New!
Get regular updates about newly solved problems
via algebra.com's RSS system.
Recent problems solved by 'funmath'
funmath answered: 2925 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 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939, >>Next
Functions/63961: determine the critical numbers and the critical points for each of the following functions
A. f(x)= x^3 + 13x^2 + 7x - 165
B. g(x)= X^3 +6x^2 - 13x - 42
C. h(x)= x^3-10x^2 + 7x + 18
THESE PROBLEMS ARE TOUGH....I REALLY NEED HELP WITH THEM...I TRIED DOING THEM BUT THE ANSWERS AREN'T RIGHT BECAUSE I KNOW THERE ARE SUPPOSED TO BE 2 ANSWERS 4 EACH BUT IM NOT SURE HOW TO GET THE SECOND NUMBER...PLEASE HELP...THANK YOU
1 solutions
Answer 44623 by funmath(2925)   on 2006-12-05 14:17:23 (Show Source):
You can put this solution on YOUR website!determine the critical numbers and the critical points for each of the following functions
A. f(x)= x^3 + 13x^2 + 7x - 165
f'(x)=3x^2+26x+7
0=3x^2+26x+7
Use the quadratic formula:
 a=3, b=26, and c=7
 and 
 and 
 and 
:
B. g(x)= X^3 +6x^2 - 13x - 42
g'(x)=3x^2+12x-13
0=3x^2+12x-13
Use the quadratic formula, a=3, b=12, and c=-13
 and 
 and 
 and 
:
C. h(x)= x^3-10x^2 + 7x + 18
h'(x)=3x^2-20x+7
0=3x^2-20x+7
Use the quadratic formula a=3, b=-20, and c=7
 or 
 or 
 or 
Happy Calculating!!!
|
Functions/63959: calculate the first derivative f'(x) for each of the following. Express your final answers using positive exponents
A. f(x)= 5/6x^3/4 + 5/6x^3/2 + 2/5x^3/2
B. f(x)=3/2x^3/2 + 3/2x^3/4 + 3/2x^2/3
C.f(x)= 5/6x^3/4 + 5/6x^3/2
I NEED HELP WITH THESE PROBLEMS...I WOULD APPRECIATE THE HELP..I'VE TRIED TO DO THEM BUT IT DOESN'T COME OUT RIGHT...
1 solutions
Answer 44622 by funmath(2925) on 2006-12-05 13:48:14 (Show Source):
You can put this solution on YOUR website!calculate the first derivative f'(x) for each of the following. Express your final answers using positive exponents
A. 
f'(x)= 
f'(x)= 
f'(x)= 
:
B. 
f'(x)= 
f'(x)= 
f'(x)= 
:
C. 
f'(x)= 
f'(x)= 
f'(x)= 
:
Happy Calculating!!!
|
Radicals/63923: Really need help with this one.
Solve the equation.
^3 sqrt(x^2) = 4
1 solutions
Answer 44611 by funmath(2925) on 2006-12-05 11:52:43 (Show Source):
You can put this solution on YOUR website!I don't really know what you mean. What did you mean by ^3? Did you mean the third root of x^2? If so, this is what you do.
Solve the equation.
3rd rt(x^2) = 4
(3rd rt(x^2))^3=4^3
x^2=64
x=+\-8
:
Check for extraneous solutions:
3rd rt((8)^2)=4
3rd rt (64)=4
4=4 x=8 checks out.
3rd rt((-8)^2)=4
3rd rt(64)=4
4=4 x=-8 also checks out.
Happy Calculating!!!
|
Exponential-and-logarithmic-functions/63849: slove algebraically log base 4 (x+41)- log base 4(2x-5)=2
1 solutions
Answer 44610 by funmath(2925) on 2006-12-05 11:42:36 (Show Source):
You can put this solution on YOUR website!slove algebraically log base 4 (x+41)- log base 4(2x-5)=2
log base 4((x+41)/(2x-5))=2 because log(a)-log(b)=log(a/b) if the bases are the same.
 because log base a (b)=x ==> a^x=b
Check:
log base 4 (121/31+41)-log base 4 (2(121/31)-5)=2
log base 4 (1392/31)-log base 4 (87/31)=2
log base 4 ((1392/31)/(87/31))=2
log base 4((1392/31)(31/87))=2
log base 4(1392/87)=2
log base 4 (16)=2
log base 4 (4^2)=2
2=2 We're right!!!
Happy Calculating!!!
|
Exponential-and-logarithmic-functions/63881: Find E^x for the following set of numbers:
–3.5, –1.4, –0.5, 3, 5, 1, 2
1 solutions
Answer 44608 by funmath(2925) on 2006-12-05 11:29:53 (Show Source):
You can put this solution on YOUR website!Find E^x for the following set of numbers:
–3.5, –1.4, –0.5, 3, 5, 1, 2
You need a calculator to do this.
e=2.718281828...
e^(-3/2)=.2231301601
e^(-1.4)=.2465969639
e^(-0.5)=.6065306597
e^(3)=20.08553692
e^(5)=148.4131591
e^(1)=2.718281828
e^(2)=7.389056099
Round off to whatever your teacher asks for.
Happy Calculating!!!
|
logarithm/63947: Thank you for helping me with the solution to the following problem. Our solutions do not seem to be going in the same direction would you please assist as to what I am doing wrong. This is as far as I could get with the problem.
Problem: 3log(X^2)-4log(X^2)+log(2X^3):
3log(X^2)-4log(X^2)+log(2X^3):
log((X^2)^3)-log((X^2)4)+log(2X^3)
log(X^6)-log(X^8)+log(2X^3)
log(X^-8/X^6,2X^3)log(X^-8 I am stuck here with my completion.
1 solutions
Answer 44607 by funmath(2925) on 2006-12-05 11:17:11 (Show Source):
You can put this solution on YOUR website!Problem: 3log(X^2)-4log(X^2)+log(2X^3):
If you're the same person I just answered this for, there is more than one way to skin this cat, however you should still come up with the same conclusion. Doing it your way:
3log(X^2)-4log(X^2)+log(2X^3):
log((X^2)^3)-log((X^2)4)+log(2X^3)
log(X^6)-log(X^8)+log(2X^3)
log(x^6/x^8)+log(2x^3) because loga-logb=log(a/b)
log(1/x^2)+log(2x^3) reduce
log((1/x^2)(2x^3)) because loga+logb=log(ab)
log(2x^3/x^2)
log(2x) reduce
Happy Calculating!!!
|
test/63931: calculate the first derivatives f(x) for each of the following:
show all work
A)f(x)= 2/3x3/4 + 3/4x2/3+ 5/6x2/3
B) f(x)= 2/5x3/2 + 5/6x3/4 + 5/6x3/2
C) f(x)= 3/4x2/3 +5/6x3/2 + 3/4x3/2
1 solutions
Answer 44606 by funmath(2925) on 2006-12-05 11:04:48 (Show Source):
You can put this solution on YOUR website!I am assuming that the fractions after the variables are exponents, let me know if I'm not interpretting you correctly:
calculate the first derivatives f(x) for each of the following:
show all work
A)f(x)= 2/3x3/4 + 3/4x2/3+ 5/6x2/3
f'(x)= 
f'(x)= 
f'(x)= 
:
B) f(x)= 2/5x3/2 + 5/6x3/4 + 5/6x3/2
f'(x)= 
f'(x)= 
f'(x)= 
:
C) f(x)= 3/4x2/3 +5/6x3/2 + 3/4x3/2
f'(x)= 
f'(x)= 
f'(x)= 
Happy Calculating!!!
|
Graphs/63938: y = |x|
1 solutions
Answer 44596 by funmath(2925) on 2006-12-05 10:20:19 (Show Source):
You can put this solution on YOUR website!y = |x|
What are your directions?
This is an absolute value function, if you need to graph it, plot a couple of positive and negative x's.
When x=0
y=|0|
y=0 Plot(0,0)
When x=1
y=|1|
y=1 Plot(1,1)
When x=2
y=|2|
y=2 Plot(2,2)
When x=-1
y=|-1|
y=1 Plot(-1,1)
When x=-2
y=|-2|
y=2 Plot (-2,2)
Connect your points:
Happy Calculating!!!
|
logarithm/63943: 3log(X^2)-4log(X^2)+log(2X^3)
1 solutions
Answer 44595 by funmath(2925) on 2006-12-05 10:15:39 (Show Source):
You can put this solution on YOUR website!Are the directions to express as a single log, or to simplify?
I am going to express as a single log, then simplify.
3log(X^2)-4log(X^2)+log(2X^3)
-log(x^2)+log(2X^3)
log(X^-2)+log(2X^3)
log(1/X^2)+log(2X^3)
log(2X^3/X^2)
log(2X) <==single log
log(2)+log(X) <==simplified
Happy Calculating!!!
|
Quadratic-relations-and-conic-sections/63939: y= 1/x
1 solutions
Answer 44592 by funmath(2925) on 2006-12-05 09:57:29 (Show Source):
You can put this solution on YOUR website!y= 1/x
I'm not sure what you want. This is a hyperbolic function.
If you need to graph this, plot some points.
There is a vertical asymptote at x=0, because the funciton is undefined when the denominator = 0.
There is a horizontal asymptote at y=0 because there is nothing we can do to make the function =0.
Plot two points on both sides of the vertical asymptote:
Let x=-1
y=1/-1=-1 Plot (-1,-1)
Let x=-2
y=1/-2 Plot(-2,-1/2)
Let x=1
y=1/1=1 Plot(1,1)
Let x=2
y=1/2 Plot (1,1/2)
The graph will look like this:
Happy Calculating!!!
|
Linear_Algebra/63918: This question is from textbook algebra and trigonmetry struture method
with a tail wind, a helicopter traveled 300mi in an hour and 40 min. the return trip aganst the same wind took 20 min longer. find the wind speed and also the air speed of the helicopter.
1 solutions
Answer 44589 by funmath(2925) on 2006-12-05 09:20:20 (Show Source):
You can put this solution on YOUR website!with a tail wind, a helicopter traveled 300mi in an hour and 40 min. the return trip aganst the same wind took 20 min longer. find the wind speed and also the air speed of the helicopter.
The trick to this one is remembering to convert your time in minutes to time in hours.
The time with the tail wind is: 40min(1hr/60min)=40hr/60=(2/3)hr
Let the rate of the helicopter be: h
Let the rate of the wind be: w
The distance formula is: d=rt, where d=distance, r=rate, and t=time
so with the wind:
300=(2/3)(h+w)
:
The time against the wind is (40+20)min=60min=1 hr
Therefore:
300=1(h-w)
300=h-w
300+w=h Substitute this into the equation with the wind and solve for h:
300=(2/3)((300+w)+w)
300=(2/3)(300+2w)
(3/2)(300)=(3/2)(2/3)(300+2w)
450=300+2w
450-300=300-300+2w
150=2w
150/2=2w/2
75=w The speed of the wind is 75 m/h
Substitute that into the equation aganst the wind and solve for h.
300+75=h
375=h The speed of the helicopter is 375 m/h.
:
Sanity check:
If the helicopter went 375 m/h and the wind was 75 m/h, will the helicopter fly 300 miles in the allotted time with and against the wind?
With the wind: (2/3)(375+75)=300
(2/3)(450)=300
300=300 so far we're right.
Against the wind: (1)(375-75)=300
300=300 we're right if we understood the question and converted our time right.
Happy Calculating!!!
|
Travel_Word_Problems/63919: This question is from textbook algebra and trigonmetry struture method
with a tail wind, a helicopter traveled 300mi in an hour and 40 min. the return trip aganst the same wind took 20 min longer. find the wind speed and also the air speed of the helicopter.
1 solutions
Answer 44588 by funmath(2925) on 2006-12-05 09:19:47 (Show Source):
You can put this solution on YOUR website!with a tail wind, a helicopter traveled 300mi in an hour and 40 min. the return trip aganst the same wind took 20 min longer. find the wind speed and also the air speed of the helicopter.
The trick to this one is remembering to convert your time in minutes to time in hours.
The time with the tail wind is: 40min(1hr/60min)=40hr/60=(2/3)hr
Let the rate of the helicopter be: h
Let the rate of the wind be: w
The distance formula is: d=rt, where d=distance, r=rate, and t=time
so with the wind:
300=(2/3)(h+w)
:
The time against the wind is (40+20)min=60min=1 hr
Therefore:
300=1(h-w)
300=h-w
300+w=h Substitute this into the equation with the wind and solve for h:
300=(2/3)((300+w)+w)
300=(2/3)(300+2w)
(3/2)(300)=(3/2)(2/3)(300+2w)
450=300+2w
450-300=300-300+2w
150=2w
150/2=2w/2
75=w The speed of the wind is 75 m/h
Substitute that into the equation aganst the wind and solve for h.
300+75=h
375=h The speed of the helicopter is 375 m/h.
:
Sanity check:
If the helicopter went 375 m/h and the wind was 75 m/h, will the helicopter fly 300 miles in the allotted time with and against the wind?
With the wind: (2/3)(375+75)=300
(2/3)(450)=300
300=300 so far we're right.
Against the wind: (1)(375-75)=300
300=300 we're right if we understood the question and converted our time right.
Happy Calculating!!!
|
Linear-equations/63929: What is the equation for the line that passes through the point (-2,2) and has a slope of 5?
a. y = 5x + 2
b. y = 5x + 12
c. y = 5x - 2
d. none of these
1 solutions
Answer 44580 by funmath(2925) on 2006-12-05 08:58:36 (Show Source):
You can put this solution on YOUR website!What is the equation for the line that passes through the point (-2,2) and has a slope of 5?
a. y = 5x + 2
 . y = 5x + 12
c. y = 5x - 2
d. none of these
You can find the equation of a line when give a point and a slope using the point slope formula:  , where m=slope and (x1,y1)=given point.
m=5 and (x1,y1)=(-2,2)
y-2=5(x-(-2))
y-2=5(x+2)
y-2=5x+10
y-2+2=5x+10+2
 b.
Happy Calculating!!!!
|
Geometry_Word_Problems/63893: A 18-FOOT LADDER IS LEANED AGAINST A WALL. IF THE BASE OF THE LADDER IS 7 FEET FROM THE WALL . hOW HIGH ON THE WAL WILL THE LADDER REACH?
1 solutions
Answer 44577 by funmath(2925) on 2006-12-05 08:53:06 (Show Source):
You can put this solution on YOUR website!A 18-FOOT LADDER IS LEANED AGAINST A WALL. IF THE BASE OF THE LADDER IS 7 FEET FROM THE WALL . hOW HIGH ON THE WAL WILL THE LADDER REACH?
The ladder the wall and the ground form a right traiangle with the ladder being the hypoteneuse and the wall and ground being the legs.
According to the pythagorean theorem  , where c is the length of the hypoteneuse and a and b are the lengths of the legs.
c=18 and a=7
If you need an exact answer then the wall is  ft tall.
If you need an approximate answer, stick it in you calculator right away:
 which is approximately 16.58312395 ft, round off to whatever value your teacher asks for.
Happy Calculating!!!
|
Linear-equations/63824: Write an equation of the line that has each pair of intercepts.
x-intercept: -3, y-intercept: 5
1 solutions
Answer 44491 by funmath(2925) on 2006-12-04 15:27:51 (Show Source):
You can put this solution on YOUR website!Write an equation of the line that has each pair of intercepts.
x-intercept: -3, y-intercept: 5
To find the equation of a line you need a point and a slope. You don't have a slope, so find it using the slope formula: 
(x1,y1)=(-3,0) and (x2,y2)=(0,5)
The slope intercept form of a line is  , where m=slope and b=y-intercept.
m=5/3 and b=5
Happy Calculating!!!!
|
Radicals/63621: x-√x-0, perform the following:
sovle for all values of x that satisfies the equation.
answer:
show work
1 solutions
Answer 44386 by funmath(2925) on 2006-12-03 08:14:06 (Show Source):
You can put this solution on YOUR website! I think you meant the second - to be =.
sovle for all values of x that satisfies the equation.
answer:
x=0 and x=1
show work
x=0 and x-1=0
x=0 and x-1+1=0+1
x=0 and x=1
Check:
For x=0
 x=0 works!!!
For x=1
x=1 also checks!
Happy Calculating!!!
|
Probability-and-statistics/63652: This question is from textbook Algebra and Trigonometry Structure and Method
Hello, I'm Alex. Could I please ask your assistance on this Homeschool American School Problems because I don't have a teacher here to help?
Suppose there are 10 items on a true-false test. The person taking the test does not read the questions; he just answers them randomly. What is the probability of his guessing all answers correctly?
1 solutions
Answer 44385 by funmath(2925) on 2006-12-03 08:06:29 (Show Source):
You can put this solution on YOUR website!Hi Alex,
Suppose there are 10 items on a true-false test. The person taking the test does not read the questions; he just answers them randomly. What is the probability of his guessing all answers correctly?
There is a 1/2 chance of getting each one right:
(1/2)(1/2)(1/2)(1/2)(1/2)(1/2)(1/2)(1/2)(1/2)(1/2)
(1/2)^10=1/1024
If you need it in decimal form: .0009765625
Happy Calculating!!!
|
logarithm/63651: I have this question and none of my notes seem to relate to this can you help explain how to get the correct answer?
2ln(x2) - 3ln(x) = 2
The 2 after the x above is x squared couldn't find little 2.
Thankyou
1 solutions
Answer 44382 by funmath(2925) on 2006-12-03 07:57:33 (Show Source):
|
Linear-systems/63631: This question is from textbook An Incremental Development
please help me to solve the following
Use substitution to solve
4x + y = 17 and 3x - 5y = 30
1 solutions
Answer 44379 by funmath(2925) on 2006-12-03 07:47:57 (Show Source):
You can put this solution on YOUR website!Use substitution to solve
E1: 4x + y = 17
E2: 3x - 5y = 30
Solve E1 for y and substitute it into E2 for y and solve for x.
E1: -4x+4x+y=-4x+17 --> y=-4x+17
E2: 3x-5(-4x+17)=30
3x+20x-85=30
23x-85=30
23x-85+85=30+85
23x=115
23x/23=115/23
x=5
Substitute x=5 into E1 and solve for y:
E1: 4(5)+y=17
20+y=17
-20+20+y=-20+17
y=-3
The solution: (x,y)=(5,-3)
Check the solution by substituting 5 in for x and -3 in for y in both equations and see if the equations balance.
E1: 4(5)+(-3)=17
20-3=17
17=17 E1 checks.
E2: 3(5)-5(-3)=30
15+15=30
30=30 E2 also checks, so we know we're right!
Happy Calculating!!!
|
|
