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Arranging chairs in a row 2021-01-26
aiyana pose la question :
hi i need help with this a teacher wants to arrange 16 chairs in a equal rows in his class room
Harley Weston lui répond.
A penny is thrown from the top of a building 2018-03-16
Zoraida pose la question :
A penny is thrown from the top of a 26.7-meter building and hits the ground 3.39 seconds after it was thrown. The penny reached its maximum height above the ground 0.89 seconds after it was thrown.

a. Define a quadratic function, h, that expresses the height of the penny above the ground (measured in meters) as a function of the number of seconds elapsed since the penny was thrown, t. b. What is the maximum height of the penny above the ground?

Penny Nom lui répond.
A geometric series 2018-03-13
nathi pose la question :
Hi I am really struggling with this question please help !!!!
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year.
assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres. The maximum height part is not answered.

Penny Nom lui répond.
Exponential growth 2016-01-26
Paul pose la question :
The value of a stamp was 0.03 in 1851. The value in 2011 is $50,000. If the value increased exponentially, what is the annual growth rate?
Penny Nom lui répond.
How fast did Jessica grow? 2014-04-10
jasmine pose la question :
when she was 14 jessica was 5 feet, 4inches tall . at 18 she is now 6 feet, 2inches tall .how fast did jessica grow during this time
Robert Dawson lui répond.
The growth of a tree 2014-02-16
Emily pose la question :
If a tree is 10 ft tall after 2 years and 25 ft tall after 5 yrs , find the rate of change of growth Of the tree if y is the height in ft and x is the number of years.
Penny Nom lui répond.
Row echelon form 2013-03-15
Shawn pose la question :
Please help me put matrix in row echelon form:

1 9 8 0
5 8 1 35
1 -4 -1 17

Penny Nom lui répond.
An arrow is shot straight up in the air 2012-12-06
heather pose la question :
The skywalk is a glass bottomed platform that hangs over the edge of the Grand Canyon and is suspended 4000 feet above the floor of the canyon. If a tourist shot an arrow straight up in the air from the observation platform, the arrow's height could be modeled by H(t) =-16^2 + 240 + 4000 where H(t) is the height of the arrow above the canyon floor in feet t seconds after being shot, t>0.
(a) Find H(5) and explain its meaning

Penny Nom lui répond.
Row echelon form 2012-09-05
Jennifer pose la question :
Hello, my name is Jennifer. I am a 12th grader in Pre-Calculus and I was wondering if you may help me with Row Echelon Form.

x + 2y - 3z = -5
-2x - 4y - 6z = 10
3x + 7y - 2z = -13

Penny Nom lui répond.
Percentage increase 2012-08-01
Jay pose la question :
When calculating percentage growth, why is (y-x)/x the same as (y/x)-1 ??? (I seem to be stuck on the simple algebra here)...

e.g. 2011, toy was £5, 2012, toy is £10. What is the percentage increase? So, (10-5)/5 = 1 (i.e. 100% increase), AND, (10/5)-1 = 1 (i.e. also 100% increase).

Thanks in advance.

Penny Nom lui répond.
Parametric equations 2 2012-02-25
Kathy pose la question :
If the angle at time 0 is not 45 degrees how can you find the initial velocity? Ball thrown from height of 7 feet. Caught by receiver at height of 4 feet after traveling 90 feet down the field. Find initial velocity. You had a similar problem answered but the angle was 45 degrees so the cos and sin were equal and the equations were simpler to work with. Thank you!
Harley Weston lui répond.
Mathematics and a musical dilemma 2011-01-19
rahul pose la question :
how is mathematics applied in entertainment?
Harley Weston lui répond.
An exponential equation 2010-10-19
Sandi pose la question :

Question from sandi, a student:

I have several questions similar to this one and was wondering if you could walk me through this one. I'm totally lost on how to do it.
Paramecia reproduce by splitting in two. In a laboratory flask, a colony of paramecia had an initial population of 500. Each day, the population of the paramecia was counted. The results are as listed.
Time (in days)------Population
0-----------------------500
1-----------------------600
2-----------------------720
3-----------------------864
4----------------------1037
5---------------------1244
6---------------------1493
7----------------------1792
8---------------------2150
1.)Using graphing calculator make a scatter plot of the data in table.
I think I did this part right I set my window at Xmin=0 Xmax=10 Xscl=1 Ymin=0 Ymax=2500 Yscl=100 Xres=1
2.) Determine an exponential equation to represent the population as a function of time without using a graphing calculator.I have no clue how to do this.
3.)Suppose the flask and food supply is large enough to support the trend of the population growth. Estimate the population of the colony when the time is 10 days.


Penny Nom lui répond.
Linear growth 2010-01-27
S. pose la question :
I. Linear Growth:
Suppose that the town has a fixed increase in population growth number of population increase each year.

Choose the amount of population growth each year = 200 (Hint: Choose a whole number for your growth rate, rather than a percent.)

a) Fill in the following chart:

Year (t) Population (P)
t = 0
(2010) 1000

t = 1
(2011) 1000+200=1200

t = 2
(2012) 1000+400=1400

t = 3
(2013) 1000+600=1600

b) Find a linear equation in the form P = mt + b (y = mx + b), which gives the population, P, t years from 2010.

.
.
.

Melanie Tyrer lui répond.
Growth rates 2010-01-26
Bhavya pose la question :
Dear Sir/Ma'am,

I read in the text book that the growth rates of these 3 functions are as below- n2/3 < n/lg n < n0.99

I tried the substitution method to check the correctness of this. But it gets really tough as n increase.

Is there any simpler way to understand the correctness of these growth rates?

Thanks and Regards,
Bhavya

Robert Dawson lui répond.
Odds and evens in an n by n+1 table 2010-01-21
Shankar pose la question :
The boxes of an n * (n+1) table ( n rows and n+1 columns) are filled with integers. Prove that one can cross out several columns ( not all of them !) so that after this operation all the sums of the numbers in each row will be even.
Robert Dawson lui répond.
A linear system 2009-03-13
Rasanga pose la question :
Use the row echelon form of the augmented matrix to solve the following linear system.
X1+2X2+X4=6
X3+6X4=7
X5=1

Harley Weston lui répond.
Augmented matrix: independent, dependent, or inconsistent? 2009-02-23
Anna pose la question :
Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent, dependent, or inconsistent.

x + y + z = 11
x - y + 3z = 5
2x + 2y + 2z = 15

Harley Weston lui répond.
Annual percent growth 2008-12-13
Joe pose la question :
If Wall-Mart had sales of $58,200,000,000 in the year 2002 and $90,800,000,000 in the year 2006.

1. Find what percent that increase is of the 2002 sales? I came up with (9.08*10^10 - 5.82*10^10) / 5.82*10^10 * 100 = 56.01% increase. Is this correct?

2. What was the percent GROWTH in Wal-Mart's sales from 2002-2006? I am having trouble figuring out how to do the Growth problem. I would appreciate any help.

Harley Weston lui répond.
Using the augmented matrix 2008-10-17
Karlena pose la question :
I am supposed to write the augmented matrix of the system and use the matrix method to solve the system. I must show my work algebraically

x+y+2z=30
2x+3y+2z=53
x+2y+3z=47

Harley Weston lui répond.
Microwave ovens and probability 2008-09-04
Vi pose la question :
A microwave oven manufacturer claims that only 10% of the ovens it makes will need repair in the first year. Suppose three recent customers are independently chosen.
a. If the manufacturer is correct, what is the probability that at least two of the three ovens will need repair in the first year?
b. If at least two of the three customers' ovens need repair in the first year, what inference may be made about the manufacturer's claim?

Harley Weston lui répond.
A linear system 2008-08-23
dipesh pose la question :
consider the system of equations
x-6y+2z=5
2x-9y-z=14
4x+12y-3z=19
by reducing the augm matrix to row echelon form, find the solution to the equation.

leaving the first two equations the third is changed to -3x+6y+14z=-31 show the equations have infinitely many solutions and give a general formula for them

Penny Nom lui répond.
A linear model 2008-05-09
Shelby pose la question :
How would you write a linear model to represent the population of a city that has a population of 547,725 and a growth rate of -25,195 per year with t represents the number of years since 1994?
Penny Nom lui répond.
A linear system 2008-03-10
sandhiya pose la question :
one group of people purchased 10 hotdogs and 5 soft drinks at a cost of $12.50. a second group bought 7 hotdogs and 4 soft drinks a ta cost of $9.00 find the cost of a single hot and a single soft drink.(using the row echelon form to solve)
Penny Nom lui répond.
Row echelon form 2008-02-21
cOCO pose la question :
USE ELEMENTARY ROW OPERATIONS TO WRITE THE MATRIX BELOW IN ROW ECHELON FORM.
1 1 8 - 2
2 -1 1 11
2 1 14 -11

Penny Nom lui répond.
Growth factor and growth rate 2008-02-13
william pose la question :
what is the difference between growth factor and growth rate?
Stephen La Rocque and Harley Weston lui répond.
Shooting an arrow over a wall 2007-12-11
Amy pose la question :
The path of a large arrow fired from a non torsion catapult can be modeled by y=-0.0044x^2 + 1.68x, where x is the distance the arrow travelled (in yards) and y is the height of the arrow (in yards). Given the height of a castle wall, find the safest distance from the wall to launch an arrow over a 120 yard-high wall.
Victoria West and Stephen La Rocque lui répond.
An augmented matrix 2007-11-29
Beth pose la question :
I am having troubles fiinding this augnmented matrix. I know how to do it but everytime i do it it get a different answer and its not the right answer. Could you help me to make sure I do it right?

Here is the problem:
4x - 3y = 5
2x +9y = 6

Harley Weston lui répond.
Exponential Growth 2007-11-19
lisa pose la question :
Hi i am a 8th grader who is learning about algebra and we are having test on exponent and i don't really get it i asked my teacher and she told me i should pay more attention so i want to know what exponential Growth means
Penny Nom lui répond.
Making dot arrays 2007-09-05
angela pose la question :
What do we call the numbers that cannot be arranged into 2-row arrays?
Penny Nom lui répond.
Students in rows 2007-05-17
Ashi pose la question :
the student of three classescan be made to stand into rows having same number of students. there are 24,36 and 60 students in the classes. how many maximum number of student will stand in each row.
Stephen La Rocque lui répond.
Linear growth 2007-05-11
Rebecca pose la question :
What is the definition of linear growth?
Penny Nom lui répond.
2-row arrays 2006-09-06
Liz & Samantha pose la question :
What do you call the numbers that cannot be arranged into 2-row arrays?
Penny Nom lui répond.
How much money can I borrow if I have $5 000 for a deposit? 2006-04-19
Chris pose la question :
I have a sum of cash that I want to use as a deposit ($ 5 000) and a lender will lend me 65% of the purchase price. How do I calculate the maximum value I can borrow?
Stephen La Rocque lui répond.
Exponential decay 2006-03-29
Casey pose la question :
Fifty milligrams of a drug was injected into a patient at 6am. The drug is known to be eliminated according to the law of exponential decay. At 8.30am it was determined that 60% of the drug remained in the body. How many milligrams will remain in the body at midday?
Penny Nom lui répond.
Make 2 rows of 4 circles with only 6 circles 2006-01-31
Sarah pose la question :
Moving as many circles as you need, make 2 rows of 4 circles only having 6 circles?
Chris Fisher lui répond.
A matrix problem 2005-04-04
Alan pose la question :
Let A = 1-10
2-12
abc

where a, b, c are constant real numbers. For what values of a, b, c is A invertible? [Hint: Your answer should be an equation in a, b, c which satisfied if and only if A is invertible.]


Judi McDonald lui répond.
Two matrix problems 2005-03-30
Sue pose la question :
Question 1
Suppose all matrices in the equation below are square and invertible. Solve for x .

BA-1XB-1 + 2BA + In = 0 (the symbol "0" here denotes the matrix of all 0's in it)

Also, A-1 or B-1 is indicating inverse and "In" = for example, A-1 times A
I hope you understand the above. I have to show all the steps.

Question 2
Suppose we consider the set of all 2x2 matrices along with the operations of matrix addition and multiplication. Do they form a field? Why or why not?
I think the answer is no because under multiplication it is not commutative and not all square matrices are invertible. I not positive so I'd like some help.

Penny Nom lui répond.
A matrix construction problem 2005-03-14
Marcelo pose la question :
I want to know if is it possible to solve this problem:
I have an empty NxM matrix and I know totals (sum) by rows and totals by column.
Is there any algorithm to fill the matrix so that the summary of columns and rows gives the original values I have?

Harley Weston lui répond.
Payment plus interest 2004-09-14
Penny pose la question :
Brian wants to borrow some money from Margaret.
After three years he is to pay X back plus one interest sum of 25%. If he is pays back a total of $3800, what was the original sum borrowed?

Penny Nom lui répond.
Row echelon form 2004-07-24
Michael pose la question :
My name is Michael and I'm in the 11th grade. I have a Math question that I can't solve. The problem is system of equations that I need to do in augmented matrix form, find the row echelon form, and solve it by using back substitution.

2x + 3y + 7z =13
3x + 2y - 5z = -22
5x+ 7y - 3z = -28

Penny Nom lui répond.
Aunt Lucy's letter 2004-06-27
Olivia pose la question :
"Dear bob, now that i am getting on (70 today). i want to give you some of my money, i shall give you a sum each year, starting now. you can choose which of the following schemes you would like me to use.

a) £100 now, £90 next year,£80 the yaer after and so on.
b) £10 now, £20 next year, £ 30 the next year and so on.
c) £10 now, 1.5 times as much next year, 1.5 times as much the year after that and so on.
d)£1 now, £2 next year, £ 4 the year after, £8 the year after and so on.

of course these schemes will only operate while i am alive. i look forward to hearing which scheme you choose and why! Best wishes, Aunt Lucy."

Penny Nom and Claude Tardif lui répond.
Augmented matrix 2002-12-31
Michelle pose la question :
I am trying to augment a matrix so that i can find the values of the variables a, b, and c. For the life of me i can't find a solution to the matrix: 3 -5 2 ' 22 2 3 -1 ' -9 4 3 3 ' 1 I thank you for your help, Michelle
Penny Nom lui répond.
An augmented matrix 2002-04-20
A student pose la question :
Hi my math teacher asked us to solve an augmented matrix. I am in twelfth grade and need help. The book we are working on is college algebra. Here it is

a+2b+c=0
2a+5b+4c=-1
a-b-9c=-5


Penny Nom lui répond.
Conservation, consumption and population growth 2001-06-04
Steve pose la question :
I'm trying to quantify the relation between conservation/consumption and population growth. For instance let's consider California:

The 2000 census states that California's population grew from 29,760* in 4-1990 to 33,871 in 4-2000. I want to find r or rate of growth per year. Based on the exponential growth formula for population growth:
.
.
.


Penny Nom lui répond.
Population growth 2001-05-01
Gina pose la question :
Suppose the population of a country increases at a steady rate of 3% a year. If the population is 50 million at a certain time, what will it be 25 years later? Define the recurrence relation that solves this problem.
Penny Nom lui répond.
Borrowing from zero 2001-03-30
Nikki pose la question :
Here is the problem:

5,033.56
- 866.20

Now I know this equals 4,167.36 which I figured out on the calculator just to make sure. But when I did it by hand, I kept ending up with 5,167.36, which I knew was impossible. What am I doing wrong??


Leeanne Boehm and Claude Tardif lui répond.
Crown molding mitre cuts 2000-11-06
Jim Tomfohrde pose la question :
My question has to do with making mitre cuts when installing crown molding. Crown molding is the trim that is put up at the top of walls with one edge on the wall and the other edge on the ceiling. To make a mitre cut on your mitre saw for a 90-degree corner you can lay the molding flat on the saw base, set the bevel of the blade to 34 degrees and the mitre to 31.5 degrees (these may be slightly appoximate). Of course depending on which piece of molding you're cutting you will cut one end or the other, or use the left or right end. These angles allow the cuts to line up and form a seamless corner when they're put in place on the wall/ceiling at 90 degrees. My question is this - is there some mathematical formula from which the 34 degrees and 31.5 degrees are derived. I want to know this because in many cases the corner is not 90 degrees but can be more or less, and in these instances I would like to know if I can calculate the bevel and mitre to use based on the angle of the corner.
Harley Weston lui répond.
A colony of bacteria 2000-04-22
Nicci Demmin pose la question :
Suppose that the bacteria in a colony can grow unchecked, by the law of exponential change. The colony starts with one bacterium and doubles every half hour. How many bacteria will the colony contain at the end of 50 hours?
Penny Nom lui répond.
Borrowing 2000-04-17
A college student pose la question :
How would you explain borrowing to an elementary school student?
Penny Nom lui répond.
A system of equations in five unknowns 2000-03-20
Will pose la question :
I have been having some problem with the following question for some time. I would appreciate any help on solving the problem or a solution.

Q: Assume that a system of equations in the unknowns x1, x2, x3, x4 and x5 when converted to row echelon form gives

.
.
.

Penny Nom lui répond.
Rowing on the Charles River. 1997-09-17
Fawwaz Muraisi pose la question :
On the Charles River in Boston, the Harvard bridge and the Longfellow bridge are 1 mile apart. The MIT crew starts rowing upstream at the Longfellow bridge. As the crew passes under the Harvard bridge, the coxswain's hat falls into the river. Ten minutes later, the coxswain notices and turns the boat around instantaneously. He has t he crew row back to get it, rowing at the same constant rate. By the time the team reaches the hat, they are back at the Longfellow bridge.

How fast is the river flowing?
Harley Weston lui répond.

 
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