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, >>Nextlogarithm/61801: This question is from textbook
Please help with the following problem: e^x = 2^x+1
1 solutions
Answer 42616 by funmath(2925)   on 2006-11-17 13:34:57 (Show Source):
You can put this solution on YOUR website!e^x = 2^(x+1)
ln(e^x)=ln(2^(x+1))
xln(e)=(x+1)ln(2)
x(1)=(x+1)ln(2)
x=xln(2)+ln(2)
x-xln(2)=ln(2)
x(1-ln(2))=ln(2)
x(1-ln(2))/(1-ln(2))=ln(2)/(1-ln(2))
x=ln(2)/(1-ln(2))
x=2.258891353 approximatlely.
Happy Calculating!!!
|
Functions/61882: Use the defination of inverse function to show analytically that f and g are inverse:
f(x) = 4x+3 and g(x)= x-3/4
1 solutions
Answer 42614 by funmath(2925) on 2006-11-17 13:17:29 (Show Source):
You can put this solution on YOUR website!Use the defination of inverse function to show analytically that f and g are inverse:
In order to be inverses, their composites have to equal x.
f(x) = 4x+3 and g(x)= (x-3)/4
(fog)(x)=f(g(x))=f((x-3)/4)=4((x-3)/4)+3=x-3+3=x
(gof)(x)=g(f(x))=g(4x+3)=((4x+3)-3)/4=4x/4=x
They are inverses of each other.
Happy Calculating!!!!
|
Functions/61863: I need some help with a word problem Please.
A bank compounds interest continuously. If you invest $500 at 4% at that bank for 5 years, what will your balance be? Use formula A= 500e^0.04t
where A is the balance in the account and t is in years.
1 solutions
Answer 42608 by funmath(2925) on 2006-11-17 11:57:54 (Show Source):
You can put this solution on YOUR website!A bank compounds interest continuously. If you invest $500 at 4% at that bank for 5 years, what will your balance be? Use formula A= 500e^0.04t
where A is the balance in the account and t is in years.
A=$610.70
Happy Calculating!!!
|
Equations/61870: what is the value of p in 6p-7=2p+9 and how did you get that answer?
1 solutions
Answer 42602 by funmath(2925) on 2006-11-17 11:20:01 (Show Source):
You can put this solution on YOUR website!Do the inverse operations to both sides in order to isolate p. (If something that you need to move is added, subtract it, if its subtracted, add it, if it's multiplied, divide it, if it's divided multiply it.)
6p-7=2p+9
6p-2p-7=2p-2p+9
4p-7=0+9
4p-7=9
4p-7+7=9+7
4p=16
4p/4=16/4
:
Check by subtituting 4 in for p in the original equation and see if both sides =.
6(4)-7=2(4)+9
24-7=8+9
17=17 We're right!!!!
Happy Calculating!!!
|
logarithm/61860: Is the expression log1 512 an expression that can be evaluated?
1 solutions
Answer 42592 by funmath(2925) on 2006-11-17 10:15:52 (Show Source):
You can put this solution on YOUR website!Is the expression log1 512 an expression that can be evaluated?
No. There is no power you can raise 1 to to get 512.
:
Another thing you can do to prove this to yourself is to try to solve it using change of bases.
log1 512=(ln(512))/(ln(1))=ln(512)/0=undefined
:
You can try putting ln(512)/ln(1) into your calculator, the ti-83 says, "ERR:DIVIDE BY 0".
:
Happy Calculating!!!!
|
logarithm/61859: Could someone help show how to express this in a single log and simplify if possible?
log10 x + log10 y
1 solutions
Answer 42588 by funmath(2925) on 2006-11-17 10:10:45 (Show Source):
You can put this solution on YOUR website!log10 x + log10 y When logs of like bases are added you can write them this way.
log10 (xy)
It is similar to rules involving exponents 
Happy Calculating!!!!
|
Equations/61864: can you help solve this equation?
3x^2+9bx=ax +3ab
So far I've tried
3x^2+9bx-ax-3ab=0
-(a-3x)(3b+x)=0
I am to solve for x
Thanks
1 solutions
Answer 42587 by funmath(2925) on 2006-11-17 10:06:46 (Show Source):
You can put this solution on YOUR website!When I factored I got (I don't know where you got the -, but you would get the same thing I got if you solved for x.) If the directions say solve, you solve for x.
(3x-a)*(x+3b)=0
3x-a=0 and x+3b=0
3x-a+a=0+a and x+3b-3b=0-3b
3x=a and x=-3b
3x/3=a/3 and x=-3b
x=a/3 and x=-3b
:
Check when x=a/3
(3(a/3)-a)(a/3+3b)=0
(a-a)(a/3+3b)=0
0(a/3+3b)=0
0=0
When x=-3b
(3(-3b)-a)(-3b+3b)=0
(-9b-a)(0)=0
0=0
We're right!!!
Happy Calculating!!!
|
Rational-functions/61752: use synthetic division:
Problem: x(to the third) -2x(squared) -x +2 divided by x-2
the answer I got was:
x(squared) + x +4/x-2
but i'm not sure if I did it right, please help!
1 solutions
Answer 42497 by funmath(2925) on 2006-11-16 13:54:06 (Show Source):
|
Linear-systems/61694: This question is from textbook Alegbra Concepts and applications
please help
Use substitution to solve for x and y
3x - y = 3
y = 2x - 1
1 solutions
Answer 42493 by funmath(2925) on 2006-11-16 13:13:26 (Show Source):
You can put this solution on YOUR website!Use substitution to solve for x and y
E1: 3x - y = 3
E2: y = 2x - 1
:
Substitute 2x-1 from E2 in for y in E1 and solve for x.
:
3x-(2x-1)=3
3x-2x+1=3
x+1=3
x+1-1=3-1
x=2
:
Substitute 2 in for x in E2 and solve for y.
:
y=2(2)-1
y=4-1
y=3
:
Therefore the solution is (x,y)=(2,3)
:
Sanity Check, does that solution work for both E1 and E2.
3(2)-(3)=3--->6-3=3--->3=3 E1 Checks
3=2(2)-1--->3=4-1--->3=3 E2 Checks
Happy Calculating!!!
|
Linear-systems/61681: I sent this problem in and made an error on how it has to be solved The system is to be solved by addition. 5x-3y=13 4x-3y=11 Thanks
1 solutions
Answer 42451 by funmath(2925) on 2006-11-16 08:27:03 (Show Source):
You can put this solution on YOUR website!E1: 5x-3y=13
E2: 4x-3y=11
:
This is the elimination method (also known as the addition method).
Multiply the E2 by -1 and add it to E1 and the y's will be eliminated so that you can solve for x.
:
-1(4x-3y)=-1(11) --> -4x+3y=-11
:
5x-3y=13
-4x+3y=-11
__________
x+0=2
x=2
:
Substitute 2 in for x in either equation and solve for y.
4(2)-3y=11
8-3y=11
8-8-3y=11-8
-3y=3
-3y/-3=3/-3
y=-1
:
Therefore, your solution is: (x,y)=(2,-1)
Happy Calculating!!!
|
Linear-systems/61680: please help me solve this is what I got 5x-3y=13
4x-3y=11 My answer is x=3 and y =1 I do not think this is correct. please help.
1 solutions
Answer 42449 by funmath(2925) on 2006-11-16 08:23:09 (Show Source):
You can put this solution on YOUR website!E1: 5x-3y=13
E2: 4x-3y=11
:
This is the elimination method.
Multiply the E2 by -1 and add it to E1 and the y's will be eliminated so that you can solve for x.
:
-1(4x-3y)=-1(11) --> -4x+3y=-11
:
5x-3y=13
-4x+3y=-11
__________
x+0=2
x=2
:
Substitute 2 in for x in either equation and solve for y.
4(2)-3y=11
8-3y=11
8-8-3y=11-8
-3y=3
-3y/-3=3/-3
y=-1
:
Therefore, your solution is: (x,y)=(2,-1)
Happy Calculating!!!
|
Triangles/61683: This question is from textbook
THE SECOND ANGLE OF A TRIANGLE IS TWO TIMES AS LARGE AS THE FIRST.THE THIRD ANGLE IS 10DEGREES MORE THAN THE SECOND ANGLE. FIND THE MEASURE OF THE FIRST ANGLE.
1 solutions
Answer 42446 by funmath(2925) on 2006-11-16 08:14:42 (Show Source):
You can put this solution on YOUR website!THE SECOND ANGLE OF A TRIANGLE IS TWO TIMES AS LARGE AS THE FIRST.THE THIRD ANGLE IS 10 DEGREES MORE THAN THE SECOND ANGLE. FIND THE MEASURE OF THE FIRST ANGLE.
Let the first angle be: x
Then the second angle is: 2x
Then the third angle is: 2x+10
Angles of triangles add to = 180
:
1st+2nd+3rd=180
(x)+(2x)+(2x+10)=180
5x+10=180
5x+10-10=180-10
5x=170
5x/5=170/5
x=34
:
The 1st angle is: x=34 degrees.
:
For fun find out the other angles too.
2nd angle: 2x=2(34)=68 degrees
3rd angle: 2x+10=2(34)+10=78 degrees.
:
Sanity Check, if you add all three angles do you get 180?
34+68+78=180 yes!!!
:
Happy Calculating!!!
|
Rational-functions/61512: Use calculus to determine the relative extrema of f(x)=x-lnx
Find the equation of the tangent line at x=1
please help, i'm so confused!
1 solutions
Answer 42393 by funmath(2925) on 2006-11-15 17:56:24 (Show Source):
You can put this solution on YOUR website!Use calculus to determine the relative extrema of f(x)=x-lnx
Find the equation of the tangent line at x=1
To find the relative extrema take the first derivative and find the numbers that make it 0 or undefined as long as the original function is defined there.
f'(x)= 
It's undefined at 0, but so is the original function, so we can't have a relative extrema there.
f(1)=1-ln(1)
f(1)=1-0
f(1)=1
There is a relative extrema at (1,1)
f''(x)= 
f''(1)= 
f''(1)=1 The second derivative is positive, so it's a local min.
:
f'(1)=1-1/1
f'(1)=1-1
f'(1)=0 The slope of the tangent line is 0.
:
We already found that f(1)=1
The equation of line with the slope of 0 going through the point (1,1) is 
Happy Calculating!!!
|
Circles/61514: This question is from textbook College Algebra with modeling and visualization
Find the standard equation of the circle that satisfies the conditions.
Center (-1,-3), passing through the point (3,0)
1 solutions
Answer 42341 by funmath(2925) on 2006-11-15 10:28:54 (Show Source):
You can put this solution on YOUR website!Find the standard equation of the circle that satisfies the conditions.
Center (-1,-3), passing through the point (3,0)
In order to write an equation for a circle you need a center and a radius. You're missing a radius, but you can find it with the information that they gave you. The radius is the distance from the center to any point of the circle.
The distance formula is r= 
(x1,y1)=(-1,3) and (x2,y2)=(3,0)
r= 
r= 
r= 
r= 
r= 
Now that we have a center (h,k)=(-1,-3) and a radius r=5.
The standard form of a circle:  , (h,k) is the center, and r is the radius.
:
Happy Calculating!!!
|
Rational-functions/61468: State the coordinates of the vertex of the parabola whose equation is
y = 3(x - 2)2 + 5
(-2, -5)
(-2, 5)
(2, -5)
(2, 5)
none of these
1 solutions
Answer 42339 by funmath(2925) on 2006-11-15 09:09:55 (Show Source):
You can put this solution on YOUR website!State the coordinates of the vertex of the parabola whose equation is
y = 3(x - 2)^2 + 5
(-2, -5)
(-2, 5)
(2, -5)
(2, 5) <-- answer
none of these
:
The vertex form of a quadratic eqution is:
 , the vertex is (h,k)
In this case h=2 and k=5, the vertex is (h,k)=(2,5).
:
Happy Calculating!!!
|
Polynomials-and-rational-expressions/61503: 6p5 + 4p3 - 8p4 + 10p2. Please show me how to solve? (Exponents and Polynomials)
1 solutions
Answer 42337 by funmath(2925) on 2006-11-15 08:57:24 (Show Source):
You can put this solution on YOUR website!6p^5+4p^3-8p^4+10p^2
Please show me how to solve? (Exponents and Polynomials)
You can't solve this. You can factor out a GCF, you can put it in decending or ascending order, you can tell the degree, but you can't solve it.
What do your directions say?
:-)
|
Linear-systems/61390: Solve the system by substitution. 3x + 3y = 6
y = –4x – 10
1 solutions
Answer 42335 by funmath(2925) on 2006-11-15 08:47:17 (Show Source):
You can put this solution on YOUR website!Solve the system by substitution.
E1: 3x+3y=6
E2: y=–4x–10
:
Substitute -4x-10 in for y in E1 and solve for x.
3x+3(-4x-10)=6
3x-12x-30=6
-9x-30=6
-9x-30+30=30+6
-9x=36
x=-4
Substitute -4 in for x in E2 and solve for y.
y=-4(-4)-10
y=16-10
y=6
The solution (x,y)=(-4,6)
:
Check the solution in both equations.
3(-4)+3(6)=6
-12+18=6
6=6 The solution checks in E1.
:
6=-4(-4)-10
6=16-10
6=6 The solution checks in E2.
We're right!!!
Happy Calculating!!!
|
Rational-functions/61469: If y = 3x2 - 6x - 4 is put into general form, what is the value of "a" ?
-4
-1
2
3
none of these
1 solutions
Answer 42333 by funmath(2925) on 2006-11-15 08:32:16 (Show Source):
You can put this solution on YOUR website! If  is put into general form, what is the value of "a" ?
-4
-1
2
none of these
:
The standard form of a quadratic equation is  .
For this equation a=3, b=-6, and c=-4
:
Happy Calculating!!!
|
Angles/61509: This question is from textbook
find the missing angle measure. x at tip top,110 and 25 bottom
1 solutions
Answer 42332 by funmath(2925) on 2006-11-15 08:21:39 (Show Source):
You can put this solution on YOUR website!I am assuming that you're trying to find the missing angle of a triangle. The angles of a triangle add to equal 180 degrees.
find the missing angle measure. x at tip top,110 and 25 bottom
 degrees
:
Happy Calculating!!!
|
|
