Tutors Answer Your Questions about Quadratic Equations (FREE)
Question 994711: 1022four=244n.find n quadratically
Answer by Alan3354(47455) (Show Source):
Question 994712: If 321n=232seven.find n quadratically
Answer by Alan3354(47455) (Show Source):
Question 994539: Say whether the graph of the equation y=x^2+4x1 opens up, down, left, or right.Give the coordinates of the vertex and the equation of the axis of symmetry.Write your quadratic function in vertex form. Find the maximum or minimum value. Explain how you can determine this value.
Found 2 solutions by MathTherapy, josgarithmetic: Answer by MathTherapy(4047) (Show Source): Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! Coefficient on leading term is . Parabola is concave down. (Opens downward).
Complete the Square to help change to standard form.
Vertex is (2,5).
Question 994300: The perimeter of a backyard is 560 feet. If the width is 125 feet less than the length, find the length of the yard.
Answer by addingup(248) (Show Source):
You can put this solution on YOUR website! The perimeter is: 2L+2W= 560 (1st formula)
And the problem says that:
W= L125 Now apply the first formula using this value for W:
2L+2(L125)= 560 Multiply on left
2L+2L250= 560 Add L on left and add 250 to both sides:
4L= 810 Divide both sides by 4
L= 202.5 OK, we have our Length. And the problem says that the Width is 202.5125= 77.5. Let's prove that we have the correct answer:
2L+2W= 560
2(202.5)+2(77.5)= 560
405+155= 560
560= 560 We have the right answer.
Question 994206: Solve the equation:
Ally inherits $65,000 and decides to invest part of it in an education account for her daughter and the rest in a 10year CD. If the amount she puts in the education account is $12,000 more than twice the amount she puts in the CD, how much money does Ally invest in each account?
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! Ally inherits $65,000 and decides to invest part of it in an education account for her daughter and the rest in a 10year CD. If the amount she puts in the education account is $12,000 more than twice the amount she puts in the CD, how much money does Ally invest in each account?

In Ed. account: E
In CD account:: C

Equations:
E + C = 65000
E  C = 12000

2E = 77000
E = 38500
C = 38500+12000 = 50500

Cheers,
Stan H.

Question 994153: The length of a rectangle is 10 cm more than its width. The area of the rectangle is 56 cm2.
Calculate the width of the rectangle.
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! The length of a rectangle is 10 cm more than its width. The area of the rectangle is 56 cm2.
Calculate the width of the rectangle.
=============
Find a pair of factors of 56 that differ by 10.
Question 994128: (a)If the quadratic equation of 6x^2－7x＝2k has two distinct real roots,
(i) find the range of possible values of k,
(ii) find the roots of the equation when k is the smallest integer in (a)(i)
(b) Using the result of (a)(ii), solve －3(x＋p)^2＋7/2(x＋p)－5/6＝0, where p is a constant. (give the answers in terms of p.)
Answer by solver91311(20879) (Show Source):
Question 994123: What is the answer if you derive a Q.F from table or graph given point (0,5),(4,1),(3,13)
Answer by solver91311(20879) (Show Source):
Question 994062: The edges of three cubes are consecutive odd integers. If the cubes are stacked on a deck, as shown, the total exposed surface area is 381. Find the lengths of the sides of the cubes.
Answer by Alan3354(47455) (Show Source):
Question 994033: The graph of Quadratic equation of opens up if(?) and down if(?). Explain why or how that statement is true.
(Hint: consider what happens as x gets more and more positive or more and more negative.)
Answer by Boreal(1464) (Show Source):
You can put this solution on YOUR website! f(x)=x^2. This opens up downward. As x^2 gets larger, x^2 gets larger negative, so the graph goes down with increasing positive or negative x.
f(x)=x^2, here, when x is positive or negative x^2 is always positive, like the first case. But there is no negative sign in front of the x^2, so the graph opens upward.
Question 994034: In general, why might it be important to solve an equation for different variables?
For example, the equation for degrees Fahrenheit is given by, where C is degrees Celsius. In this example, why—or when—would we want to solve for C? Feel free to discuss other examples.
Answer by Boreal(1464) (Show Source):
You can put this solution on YOUR website! If you are in any other country in the world and say what the temperature is in Fahrenheit, they will not be able to understand what you mean. They use Celsius, and you have to convert it to Celsius.
If you are asked to give a medication in a dose of 18 mg/kg, and the person weighs 154 pounds, how many kg are in 154 pounds?
If you are in Europe, they measure fuel economy by number of liters of fuel it takes to go 100 km. In order to do this, you need to convert gallons to liters and miles to kilometers. These are a few of the examples, and this is just metricEnglish. There are many other equations in multiple variables that one may have to solve to determine, for example, what percentage of a change is due to normal variability and what is due to a change in the system itself.
Question 993886: Hi
I am given this equation, h= height (meters), t= time (seconds)
h=2t(50t)
How long is the rocket in air?
I just applied the null factor law for that equation, and got:
2t = 0
t=0
and
50t=0
t=50
t=50
Does that mean the rocket was in the air for 50 seconds?
or did i do something wrong or did not take in to account
thank you
Found 2 solutions by Theo, Alan3354: Answer by Theo(5548) (Show Source):
You can put this solution on YOUR website! it appears the rocket was in the air for 50 seconds.
your equation was h = 2t * (50  t)
this is a quadratic equation.
when you set it equal to 0, you find the xintercepts.
those occur at t = 0 and t = 50.
since the coefficient of the leading term is negative, the quadratic equation points up and opens down.
to see this easier, simplify the equation by multiplying the factors out.
2t * (50  t) = 100t  t^2
reorder the terms to get h = t^2 + 100t
the leading coefficient is negative which makes the parabola (graph of a quadratic equation is a parabola) point up (maximum point is on top) and open down.
since all value of t have the graph positive between 0 and 50, that's the time that the graph of the equation is above the xaxis which represents the time the rocket is in the air.
here's what the graph of your equation looks like:
i used x instead of t because that's what the graphing software requires.
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! I am given this equation, h= height (meters), t= time (seconds)
h=2t(50t)
How long is the rocket in air?
I just applied the null factor law for that equation, and got:
2t = 0
t=0
and
50t=0
t=50
t=50
Does that mean the rocket was in the air for 50 seconds?
or did i do something wrong or did not take in to account
===========================
No, you got it right.
It's launched at t = 0 and impacts at t = 50.
=========================
PS This is not a rocket. Rockets have thrust engines and accelerate upward. This is just a projectile.
Question 993880: Hi
i am wondering if this quadratic expression can be factored in anyway:
3x^226
I tried
Not sure if this works :s
Found 2 solutions by Theo, Alan3354: Answer by Theo(5548) (Show Source):
You can put this solution on YOUR website! yes, it will work.
the two equations are equivalent.
is equal to:
which is equal to:
if you graph both equations, they will be identical.
here's the graph of both equations on the same graph.
since the equations are identical, it looks like one graph.
this is the graphing statement enclosed in 3 opening brackets at the beginning and 3 closing brackets at the end.
i used [ instead of { and i used ] instead of } so you can see the formula easily without having to go to the source.
[[[graph(600,600,10,10,30,30,3*(x^226/3),3*(xsqrt(26/3))*(x+sqrt(26/3)))]]]
Answer by Alan3354(47455) (Show Source):
Question 993876: A 1.8 meters tall person walks across the path of the javelin. He is 58 meters away from where the javelin was launched. Will he be hit by the javelin? Justify your answer.
The quadratic equation i'm given is:
Do I replace 'x' with 58 and solve for y? so i know the height of the javelin at x=58 or 58 meters away to see if the javelin hit the person?
Like,
y ≈ 3.29m
Hence the javelin does not hit the person that is 1.8 meters tall.
Is this how i 'justify'?
Answer by Alan3354(47455) (Show Source):
Question 993728: 2x^2+3b4=0
Answer by ikleyn(988) (Show Source):
Question 993631: Where do lines y = x  1 and y = 5x + 11 intersect?
Found 2 solutions by stanbon, Cromlix: Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! Where do lines y = x  1 and y = 5x + 11 intersect?

Substitute and solve for "x"::
x1 = 5x+11
6x = 12
x = 2

Solve for "y"::
y = x  1
y = 1

Cheers,
Stan H.

Answer by Cromlix(3061) (Show Source):
You can put this solution on YOUR website! Hi there,
Solve as simultaneous equations by elimination.
y = x  1......(1)
y = 5x + 11...(2)
Rearrange
y  x = 1.....(1)
y + 5x = 11....(2)
Multiply (1) by 5
5y  5x = 5...(1)
y + 5x = 11...(20
Add (1) + (2)
6y.....= 6
y......= 1
Substitute y = 1 into Equatn(1)
y = x  1
1 = x  1
x = 2
The lines intersect at (2,1)
Hope this helps :)
Question 993370: A javelin is thrown from a height of 2m above the ground.
It lands 60 meters away. The path of the javelin can be represented by the equation
a) What does x and y represent in this situation?
b)If it is known that the point (10,15) lies on the path given by the equation , use algebra and all the information given in a) and b) to show
that:
, and c = 2
c)Hence find the height of the javelin after travelling 20m horizontally
For a) Does y represent the height of the javelin, and x represent the horizontal distance traveled?
For b) I have no idea :c
For c) Really stuck!
It would be very helpful if you could draw up a graph too!! Thanks for help!!
Answer by MathLover1(11324) (Show Source):
You can put this solution on YOUR website! a) What does and represent in this situation?
represent height (dependent variable,depends on how changes )
represent the path (dependent variable,it is a variable that stands alone and isn't changed by the other variables you are trying to measure )
b)
If it is known that the point (,) lies on the path given by the equation , use algebra and all the information given in a) and b) to show that:
, and
if the point (,)=(,), we have
..............eq.1
if , and , we have equation like this:
...now,show that when
c)
Hence find the height of the javelin after traveling horizontally
Question 993056: (k  2)x^2 + 50x + 2k + 3 = 0
How do I find the value of k if the roots are reciprocal
The ans is 5 but i don't know the method
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! (k  2)x^2 + 50x + 2k + 3 = 0
How do I find the value of k if the roots are reciprocal
The ans is 5 but i don't know the method

Roots are:: [50+sqrt[50^2  4(k2)*3]/2

If they are reciprocal::
[50 + sqrt(50^212(k2)]/2 = 1/[50sqrt(50^212(k2)]/2

Solve for "k"
=====
Cheers,
Stan H.

Question 992750: 2[(x)/(x+2)]^2  3[(x)/(x+2)]  9 = 0
Can you help me?
Found 2 solutions by AnlytcPhil, Edwin McCravy: Answer by AnlytcPhil(1539) (Show Source): Answer by Edwin McCravy(13211) (Show Source):
Question 992751: 3x + 14 = 5
Can you help me solve this?
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! 3x + 14sqrt( x ) = 5

3(sqrt(x))^2 + 14sqrt(x)  5 = 0

Let w = sqrt(x)

Rewrite your quadratic as::
3w^2 + 14w  5 = 0

Factor::
3w^2 + 15ww 5 = 0
3w(w+5)(w+5) = 0
(w+5)(3w1) = 0

w = 5 or w = 1/3

Now, solve for "x"
sqrt(x) = 5 or sqrt(x) = 1/3

x = 25 or is extraneous since sqrt(25) = 5, by definition; or x = 1/9

Cheers,
Stan H.

Question 992752: 5x^(1/3) + 3x^(2/3) = 8
Can you help me? I hope I wrote it right; it's 5x to the one third plus 3x to the two thirds. Thank you!
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! 5x^(1/3) + 3x^(2/3) = 8

Rewrite as::
3(x^(1/3))^2 + 5(x^(1/3))  8 = 0

Note:: This is a quadratic equation. The variable is x^(1/3)

Let x^(1/3) = w

Rewrite the equation as::
3w^2 + 5w  8 = 0
Factor::
3w^2 + 8w3w  8 = 0
w(3w+8)  (3w+8) = 0
(3w+8)(w1) = 0

w = 8/3 or w = 1

Now, solve for "x"
x^(1/3) = (8/3) or x^(1/3) = 1

x = (8/3)^3 or x = 1^3

x = 512/27 or x = 1

Cheers,
Stan H.

Question 992640: Write the expression (x9)^24 in factored form and identify a,r, and s. assume r is less than or equal to s.
factor form= a(xr)(xs)
Answer by josgarithmetic(13975) (Show Source):
Question 992637: Put the function 2x^2+12x+3 in vertex form and state the values of a,h, and k.
vertex form= a(xh)^2+k
Answer by josgarithmetic(13975) (Show Source):
Question 992635: Put the equation y=4x^2+7x+6 in vertex form and state the values of a, h, and k. Enter the exact answers.
Vertex form= a(xh)^2+k
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! Put the equation y=4x^2+7x+6 in vertex form and state the values of a, h, and k. Enter the exact answers.
Vertex form= a(xh)^2+k

y6 = 4(x^2+(7/4)x)

4(x^2+(7/4)x+(7/8)^2) = y  6 +4(7/8)^2

4(x+(7/8))^2 = y  6 + 49/16

4(x+(7/8))^2 = y(47/16)

y = 4(x+(7/8))^2 + (47/16)

a = 4
h = 7/8
k = 47/16

Cheers,
Stan H.

Question 992634: Find the minimum value of x^22x8, if it has one.
Answer by MathLover1(11324) (Show Source):
You can put this solution on YOUR website!
Does the graph of: have a maximumum and minimum?
Well, it may have a maximum or it may have a minimum, but it doesn't have both!
The graph of a quadratic equation (), such as this, is called a "parabola" and a parabola has a maximum or a minimum depending upon whether it opens upwards (has a minimum) or opens downwards (has a maximum).
You can tell which way the parabola opens by inspecting the coefficient of the term, which is +1 in your problem.
If this coefficient is positive, then the parabola opens upwards and the graph has a minimum.
If the coefficient is negative,then the parabola opens downwards and the graph has a maximum.
The maximum/minimum point (also known as the "vertex") can be found as follows:
The xcoordinate of this point is:
The a is the coefficient of the term and the b is the coefficient of the term.
In your equation, and , so
This is the xcoordinate of the vertex.
To find the ycoordinate, substitute into the given quadratic equation and solve for :
Substitute .
The vertex (or the in this case) is at (, )
Let's see what the graph looks like:
Question 992497: 1/^x2 + 5/x + 6 = 0
Can you help me solve this equation?
Answer by rothauserc(2272) (Show Source):
You can put this solution on YOUR website! ***********************************
is 1/^x2 really 1/(x^2)?, if yes then
***********************************
1/^x2 + 5/x + 6 = 0
multiply both sides of = by x^2
1 + 5x + 6x^2 = 0
rearrange terms
6x^2 + 5x + 1 = 0
factor polynomial
(3x + 1) * (2x + 1) = 0
the two solutions are
x = 1/3 and x = 1/2
**********************************
check the solutions
1) x = 1/3
(1 / (1/9)) + (5/(1/3)) + 6 = 0
9  15 + 6 = 0
0 = 0
**********************************
2) x = 1/2
(1 / (1/4)) + (5/(1/2)) + 6 = 0
4 10 + 6 = 0
0 = 0
our answers check
Question 992402: Let f(x) = 3x4 − 14x2 + 4x − 5.
Find the local maximum and minimum values of f and the values of x at which they occur.
Find the intervals on which f is increasing and on which f is decreasing.
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! Let f(x) = 3x4 − 14x2 + 4x − 5.
Find the local maximum and minimum values of f and the values of x at which they occur.
Find the intervals on which f is increasing and on which f is decreasing.
f'(x) = 12x^3  28x + 4

Solve 12x^3  28x +4 = 0
3x^3  7x + 1 = 0

x = 1.59 or 0.144 or 1.45

f"(x) = 36x^2  28
f"(1.59) > 0 so min at x = 1.59
f"(0.144) < 0 so max at x = 0.144
f"(1.45) > 0 so min at x = 1.45

Cheers,
Stan H.

Question 992364: Write an equation that has the given solutions. Thank you!!
i, −i
Answer by ikleyn(988) (Show Source):
Question 992365: Write an equation that has the given solutions. (There are many correct answers.)
8, , and
Answer by ikleyn(988) (Show Source):
Question 992362: Write an equation that has the given solutions.
6/5 and 5/9
Answer by MathLover1(11324) (Show Source):
Question 992241: A person standing close to the edge on the top of a 270foot building throws a baseball vertically upward. The quadratic equation
\qquad\qquad h = 16 t^2 + 160 t + 270
models the ball's height \, h \, above the ground in feet, t seconds after it was thrown.
How high is the ball after 5 seconds?
??feet.
How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second.
?? seconds.
(I plugged in 5, then set it equal to 0, none of it worked, I'm probably doing it wrong)
Answer by rothauserc(2272) (Show Source):
You can put this solution on YOUR website! h = 16 t^2 + 160 t + 270
to find the height of the ball after 5 seconds substitute 5 for t
h = 16(5^2) + (160*5) + 270
h = 670 feet high after 5 seconds
*****************************************************************
to find when the ball hits the ground, set h = 0 and solve the quadratic for t
16 t^2 + 160 t + 270 = 0
multiply both sides of = by 1
16t^2  160t  270 = 0
use quadratic formula to solve for t
t = (160 + sqrt(160^2  (4*16*(270)))) / (2*16) = 11.471089553 approx 11.5
t = (160  sqrt(160^2  (4*16*(270)))) / (2*16) = −1.471089553 approx 1.5
****************************************************************************
we want the positive value for t
t = 11.5 seconds for the ball to hit the ground
Question 992267: Construct the quadratic equation in the form az2+bz+c =0 having the following solutions. Find the coefficients a, band c for each equation.
(a)
(a) z=7, z=−2.
___ z2+ ___ z+ ___ =0
(b) z=−3+4i, z=−3−4i.
___ z2+ ___ z+ ___ =0
Answer by solver91311(20879) (Show Source):
Question 992292: y^2  x^2 = 32 and y  x = 2 ...what's the value of x and y....thank you
Answer by MathTherapy(4047) (Show Source):
You can put this solution on YOUR website!
y^2  x^2 = 32 and y  x = 2 ...what's the value of x and y....thank you
 eq (i)
y = 2 + x  Solving 2nd equation for y  eq (ii)
1) Substitute 2 + x for y in eq (i)
2) Combine all liketerms and solve equation for x
3) Substitute value for x in eq (ii) to obtain value for y
Question 992229: A man built a walk of uniform width around a rectangular pool. If the area of the walk is 245 square feet and the dimensions of the pool are 6 feet by 22 feet, how wide is the walk?
Answer by josgarithmetic(13975) (Show Source):
Question 992195: A rectangle is 6 times as long as it is wide. The area is 96 square feet. What is the perimeter of the rectangle?
Found 2 solutions by stanbon, Alan3354: Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! A rectangle is 6 times as long as it is wide. The area is 96 square feet. What is the perimeter of the rectangle?

width:: x
length:: 6x

Equation:
x*6x = 96

6x^2 = 96

x^2 = 16

x = 4 (width)
6x = 24 (length)

Perimeter = 2(length+width)
P = 2(24+4)
P = 2(28)
P = 56

Cheers,
Stan H.

Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! A rectangle is 6 times as long as it is wide. The area is 96 square feet. What is the perimeter of the rectangle?

L = 6W
L*W = 96

6W*W = 96
W*W = 16
W = 4 ft

Perimeter = 2W + 2L
Question 992196: Solve the following equation. Separate your answers with commas. Repeated roots should only be entered once.
1/x7 + 1/x2 = 9/14
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! Solve the following equation. Separate your answers with commas. Repeated roots should only be entered once.
1/x7 + 1/x2 = 9/14

Multiply thru by 14(x2)(x7) to get:
14(x2) + 14(x7) = (x2)(x7)

28x 126 = x^2  9x + 14

x^2  37x + 140 = 0

x = 32.72... or x = 4.28...
=============
Cheers,
Stan H.

Question 992194: A person standing close to the edge on the top of a 270foot building throws a baseball vertically upward. The quadratic equation
h = 16 t^2 + 160 t + 270
models the ball's height \, h \, above the ground in feet, t seconds after it was thrown.
How high is the ball after 5 seconds?
How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second.
Answer by Alan3354(47455) (Show Source):
Question 991925: Please help me solve the question
Find the whole number such that twice its square added to itself makes 10.
Answer by macston(4006) (Show Source):
Question 991899: 1+2+3=40
2+3+4=85
3+4+5=148
4+5+6=229
5+6+7=???
Answer by ikleyn(988) (Show Source):
You can put this solution on YOUR website! .
Ask somewhere in the site on puzzles,
not in the algebra.com
By the way, this system has 5 equations and 7 unknowns.
So you can choose 1 and 2 by the arbitrary way,
then to determine 3,
then to determine 4,
and so on step by step . . . till get 7.
The solution is not unique. It depends on two arbitrary constants.

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210
