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Recent problems solved by 'stanbon'
stanbon answered: 57135 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>Next
Human-and-algebraic-language/170080: 1. A) Write the sentence (-x)2 ¹ -x2 in words.
In your own words explain why (-x)2 and -x2 are not equivalent. Provide an example to support your explanation.
B) Evaluate (a) 3x0 and (b) (3x)0 when x is not 0. Are the results different? If so, explain in your own words why they are different. If not, then state so.
1 solutions
Answer 125527 by stanbon(57203)   on 2008-11-29 08:16:59 (Show Source):
You can put this solution on YOUR website!1. A) Write the sentence (-x)2 ¹ -x2 in words.
In your own words explain why (-x)2 and -x2 are not equivalent. Provide an example to support your explanation.
---
(-x)^2 = (-x)(-x) = x^2
---
-x^2 = -(x)(x)
========================
B) Evaluate
(a) 3x0 = 0
(b) (3x)^0 when x is not 0.
(3x)^0 = 1
==========================
Are the results different? If so, explain in your own words why they are different. If not, then state so.
Comment: I'll leave the comments to you.
Cheers,
Stan H.
|
Human-and-algebraic-language/170081: 2. A student writes down the following as part of her response:
a ) 32 ´ 33 = 729. and b) 3 -2 = -9.
Are her answers correct? If not, explain why you think her answers are incorrect.
Include in your explanation what she did wrong, if any.
What would you advise her to do instead?
1 solutions
Answer 125526 by stanbon(57203) on 2008-11-29 08:12:54 (Show Source):
You can put this solution on YOUR website!2. A student writes down the following as part of her response:
a ) 32 ´ 33 = 729.
Correct Answer:::::32*33 = 1056
------------------
b) 3 -2 = -9.
Correct Answer::::3-2 = 1
Are her answers correct? If not, explain why you think her answers are incorrect.
Comment:::I'll leave that to you.
Cheers,
Stan H.
Include in your explanation what she did wrong, if any.
What would you advise her to do instead?
|
Miscellaneous_Word_Problems/170059: THE ELECTRIC CURRENT I, IN AMPERES, IN A CIRCUIT VARIES DIRECTLY AS THE VOLTAGE V. WHEN 12 VOLTS ARE APPLIED, THE CURRENT IS 4 AMPERES. WHAT IS THE CURRENT WHEN 18 VOLTS ARE APLLIED?
1 solutions
Answer 125521 by stanbon(57203) on 2008-11-29 07:58:28 (Show Source):
You can put this solution on YOUR website!THE ELECTRIC CURRENT I, IN AMPERES, IN A CIRCUIT VARIES DIRECTLY AS THE VOLTAGE V. WHEN 12 VOLTS ARE APPLIED, THE CURRENT IS 4 AMPERES. WHAT IS THE CURRENT WHEN 18 VOLTS ARE APPLIED?
-----------
I = kV
Find "k":
4 = k*12
k = 4/12 = 1/3
-----------
Equation: I = (1/3)V
If 18 volts are applied you get:
I = (1/3)*18
I = 6 amps.
==============
Cheers,
Stan H.
|
logarithm/170034: The question is rewrite the following expression using one or more properties of logarithims and evaluate without a calculator.
log4- log 400,000=
I have searched and cannot find any examples of how to solve this problem. Thank you for your help, Jackie
1 solutions
Answer 125512 by stanbon(57203) on 2008-11-28 23:15:13 (Show Source):
|
Exponential-and-logarithmic-functions/170051: Please help me with:
The speed of the current in a river is 2mph. Jay travels 20 miles upstream and then 20 miles downstream in a total time of 5 1/3 hours. Find the speed of the boat.
Let s be the speed of the boat.
1 solutions
Answer 125510 by stanbon(57203) on 2008-11-28 23:08:52 (Show Source):
You can put this solution on YOUR website!The speed of the current in a river is 2mph. Jay travels 20 miles upstream and then 20 miles downstream in a total time of 5 1/3 hours. Find the speed of the boat.
Let s be the speed of the boat.
---------------------------------------
Upstream DATA:
distance = 20 miles ; rate = s-2 mph ; time = d/r = 20/(s-2) hrs.
---------------------------
Downstream DATA:
distance = 20 miles ; rate = s+2 mph ; time = d/r = 20(s+2) hrs.
---------------------------
EQUATION:
time + time = 16/3 hrs
20/(s-2) + 20/(s+2) = 16/3
60(s+2) + 60(s-2) = 16(s^2 - 4)
120s = 16s^2 - 64
16s^2 - 120s - 64 = 0
2s^2 - 15s - 8 = 0
s = [15 +- sqrt(225 -4*2*-8)]/4
s = [15 +- sqrt(289)]/4
s = [15 +- 17]/4
Positive solution:
s = 8 mph (speed of the boat)
================================
Cheers,
Stan H.
|
Travel_Word_Problems/170053: If you had driven one mile at 30 mph, how fast must you drive the second mile so your average speed for the trip is 60mph.
Hint: The answer is not 90 mph.
1 solutions
Answer 125509 by stanbon(57203) on 2008-11-28 22:58:28 (Show Source):
You can put this solution on YOUR website!If you had driven one mile at 30 mph, how fast must you drive the second mile so your average speed for the trip is 60mph
---------------------
1st mile DATA:
distance = 1 mile ; rate = 30 mph ; time = d/r = 1/30 hr
-------------------------
2 mile DATA
distance = 2 miles ; rate = 60 mph; time = d/r = 2/60 = 1/30 hr
---------------------------
2nd mile Information
distance = 1 mile ; time = (1/30)hr - (1/30)hr = 0 hrs
================================
You cannot average 60 mph by driving the 2nd mile at any speed.
The time required to drive the 2 miles at 60 mph is the same
as the time required to drive the 1st mile at 30 mph. After
the 1st mile you have used up all the time you need.
================================
Cheers,
Stan H.
|
Exponential-and-logarithmic-functions/170000: Please help.
Construct and simplify the difference quotient for f(x)= x^2-x.
Thanks
1 solutions
Answer 125468 by stanbon(57203) on 2008-11-28 17:01:48 (Show Source):
You can put this solution on YOUR website!Construct and simplify the difference quotient for f(x)= x^2-x.
-------------
Difference quotient: [f(x+h)-f(x)]/h
-------------
f(x+h) = (x+h)^2 - (x+h) = x^2+2hx+h^2-x-h
f(x) = x^2 - x
----------------------
Subtracting you get:
f(x+h)-f(x) = 2hx+h^2-h
----------------------
Dividing by h you get: 2x-1+h
----------------------
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/170004: A parabolic satellite television antenna has a diameter of 6 feet and is 1.6 feet deep. How far is the focus from the vertex?
I have tried every formula that I can think of to get this one to work out correctly for me and I'm coming up short.
Please help.
Thank you in advance
1 solutions
Answer 125467 by stanbon(57203) on 2008-11-28 16:53:54 (Show Source):
You can put this solution on YOUR website!A parabolic satellite television antenna has a diameter of 6 feet and is 1.6 feet deep. How far is the focus from the vertex?
----------------------------
Draw the parabola on an xy coordinate grill.
Put the vertex at (0,1.6)
Then the parabola will meet the x-axis at (-3,0) and (3,0)
----------------
So the equation of the parabola will be y = -x^2 + 1.6
or x^2 = -y - 1.6
or x^2 = -(y+1.6)
-----------------
This has the form x^2 = 4p(y-k), so 4p = -1 and p = -1/4
---
The distance from the vertex to the focus is p so the
focus is at y = 1.6-(1/4) = 1.6-0.25 = 1.375
-------------------
Ans: the focus is (1/4) ft. from the vertex.
======================
Cheers,
Stan H.
|
Inequalities/169961: solve the inequality
3x/7x-2>x/x+1
My answer is (-infinity,-1)u (2/7, infinity)
1 solutions
Answer 125458 by stanbon(57203) on 2008-11-28 14:49:15 (Show Source):
You can put this solution on YOUR website!solve the inequality
[3x/(7x-2)] > [x/(x+1)]
x cannot be 2/7 and cannot be -1
------------
Draw a number line and plot x = -1 and x= 2/7
Test points in the resulting intervals to see where the solution set lies.
--------
Let x = -2 to get (3*-2)/(-16) > (-2/(-1) or -1/16 > 2; false
Let x = 0 to get (3*0)/(7*0-2) > 0/(0+1) or 0 >0; false
Let x = 1 to get (3*1)/(7*1-2) > 1/(1+1) or 3/5 > 1/2; true
----------------
Solution:
x > 2/7
=====================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/169971: A truck carrying 3600 cubic feet of cargo consisting of washing machines and refrigerators was hijacked. The washing machine are worth $300 each and are shipped in 36 cubic-foot cartons. The refrigerators are worth $900 each and are shipped in 45 cubic-foot cartons. If the total value of the cargo is $51,000, then how many of each were there on the truck?
1 solutions
Answer 125455 by stanbon(57203) on 2008-11-28 14:25:31 (Show Source):
You can put this solution on YOUR website!A truck carrying 3600 cubic feet of cargo consisting of washing machines and refrigerators was hijacked. The washing machine are worth $300 each and are shipped in 36 cubic-foot cartons. The refrigerators are worth $900 each and are shipped in 45 cubic-foot cartons. If the total value of the cargo is $51,000, then how many of each were there on the truck?
-----------------
value equation: 300w + 900r = 51000
volume equation: 36w + 45r = 3600
=======================================
Rearrange:
w + 3r = 170
4w + 5r = 400
-------------------
Multiply thru 1st by 4 to get:
4w + 12r = 4*170
4w + 5r = 400
--------------------
Subtract 2nd from 1st to solve from r:
7r = 4*170-400
r = 40 (# of refrigerators)
w = 170-3r = 170-3*40 = 50 (# of washers)
===================================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/169985: 5.1.6. what are all of the trigonomic values given that cot=-3 and sin= square root 10/10
1 solutions
Answer 125453 by stanbon(57203) on 2008-11-28 14:15:25 (Show Source):
You can put this solution on YOUR website!what are all of the trigonomic values given that cot=-3 and sin= square root 10/10
---------------------
Keep in mind that x^2 + y^2 = r^2
------------
cot=-3 = -3/1
Since cot = x/y, x = -3 and y = 1
Therefore r = sqrt(-3)^2 + 1^2) = sqrt(10)
---------------------
Then:
sin = y/r = 1/sqrt(10) = sqrt(10)/10
cos = x/r = -3/sqrt(10)
tan = y/x = -1/3
csc = r/y = sqrt(10)
sec = r/x = -sqrt(10)/3
cot = -3
=========================
Cheers,
Stan H.
|
Graphs/169948: x/6 + 3y/16 = 1
need the solve for y graphing
example:y = 4/3x +2 in excel spreadsheet
1 solutions
Answer 125411 by stanbon(57203) on 2008-11-28 09:10:44 (Show Source):
You can put this solution on YOUR website!x/6 + 3y/16 = 1
need the solve for y graphing
Multiply thru by 48 to get:
8x + 9y = 48
9y = -8x + 48
y = (-8x+48)/9
-------------------
=====================
Cheers,
Stan H.
|
Quadratic_Equations/169949: This is a word problem on a worksheet that I've been given.
Katy likes to catch butterflies. The equation b = -2(x-4)^2 + 25 models this habit, where b is the number of butterflies caught for the hour and x is the number of hours after she started catching. After how many hours will Katy catch the maximum amount?
I am stumped on this question. I don't even know where to start...
Please help, thanks.
I also have some questions on a form of quadratic function. I've only done quadratic functions that are in the form y= ax^2 + bx + c. So I'm not quite sure on these 3 multiple choice questions.
Here is the information:
One form of a quadratic function is f(x) = a(x-b)^2 + c.
Here are the questions:
1. If you wanted to shift the graph of the function up, what would you do?
A. increase a
B. decrease b
C. increase c
D. decrease a
2. If you wanted to shift the graph of the function left what would you do?
A. increase b
B. decrease b
C. increase c
D. decrease a
3. If you wanted to make the parabola wider, what would you do?
A. increase a
B. decrease b
C. increase c
D. decrease a
***Note:
For question 1 I chose letter c.
For question 2 I chose letter a.
For question 3 I chose letter d.
1 solutions
Answer 125410 by stanbon(57203) on 2008-11-28 09:06:49 (Show Source):
You can put this solution on YOUR website!This is a word problem on a worksheet that I've been given.
Katy likes to catch butterflies. The equation b = -2(x-4)^2 + 25 models this habit, where b is the number of butterflies caught for the hour and x is the number of hours after she started catching. After how many hours will Katy catch the maximum amount?
I am stumped on this question. I don't even know where to start...
Please help, thanks.
---
Your equation shows the vertex form of the quadratic. When x = 4, b=25
and that is the vertex of the prabola which opens downward from that point.
The maximum b-value occurs when x = 4
===============================================
I also have some questions on a form of quadratic function. I've only done quadratic functions that are in the form y= ax^2 + bx + c. So I'm not quite sure on these 3 multiple choice questions.
Here is the information:
One form of a quadratic function is f(x) = a(x-b)^2 + c.
Here are the questions:
1. If you wanted to shift the graph of the function up, what would you do?
A. increase a
B. decrease b
Ans: C. increase c
D. decrease a
--------------------------------
2. If you wanted to shift the graph of the function left what would you do?
A. increase b
Ans: B. decrease b
C. increase c
D. decrease a
--------------------------------
3. If you wanted to make the parabola wider, what would you do?
Ans: A. increase a
B. decrease b
C. increase c
D. decrease a
===========================
Cheers,
Stan H.
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test/167891: suppose you roll two dice. find the number of elements in the event space of rolling a sum of 4
1 solutions
Answer 125408 by stanbon(57203) on 2008-11-28 08:48:49 (Show Source):
You can put this solution on YOUR website!suppose you roll two dice. find the number of elements in the event space of rolling a sum of 4
------------------------------------
(1,3)/(2,2)/(3,1)
Ans: 3
=============
Cheers,
Stan H.
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Permutations/169917: a) how many arrangements can be formed from all the letters in the word parallel?
b) In how many of these arrangements will the 3 l's be together?
1 solutions
Answer 125396 by stanbon(57203) on 2008-11-27 22:52:21 (Show Source):
You can put this solution on YOUR website!a) how many arrangements can be formed from all the letters in the word parallel?
8!/[2!*3!] = 3360
-----------------------------------
b) In how many of these arrangements will the 3 l's be together?
Consider the 3 l's to be one letter.
Ans: 6!/2! = 360
=======================================
Cheers,
Stan H.
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Permutations/169918: a)In how many ways can 4 people be seated around a circular table with 4 identical chairs?
b) in how many ways can 5 people be seated around a circular table if 1 of the chairs is an armchair?
1 solutions
Answer 125394 by stanbon(57203) on 2008-11-27 22:48:05 (Show Source):
You can put this solution on YOUR website!a)In how many ways can 4 people be seated around a circular table with 4 identical chairs?
Ans: 4!/4 = 3! = 6
----------------------------------
b) in how many ways can 5 people be seated around a circular table if 1 of the chairs is an armchair?
If that armchair implies it is a unique point in the arrangement count,
the answer is 5! = 120
===========================
Cheers,
Stan H.
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Money_Word_Problems/169580: A cashier has P 50, P 100, and P500 bills. the number of P50 bills is 5 more than 7 times the number of P100 and the number of P500 bills is four-fifths the number of P100 bills. If the total amounts that she has P18 100, how many of each type of bills are there?
please give me your representation...
thank you
1 solutions
Answer 125393 by stanbon(57203) on 2008-11-27 22:41:27 (Show Source):
You can put this solution on YOUR website! cashier has P 50, P 100, and P500 bills. the number of P50 bills is 5 more than 7 times the number of P100 and the number of P500 bills is four-fifths the number of P100 bills. If the total amounts that she has P18 100, how many of each type of bills are there?
--------------
Let # of P50 be "x":
Let # of P100 be "y":
Let # of P500 be "z":
--------------------------
EQUATIONS:
x = 7y + 5
z = (4/5)y
50x + 100y + 500z = 18100
-------------------------------
Rearrange:
50x + 100y + 500z = 18100
x -7y + 0 = 5
0 + 4y - 5z = 0
----------------------------
Use any method you know to get:
x = 152
y = 21
z = 16
==================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/169933: The amount of an investment of P dollars for t years at simple rate r is given by A = p + prt
A) Rewrite this formula by factoring ourt the greatest common factor on the right hand side.
B) Find A if $8300 is invested for 3 years at a simple rate of 15%.
1 solutions
Answer 125385 by stanbon(57203) on 2008-11-27 22:16:57 (Show Source):
You can put this solution on YOUR website!The amount of an investment of P dollars for t years at simple rate r is given by A = p + prt
A) Rewrite this formula by factoring out the greatest common factor on the right hand side.
A = p(1+rt)
----------------------------
B) Find A if $8300 is invested for 3 years at a simple rate of 15%.
A = 8300(1+0.15*3)
A = 8300(1.45)
A = 12035
----------------------------
Cheers,
Stan H.
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Geometry_proofs/169937: 1.Describe a condition which assures the diagonal of a parallelogram are congruent?
2.In what most general type of quadrilaterals are opposite angles congruent?
3.Draw a square whose vertices (corner) all lie on the same circle. How is a diameter of the square relate to a diameter( line segment through the center) of the circle.
4. Draw a kite with two right angles that is not a parallelogram. What can you say about the sum of the two interior angle which are unequal?
5. In what most general type of quadrilateral do diagonals bisect each other?
1 solutions
Answer 125381 by stanbon(57203) on 2008-11-27 22:11:09 (Show Source):
You can put this solution on YOUR website!1.Describe a condition which assures the diagonal of a parallelogram are congruent?
Ans: The parallelogram must be a rectangle.
------------------------------------------------
2.In what most general type of quadrilaterals are opposite angles congruent?
Ans: The quadrilateral must be a parallelogram.
------------------------------------------------
3.Draw a square whose vertices (corner) all lie on the same circle. How is a diameter of the square relate to a diameter( line segment through the center) of the circle.
Ans: The diagonal of the square is the diameter of the circle.
------------------------------------------------
4. Draw a kite with two right angles that is not a parallelogram. What can you say about the sum of the two interior angle which are unequal?
Ans: There sum is 180 degrees
------------------------------------------------
5. In what most general type of quadrilateral do diagonals bisect each other?
Ans: Parallelogram
====================================
Cheers,
Stan H.
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test/167927: This question is from textbook GEOMETRY
Could someone please explain to me how you can find the orthocenter, circumcenter, cetroid, and median of triangles, because it is on an upcomimg test and I am SOOO confused on how to draw them.!!!
1 solutions
Answer 125360 by stanbon(57203) on 2008-11-27 19:32:13 (Show Source):
You can put this solution on YOUR website!These require illustrations and lengthy narrative.
May I suggest you use Google and search for these
terms. You will find many sites that discuss these
topics thoroughly.
Cheers,
Stan H
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