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Exponential growth 2016-01-26
From Paul:
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?
Answered by Penny Nom.
How fast did Jessica grow? 2014-04-10
From jasmine:
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
Answered by Robert Dawson.
The growth of a tree 2014-02-16
From Emily:
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.
Answered by Penny Nom.
Row echelon form 2013-03-15
From Shawn:
Please help me put matrix in row echelon form:

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

Answered by Penny Nom.
An arrow is shot straight up in the air 2012-12-06
From heather:
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

Answered by Penny Nom.
Row echelon form 2012-09-05
From Jennifer:
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

Answered by Penny Nom.
Percentage increase 2012-08-01
From Jay:
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.

Answered by Penny Nom.
Parametric equations 2 2012-02-25
From Kathy:
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!
Answered by Harley Weston.
Mathematics and a musical dilemma 2011-01-19
From rahul:
how is mathematics applied in entertainment?
Answered by Harley Weston.
An exponential equation 2010-10-19
From Sandi:

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.


Answered by Penny Nom.
Linear growth 2010-01-27
From S.:
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.

.
.
.

Answered by Melanie Tyrer.
Growth rates 2010-01-26
From Bhavya:
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

Answered by Robert Dawson.
Odds and evens in an n by n+1 table 2010-01-21
From Shankar:
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.
Answered by Robert Dawson.
A linear system 2009-03-13
From Rasanga:
Use the row echelon form of the augmented matrix to solve the following linear system.
X1+2X2+X4=6
X3+6X4=7
X5=1

Answered by Harley Weston.
Augmented matrix: independent, dependent, or inconsistent? 2009-02-23
From Anna:
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

Answered by Harley Weston.
Annual percent growth 2008-12-13
From Joe:
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.

Answered by Harley Weston.
Using the augmented matrix 2008-10-17
From Karlena:
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

Answered by Harley Weston.
Microwave ovens and probability 2008-09-04
From Vi:
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?

Answered by Harley Weston.
A linear system 2008-08-23
From dipesh:
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

Answered by Penny Nom.
A linear model 2008-05-09
From Shelby:
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?
Answered by Penny Nom.
A linear system 2008-03-10
From sandhiya:
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)
Answered by Penny Nom.
Row echelon form 2008-02-21
From cOCO:
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

Answered by Penny Nom.
Growth factor and growth rate 2008-02-13
From william:
what is the difference between growth factor and growth rate?
Answered by Stephen La Rocque and Harley Weston.
Shooting an arrow over a wall 2007-12-11
From Amy:
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.
Answered by Victoria West and Stephen La Rocque.
An augmented matrix 2007-11-29
From Beth:
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

Answered by Harley Weston.
Exponential Growth 2007-11-19
From lisa:
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
Answered by Penny Nom.
Making dot arrays 2007-09-05
From angela:
What do we call the numbers that cannot be arranged into 2-row arrays?
Answered by Penny Nom.
Students in rows 2007-05-17
From Ashi:
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.
Answered by Stephen La Rocque.
Linear growth 2007-05-11
From Rebecca:
What is the definition of linear growth?
Answered by Penny Nom.
2-row arrays 2006-09-06
From Liz & Samantha:
What do you call the numbers that cannot be arranged into 2-row arrays?
Answered by Penny Nom.
How much money can I borrow if I have $5 000 for a deposit? 2006-04-19
From Chris:
I have a sum of cash that I want to use as a deposit ($ 5 000) and a lender will lend me 65% of the purchase price. How do I calculate the maximum value I can borrow?
Answered by Stephen La Rocque.
Exponential decay 2006-03-29
From Casey:
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?
Answered by Penny Nom.
Make 2 rows of 4 circles with only 6 circles 2006-01-31
From Sarah:
Moving as many circles as you need, make 2 rows of 4 circles only having 6 circles?
Answered by Chris Fisher.
A matrix problem 2005-04-04
From Alan:
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.]


Answered by Judi McDonald.
Two matrix problems 2005-03-30
From Sue:
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.

Answered by Penny Nom.
A matrix construction problem 2005-03-14
From Marcelo:
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?

Answered by Harley Weston.
Payment plus interest 2004-09-14
From Penny:
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?

Answered by Penny Nom.
Row echelon form 2004-07-24
From Michael:
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

Answered by Penny Nom.
Aunt Lucy's letter 2004-06-27
From Olivia:
"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."

Answered by Penny Nom and Claude Tardif.
Augmented matrix 2002-12-31
From Michelle:
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
Answered by Penny Nom.
An augmented matrix 2002-04-20
From A student:
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


Answered by Penny Nom.
Conservation, consumption and population growth 2001-06-04
From Steve:
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:
.
.
.


Answered by Penny Nom.
Population growth 2001-05-01
From Gina:
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.
Answered by Penny Nom.
Borrowing from zero 2001-03-30
From Nikki:
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??


Answered by Leeanne Boehm and Claude Tardif.
Crown molding mitre cuts 2000-11-06
From Jim Tomfohrde:
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.
Answered by Harley Weston.
A colony of bacteria 2000-04-22
From Nicci Demmin:
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?
Answered by Penny Nom.
Borrowing 2000-04-17
From A college student:
How would you explain borrowing to an elementary school student?
Answered by Penny Nom.
A system of equations in five unknowns 2000-03-20
From Will:
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

.
.
.

Answered by Penny Nom.
Rowing on the Charles River. 1997-09-17
From Fawwaz Muraisi:
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?
Answered by Harley Weston.

 
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