subtracting!
0+0=8
0=8
0=8 is a false equation which implies the system has no solution.
Answer:
a) No Solutions
Step-by-step explanation:
It might be helpful to first get the equations in terms of y = mx + b.
The first equation (4x + 4y = -8) can be rewritten like this:
4x + 4y = -8 (original equation)
4y = 4x - 8 (subtract 4x from both sides)
y = x - 4 (divide everything by 4 to get y on its own)
and now you have an equation in terms of y = mx = b, where m is 1 and b is -4.
The second equation can be written like this:
2x + 2y = -4 (original equation)
2y = 2x - 4 (subtract 2x from both sides)
y = x - 2 (divide everything by 2 to get y on its own)
and once again we have an equation with m being 1 and b being -2.
So hopefully you should see that the equations will never touch because they have the same slope. Because the equations never touch, they have no solutions. Have a look at the graph.
Let u = <-3, -5>, v = <-3, 1>. Find u + v. <-2, -8> <-8, -2> <0, -6> <-6, -4>
Answer:
<-6,-4>
Step-by-step explanation:
To find u+v, all you have to do is add the corresponding components of each.
That is for example on this problem, you would do
<-3,-5>+<-3,1>
=<-3+-3,-5+1>
=<-6,-4>.
What is the solution set of this system of equations?
y=x2-3x-4
x=y+8
A {(-1.0), (4.0)}
B. {(8.0). (0.8)}
c. {(0.0)}
D. {(2. -6)
E
There is no real solution.
Reset
Next
Answer:
No real solutions.
Step-by-step explanation:
[tex]y=x^2-3x-4[/tex]
[tex]x=y+8[/tex]
I'm going to subtract the second expression for y and plug it into the first equation.
So solving x=y+8 for y by subtracting 8 on both sides gives us y=x-8.
I'm going to insert this for the first y like so:
[tex]x-8=x^2-3x-4[/tex]
Now I'm going to move everything to one side.
I'm going to subtract x on both sides and add 8 on both sides.
[tex]0=x^2-3x-x-4+8[/tex]
Simplifying:
[tex]0=x^2-3x+4[/tex]
Now our job since the coefficient of x^2 is 1 is to find two numbers that multiply to be 4 and at the same time add up to be -3. I can't think of any such numbers.
Let's check the discriminant.
Compare [tex]x^2-3x+4[/tex] to [tex]ax^2+bx+c[/tex].
So [tex]a=1,b=-3,c=4[/tex].
The discriminant is [tex]b^2-4ac[/tex].
So plugging in our numbers we get [tex](-3)^2-4(1)(4)[/tex].
Time to simplify:
[tex](-3)^2-4(1)(4)[/tex]
[tex]9-16[/tex]
[tex]-7[/tex]
So since the discriminant is negative, then the solutions will not be real.
Which statements describe the domain and range
of g(x)? Select two options.
a. The function g(x) is defined for all real numbers x.
b. The maximum value of the range is 4.
c. The maximum value of the domain is 3.
The range of g(x) is {yl -1
d. The domain of g(x) is {x|-4
Answer:
A closed circle on the graph indicates that the point is included in domain and range. An open circle indicates that the point is not included in the domain and range.
Now based on this, we will evaluate the given options:
Option A. The function g(x) is defined for all real numbers x.
The lines on the graph contain a limited values. Hence its obvious that the domain and range is not the set of all Real numbers. Hence this option is Wrong.
Option B. The maximum value of the range is 4.
From the graph we can see that the maximum/highest value along y-axis is 4. Since there is a closed circle at (-4, 4), this value is included in the range. Hence this option is True.
Option C. The maximum value of the domain is 3
There is an open circle at the point when x is 3. Hence this point is not included in the Domain. Value of domain is numbers less than 3. Hence this option is Wrong.
Next two options are incomplete. Here are the complete options and listed correctly.
Option D. The range of g(x) is {yl -1 < y ≤ 4}
This is correct because there is an open circle at point (3, -1). Hence -1 would not be included in the range. The range will be set of all values from -1 to 4, including 4 as there is a closed circle at (-4, 4)
Option E. The domain of g(x) is {x| x ≤ -4 ≤ -1 or 0 ≤ x <3}
Since there are closed circles at points where x is -4, -1 and 0, these points would be included in the Domain. 3 wont be included in the Domain as there is an open circle.
Answer:
B and D are correct.
which of the following describes a simple event?
Answer:
I believe the answer rqould be B since only 1 thing happened
Answer: Option B
Step-by-step explanation:
Simple event is an event where all the possible outcomes have the same probability.
Are the type of events that we can write as:
P = number of a given outcome/total posible outcomes.
Here we have 3 combined options (A, C and D) that, while in parts can be described in that way, not as whole events.
The correct option is B, where the probability of getting a given number in a dice is the number of times that the number repeats (1) divided the total number of options (6), P = 1/6 for all the numbers, so this is a simple event.
The circumference of a circle is 16π inches. Show how you can use this information to calculate the same circle’s area.
Answer:
A = 64 pi inches ^2
Step-by-step explanation:
Circumference is equal to
C =2*pi*r where r is the radius
16 pi = 2 * pi *r
Divide each side by 2 pi
16pi/2pi = 2pir/2pi
8 = r
The radius is 8
To find the area, we use
A = pi r^2
=pi (8)^2
= 64 pi
Please answer this correctly
Answer:
1) 0.0008306
2) 0.00008306
3) 0.000008306
4) 0.0000008306
Step-by-step explanation:
Please mark me the brainliest... . I am sure the answers are correct.
Answer:
0.0008306
0.00008306
0.000008306
0.0000008306
Step-by-step explanation:
0.008306 ÷ 10 = 0.0008306
0.008306 ÷ 100 = 0.00008306
0.008306 ÷ 1000 = 0.000008306
0.008306 ÷ 10000 = 0.0000008306
Rosalie takes the bus everyday to school. The ride is 8 minutes long. If she goes to school for 176 days, how many minutes does she spend on the school bus?
Answer:
1408 min.
Step-by-step explanation:
8 × 176 = 1408.
Answer:
1408
Step-by-step explanation:
Find the lateral area of each prism. Round to the nearest tenth if necessary.
The dimension labeled 11 is the height of the prism.
Question 4 options:
334 units2
264 units2
299 units2
312 units2
Answer:
264 unit^2.
Step-by-step explanation:
The lateral area is the sum of the 2 sides of area 5*11 and the 2 sides of area 7^11.
That would be 2 * 5 * 11 + 2*7*11
= 264 unit^2.
For this case we have that by definition, the lateral area of a prism is given by:
[tex]LA = 2ac + 2bc[/tex]
Where:
a: It is the height
b: It is the width
c: It's the long
According to the figure we have:
[tex]a = 5 \ units\\b = 7 \ units\\c = 11 \ units[/tex]
Substituting:
[tex]LA = 2 * 5 * 11 + 2 * 7 * 11\\LA = 110 + 154\\LA = 264[/tex]
Finally, the lateral area of the prism is [tex]264 \ units ^ 2[/tex]
ANswer:
Option B
The quadratic equation x2 + 2x -- 8 = 0 can be rewritten as (x + 4)(x - 2) = 0.
What is the multiplicity of the root x = --4?
Answer:
multiplicity of 1
Step-by-step explanation:
Given the roots of an equation are
x = - 4 ← multiplicity 1
(x + 4)² = 0
x + 4 = 0 or x + 4 = 0 , hence
x = - 4 or x = - 4 , that is
x = - 4 ← with multiplicity 2
(x + 4)³ = 0
has roots x = - 4 with multiplicity 3
The multiplicity is determined by the exponent the factor is raised to
HelP MeEe
A virus that initially infected four people is spreading at a rate of 15% each week. The following function represents the weekly spread of the virus: f(x) = 4(1.15)x. Rewrite the function to show how quickly the virus spreads each day and calculate this rate as a percentage.
f(x) = 4(1.15)7x; spreads at a rate of approximately 1.5% daily
f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily
f(x) = 4(1.157)x; spreads at a rate of approximately 2.66% daily
f(x) = 4(1.02)x; spreads at a rate of approximately 0.2% daily
Answer:
f(x) = 4(1.02)^(7x); spreads at a rate of approximately 2% daily
Step-by-step explanation:
The weekly number of people infected is:
f(x) = 4(1.15)^x
So the daily number of people infected is:
f(x) = 4(1+r)^(7x)
To find the value of the daily rate r, we set this equal to the first equation.
4(1.15)^x = 4(1+r)^(7x)
(1.15)^x = (1+r)^(7x)
(1.15)^x = ((1+r)^7)^x
1.15 = (1+r)^7
1.02 = 1+r
r = 0.02
So the equation is f(x) = 4(1.02)^(7x), and the daily rate is approximately 2%.
Using exponential functions, it is found the daily function for the spread is:
[tex]f(x) = 4\left(\frac{1.15}{7}\rigth)^{x}[/tex], and it spreads at a rate of approximately 2% daily.
An exponential function has the following format:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.In this problem, the function for the weekly spread is:
[tex]f(x) = 4(1.15)^x[/tex]
A week has 7 days, thus, to find the daily spread, we divide the rate of change by 7, that is:
[tex]f(x) = 4\left(\frac{1.15}{7}\right)^x[/tex]
[tex]\frac{15}{7} \approx 2.1[/tex], thus, it spreads at a rate of approximately 2% daily.
A similar problem is given at https://brainly.com/question/23416643
what’s the equation of the line with the given properties passes through (-4,-2) and (-4,5)
Answer:
x = -4
Step-by-step explanation:
Notice that the two points given, share the same x-value even when the y-value changes. This is because the equation is going to be a vertical line at -4 on the x-axis. Being a vertical line, you cannot take its slope using the slope formula of: m = (y2 - y1) / (x2 - x1) because the denominator will result in a 0 and you cannot divide by 0 in mathematics.
How is the graph of y = 5x2 − 4 different from the graph of y = 5x2?
Answer:first equation is 4 units shifted down from the second
Step-by-step explanation:
Answer:
The graph of y = 5x²-4 differs from the graph of y = 5x² by difference of 4 units
Step-by-step explanation:
In y = 5x²-4, when y is 0 x is not 0 and when x is 0 , y is not 0
but
In y = 5x² , when y is 0 , x is 0 and vise versa.
In y = 5x² the value of y will always increase as the value of x increase.
What was Weston’s error?
In Step 2, the second fraction should have been out of a multiple of 40.
In Step 2, the multiplication relationship shown should have been division.
In Step 4, the decimal should not have been moved.
In Step 4, the decimal should have been moved two places instead of one.
Check the picture below.
Answer:
[tex]\frac{2.5}{100}=0.025\:or\:2.5\%[/tex]
Step-by-step explanation:
In step 4.
Weston made a mistake when he divided 2.5 by 100. He wrote it as he had multiplied 2.5 by 10 instead of moving the point back two decimals places to the left.
In the Step 4:
[tex]\frac{2.5}{100}= 0.025\:or\:2.5\:\%[/tex]
This can be verified by dividing 1 over 40, that'll give us 0.025
Use an inequality symbol (<,>,=,=/) to compare 5+(-4)____14+(-13)
Answer:
The answer is equal to. Each equation equals 1.
The first two terms in a geometric series are 20, 22. To two decimal places, the sum of the first k terms of the series is 271.59. Find k.
Answer:
k=9
Step-by-step explanation:
First find r=22/20=1.1
The sum of the first k terms formula is a1•(1-r^k)/(1-r)
a1=20 and the sum is 271.59
Now plug in these values in the formula and find k.
271.59=20(1-1.1^k)/(1-1.1)
When you simplify this equation, you will get k=ln(2.358)/ln(1.1)
k=9
The height of a particular triangle equals its base length. A new triangle is formed by dividing the hype by 2 and its area is 36 in^2 less than the area of the triangle. what are the height and base lengths of original triangle?
Answer:
Height and base are both 12 in
Step-by-step explanation:
Formula area triangle: area = (height * base) /2
Since for the first triangle height and base are the same we will call is x.
The area for the first triangle is
area = (x^2) /2 = 0.5x^2
The new triangle area is
first triangle - 36 = ((x/2) * x)/2
0,5x^2 - 36 = (0,5x * x)/2
0,5x^2 - 36 = (0,5x^2)/2
0,5x^2 - 36 = 0,25x^2
0,25x^2 = 36
x^2 = 144
X = square root (144) = 12 in
Let A = {1, 2, 3, 4, 5} and B = {2, 4}. What is A ∩ B?
[tex]A\cap B=\{x:x\in A \wedge x\in B\}[/tex]
[tex]A\cap B=\{2,4\}[/tex]
For this case we have the following sets:
A = {1,2,3,4,5}
B = {2,4}
We must find the intersection of both sets, the symbol ∩ denotes intersection. That is, the numbers in common of both.
We have to:
A∩B = {2,4}
Answer:
The insterseccion of both sets is:
A∩B = {2,4}
#2 and please provide explaination !
Answer:
Total overripe fruit = 48
Step-by-step explanation:
Step 1: Assume the value of oranges
Let oranges be x
Oranges = x
Apples = 32 + x
Overripe oranges = 3/5 of oranges
= 3x/5
Overripe apples = 1/3 of apples
= 1/3 (32 + x)
Step 2: Find x (oranges)
Number of overripe apples and number or overripe oranges are equal.
3x/5 = 1/3 (32 + x)
3 (3x) = 5(32 + x)
9x = 160 + 5x
4x = 160
x = 40
Step 3: Find the total number of overripe fruit.
Total overripe fruit = Overripe apples + Overripe oranges
Total overripe fruit = 1/3 (32 + x) + 3x/5
Total overripe fruit = 1/3 (32 + 40) + 3(40)/5
Total overripe fruit = 24 + 24
Total overripe fruit = 48
!!
Ari exercises 1 5/8 hours per day. If he exercises five days a week, how many total hours does he exercise in a week?
Answer:
8 1/8 hours
Step-by-step explanation:
1 5/8 * 5 = 5 25/8
5 28/5 = 5 + 3 + 1/8
= 8 1/8 hours
I think the answer is 8 1/8
Find the value of the expression. m(m + p) for m = 3 and p = 4
HELP PLEASE!
[tex]21[/tex]
Explanation:Substitute in the values. [tex]3(3+4)[/tex]Distribute. [tex]3*3\ +\ 3*4[/tex]Simplify with multiplication. [tex]9+12[/tex]Simplify with addition. [tex]21[/tex]Which of the following formulas would find the lateral area of a right cylinder
where h is the height and ris the radius?
O
A. LA = 2trh
O
B. LA = 27012
O
O
c. LA = ac rh
D. LA = 2017
SUBME
Answer:
2πrh unit^2.
Step-by-step explanation:
The lateral area is the circumference of the base * the height = 2πrh.
The lateral area of a right cylinder with height equal to h and r as the radius is 2πrh. Therefore, option C is the correct answer.
What is lateral surface area?All of the sides of the object are the lateral surface of an object, except its base and top (when they exist). The lateral surface area is the lateral surface zone. This is to be distinguished from the overall surface area, which, along with the base and top areas, is the lateral surface area.
The surface area that a cylinder's curved surface alone covers is known as the curved surface area (CSA) or lateral surface area. The curved surface area of a cylinder is computed using the formula 2πrh, where height of the cylinder is h and the radius of the base is r.
Therefore, option C is the correct answer.
Learn more about the lateral surface area here:
https://brainly.com/question/14001755.
#SPJ7
"Your question is incomplete, probably the complete question/missing part is:"
Which of the following formulas would find the lateral area of a right cylinder with height equal to h and r as the radius?
A. LA = 2πr²
B. LA = 2πr
C. LA = 2πrh
D. LA = 2πr² + 2πrh