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# Recent problems solved by 'ntnk'

 logarithm/592472: evaluate the limit! Lim (e^4t) -1/t x->0 i thought e^0=1 t=0 so 0/0 =0 but it said it was wrong i also tried infinity but it was wrong1 solutions Answer 376072 by ntnk(54)   on 2012-03-28 15:40:50 (Show Source): You can put this solution on YOUR website!I think your parentheses are misplaced, so based on the work you have shown, my guess is that your question is the following: http://latex.codecogs.com/gif.latex?%5Clim_%7Bt%5Cto%200%7D%5Cfrac%7Be%5E%7B4t%7D-1%7D%7Bt%7D First I would like to point out and emphasize the fact that 0 / 0 is not the same as 0. (However, you are correct that .) The easiest way to solve this is by using L'Hopital's rule. We can take the derivative of the numerator and the derivative of the denominator. The limit above is therefore given by the following http://latex.codecogs.com/gif.latex?%5Clim_%7Bt%5Cto%200%7D%5Cfrac%7B4e%5E%7B4t%7D%7D%7B1%7D Now we can plug in to find out that the limit is 4.
 Triangles/592346: a right triangle gas an angle whose measure is 35. what is the measurment of the third angle?1 solutions Answer 376062 by ntnk(54)   on 2012-03-28 15:20:07 (Show Source): You can put this solution on YOUR website!There are two very important facts that you must know to do these types of questions. 1. In ANY triangle, the measurements of the three angles must add up to 180. 2. In a RIGHT triangle, one of the angles measures 90 degrees. We have a right triangle with an angle measure of 35. The fact that the triangle is right tells us that one of the angles is 90. We need to find the measure of the third angle, which we will call x. Since the measures of the angles must add up to 180, we have 35 + 90 + x = 180 and we must solve for x. Simplifying a bit on the left hand side gives 125 + x = 180 Now subtract 125 from both sides to get x = 180 - 125 = 55 so the third angle is 55 degrees. I hope this helps!
 Age_Word_Problems/592782: A man is twice as old as his son.10years ago he was three times as old.how old will his son be in 5years time?1 solutions Answer 376061 by ntnk(54)   on 2012-03-28 15:16:09 (Show Source): You can put this solution on YOUR website!Let's turn the statements you give above into equations. Let's call the man's age M and the son's age S. (1) A man is twice as old as his son: M = 2 * S. Since the man's age today is M and the son's age is S, this means this means that 10 years ago, the man's age was M-10 and the son's age was S-10. (2) 10years ago he was three times as old: M-10 = 3 * (S-10). Now we can solve for the man's age an his son's age by substitution. We can plug the first equation (M=2*S) into the second one so that M - 10 = 3 * (S-10) becomes 2*S - 10 = 3 * (S-10). Now we can solve for S. First use the distributive property on the right-hand side to get 2*S - 10 = 3*S - 30 Now add 30 to both sides to get 2*S + 20 = 3*S and subtract 2*S from both sides to get 20 = S. This is the age of the son today. The question asks how old the son will be in 5 years, so the answer must be 20+5 = 25 years old. Now let's check. We think the son is 20 years old today. Since the man is twice as old, the man must be 40. Ten years ago, the man was 30 and the son was 10. Therefore the man was 3 times as old as the son ten years ago, so everything checks out. I hope this helps!
 Age_Word_Problems/592692: My Age: 39 Elijah: 12 At some point , my age will be 3 times Elijah's age. Is this correct: 3x= 3(x-27) How do I solve? Thanks!1 solutions Answer 376020 by ntnk(54)   on 2012-03-28 10:26:44 (Show Source): You can put this solution on YOUR website!The equation you have written is not quite correct. Let's see how to solve it before getting to the age question. First we use the distributive property on the right-hand side to get Then we subtract 3x from both sides to get which is obviously false, so that means the equation above does not have a solution. Let's think about what the problem is telling us. Right now you are 39 and Elijah is 12. Next year, you will be 40 and Elijah will be 13. The year after that, you will be 41 and Elijah will be 14. More generally, in X years, your age will be 39 + X and Elijah's age will be 12 + X. (For example, if we plug in X=1 or X=2, we get the statements from the previous paragraph.) We want to know when your age will be three times Elijah's age. So we take three times Elijah's age: 3 * (12 + X) and set it equal to your age: (39 + X). This gives the equation We use the distributive property on the left hand side to get Now subtract X from both sides to get Then subtract 36 from both sides to get and finally divide by 2 to get Now we can check the final answer. In 1.5 years, you will be 39+1.5 = 40.5 years old, and Elijah will be 12+1.5 = 13.5 years old. Indeed, in 1.5 years you will be 3 times older than Elijah since 13.5 * 3 = 40.5
 Age_Word_Problems/313306: A man is three times as old as his son, and his daughter is four years younger than his son. If the combined ages of all three is 81 years, find the present age of the father. Ps: Thank you, please demonstrate the work progress so I will know how to do the question next time please and thank you :D1 solutions Answer 224040 by ntnk(54)   on 2010-06-10 23:23:11 (Show Source): You can put this solution on YOUR website!So for these you have to turn the statements in the word problem into equations. A man is three times as old as his son: his daughter is four years younger than his son: combined ages of all three is 81 years: Now you can just substitute: Add 4 to both sides to get: Divide by 5 on both sides to get: Now check: and , so , so we do indeed get the combined age as 81, which means our son's age of 17 is correct! I hope that helps! -ntnk
 Matrices-and-determiminant/150001: I need some help on this equation. I need to use the gauss-jordan method solving by matrices. thanks 4x - 2y = 3 -2x + 3y = 11 solutions Answer 110104 by ntnk(54)   on 2008-07-28 13:01:03 (Show Source): You can put this solution on YOUR website!I don't know how to make matrices here, but I'll try. [ 4 -2 | 3 ] [-2 3 | 1 ] <-- That's your augmented matrix representing the system of equations. Now row one column one has to be a pivot, so row two column one must become zero. Add 1/2*row one to row two. [4 -2 | 3] [0 2 | 5/2] So you have it in the proper inverted triangle form now. Equate the components. Substitute this back into: So there is the solution: (11/8, 5,4) -ntnk
 Quadratic_Equations/131612: y=-3x^2-6x+41 solutions Answer 96242 by ntnk(54)   on 2008-03-12 21:27:18 (Show Source):
 Linear-systems/131815: This question is from textbook Solving Linear Equations: Use linear combinations to solve the system of linear equations. t + r = 1 2r - t = 21 solutions Answer 96241 by ntnk(54)   on 2008-03-12 21:22:59 (Show Source): You can put this solution on YOUR website!In any equation, solve for one variable in terms of the other and substitute into the other equation. If , then . If and , then Distributing: Combining like terms: Subtracting 2 from both sides: Dividing both sides by -3: . Substitute this back into either of the original equations to find 'r'. Therefore, , so .
 Miscellaneous_Word_Problems/131825: The problem reads: A rectangle is 5 feet longer than it is wide. The perimeter of the rectangle is 34 feet. What is the length of the rectangle? any help would be appreiciated1 solutions Answer 96240 by ntnk(54)   on 2008-03-12 21:19:25 (Show Source): You can put this solution on YOUR website!Start by actually writing out every equation that you can deduce from the problem statement. "A rectangle is 5 feet longer than it is wide." "The perimeter of the rectangle is 34 feet." What is the length of the rectangle? L = ? Substitute the first equation into the second equation, obtaining: Distributing: Combining like terms: Subtracting 10 from both sides: Dividing both sides by 4: If W = 6, then L = 11 since as stated earlier. -ntnk
 Sequences-and-series/65739: Please help me figure out this word problem. Considering yourself, your parents, your grandparents, and so on, back to your grandparents with the workd "great" used in front 40 times. What is the total number of people that you are considering. Thanks for your help.1 solutions Answer 46451 by ntnk(54)   on 2006-12-28 16:49:17 (Show Source): You can put this solution on YOUR website!Each level is 2^x (because each person has two parents and so forth.) Therefore, YOU are 2^0 = 1 (person); PARENTS are 2^1= 2 (people); GRANDPARENTS are 2^2= 4 (people); GREAT GRANDPARENTS are 2^3=8; GREAT GREAT GRANDPARENTS are 2^4=16; GREAT GREAT GREAT GRANDPARENTS are 2^5=32; and so forth. But notice that three "greats" implies 2^5. This means that x "greats" implies x+2. Therefore, 40 "greats" implies 2^42, which is the total number of people that you are considering. Also, the question is a bit unclear as to if you want to know the total number of people including yourself and parents, and grandparents, and so forth until great*40 grandparents, so if you include ALL of those people, then it will be 2^42+2^41+2^40+...+2^20+2^19+...+2^3+2^2+2^1+2^0 and so forth. and so forth ntnk
 logarithm/64600: 1. Rewrite in logarithmic form. Any help would be much appreciated1 solutions Answer 46448 by ntnk(54)   on 2006-12-28 16:39:45 (Show Source): You can put this solution on YOUR website!If a=b^c, then log(base b)a=c, therefore, if , then log(base (1/2))8=-3.
 Rational-functions/64647: This question is from textbook McDougal Littell Algebra 2 how do I graph the given function y=f(x-4)+11 solutions Answer 46446 by ntnk(54)   on 2006-12-28 16:32:52 (Show Source): You can put this solution on YOUR website! There is a horizontal shift to the right by four and a vertical shift up by 1. ntnk
 Exponential-and-logarithmic-functions/63300: solve algebraically: 1 solutions Answer 46445 by ntnk(54)   on 2006-12-28 16:25:31 (Show Source): You can put this solution on YOUR website! If x = y, then log x = log y, therefore, find the log(base3) of both sides. Log(base3)3^(2x+1)=log(base3)(1/243) This simplifies to because log(base3)(1/243)=-5 ntnk
Expressions-with-variables/54990: This question is from textbook
(-4)(10x+2)=-4
I am don't know how you would even get this one out of (). Can you please help me and show me the steps? Thanks
1 solutions

Answer 37187 by ntnk(54)   on 2006-10-06 18:01:01 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=-0.1. Graphical form: Equation was fully solved.Text form: -4*(10x+2)=-4 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( -4*(10x+2)=-4 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Moved these terms to the left
It becomes .

Look at .
Expanded term by using associative property on
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to -40*x-4 =0
It becomes .
Result:
This is an equation! Solutions: x=-0.1.

### Universal Simplifier and Solver

Done!

At the end when you have -40x-4=0, you can add four to both sides, making it -40x=4, then divide both sides by -40 to get x alone and or

real-numbers/54989: This question is from textbook Algebra 1
I am doing a multi-step problem and can't seem to grasp the point here
is the problem:

please show how you did it so I can understand better!!!
Thank you so much!
1 solutions

Answer 37185 by ntnk(54)   on 2006-10-06 17:54:27 (Show Source):
You can put this solution on YOUR website!
Read the "detailed explanation" section for the steps, but disregard everything after where its says 0=0, thats an error. It is reexplained below.
Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=12. Graphical form: Equation was fully solved.Text form: x/2+7=x/3+9 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( x/2+7=x/3+9 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Moved these terms to the left ,
It becomes .

Look at .
It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
It becomes .

Look at .
Eliminated similar terms , replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor ,
It becomes .

Look at .
Remove extraneous '1' from product
It becomes .

Look at .
Solved linear equation equivalent to 0.166666666666667*x-2 =0
It becomes .
Result:
This is an equation! Solutions: x=12.

### Universal Simplifier and Solver

Done!

Sorry, the solver messed up a bit at the end. The correct process is when you have , you add two to both sides to get . Then multiply both sides by six to get the final answer.

 Distributive-associative-commutative-properties/51733: please help me factor this equation: 1 solutions Answer 37184 by ntnk(54)   on 2006-10-06 17:47:29 (Show Source): You can put this solution on YOUR website!Both monomials are divisible by a common factor; this means that we can "factor" it out so that it can later be distributed back. You can divide both parts by and by , therefore you can factor out . The solution thus becomes because when you use the distributive property, you get the original equation back.
 Equations/49139: FIND VALUES OF X1 solutions Answer 33784 by ntnk(54)   on 2006-09-04 14:30:56 (Show Source): You can put this solution on YOUR website! The domain of this function is X IS GREATER THAN OR EQUAL TO FIVE.
 Polynomials-and-rational-expressions/40711: Please evaluate. Thanks!1 solutions Answer 26099 by ntnk(54)   on 2006-06-04 17:37:35 (Show Source):
 Quadratic_Equations/33706: If we apply the quadratic formula and find that the value of b2 - 4ac equals zero, what can we conclude about the solutions? A) The equation has no real number solutions. B) The equation has exactly one irrational solution. C) The equation has two different rational solutions D) The equation has exactly one rational solution.1 solutions Answer 20120 by ntnk(54)   on 2006-04-15 20:51:10 (Show Source): You can put this solution on YOUR website!Look at the quadratic formula. If you ignore the , by making it zero then you are left with . This is one rational solution. D) The equation has exactly one rational solution. NtNk

1 solutions

Answer 20119 by ntnk(54)   on 2006-04-15 20:45:30 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=20 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3.23606797749979, -1.23606797749979. Here's your graph:

Also, if you go back to where the equation was plugged into the quadratic equation:

It can be simplified to:

And further simplified to
by canceling the 2's
NtNk

 logarithm/33712: Express as a single logarithm and, if possible simplify log(x^3-8)-log(x-2)1 solutions Answer 20118 by ntnk(54)   on 2006-04-15 20:36:22 (Show Source): You can put this solution on YOUR website!First, note that when factoring a binomial in the form: , it is simplified as . You can use the distributive property to verify this. Also, note that the quotient property of logarithms states: . First, replace with . Use the first property I explained. This will simplify to . Use the second property. . Simplify by canceling the and you are left with the answer: NtNk
 Equations/33707: Solve the equation. Express radicals in simplest form. 5x^2 = 351 solutions Answer 20115 by ntnk(54)   on 2006-04-15 20:21:44 (Show Source): You can put this solution on YOUR website! Subtract 35 from both sides to set it equal to zero. Divide everything by 5. Simplify: Take the square root of both sides. Simplify. or NtNk
 Graphs/19669: hi, need help desperately. graph the equation, identifying the y-intercept. y = 2x -5 thanks so much1 solutions Answer 9607 by ntnk(54)   on 2005-11-16 20:42:49 (Show Source): You can put this solution on YOUR website! When an equation is written in slope-intercept form, , b is known as the y-intercept. In this case, m (the slope) would be 2 and b would be -5.
 Polynomials-and-rational-expressions/13551: i dont understand how to do this work.... solve for x (4x+1)-(x+4)=18 i know that you have to remove par. so i did that and then my teacher told me to combine like terms.. that leaves me with 3x+5=18 then now i subtract 5 from both sides... that leaves me with 3x=13 i dont think that i did that right but i always get stuck on certain parts can you please help me to try to understand how to do this? any help would be appreciated1 solutions Answer 6842 by ntnk(54)   on 2005-10-02 22:43:35 (Show Source): You can put this solution on YOUR website!(4x + 1) - (x + 4) = 18 Set this equation up vertically it might be easier: 4x + 1 -1x - 4 ------- 3x + -3 ... REMEMBER TO SUBTRACT THE 4 FROM THE ONE, NOT ADD THEM 3x - 3 = 18 Add 3 to each side: 3x - 3 + 3 = 18 + 3 3x = 21 Divide both sides by 3: 3x/3 = 21/3 Check: (4(7) + 1) - (7+4) = 18 (28 +1) - (11) = 18 29 - 11 = 18 18 = 18 Solved By: NtNk
 Expressions-with-variables/13559: I have three problems that do not have instructions as to what to do. I see the equal sign and assume I am to solve the equation. The problem is stated 5(t+3)+9 = 3(t-2)+6 Only because when I put in the answer that seems obvious it is usually wrong, I thought an answer to whether this is true or not will help me to know if I'm on the right track before going on. I have 5t+15+9 = 3t-6+6 on first line 5t + 24 = 3t on second line -5t -5t 24 = -2t (/)-2 + (/) -2 -12 = T ( T = -12 )1 solutions Answer 6840 by ntnk(54)   on 2005-10-02 22:25:22 (Show Source): You can put this solution on YOUR website!Your answer and method of solving is absolutely correct. If you want to be sure, substitute your value of t into the problem: Your answer is correct! Solved By: NtNk
 Linear-equations/13561: Help on this please. -2x + 5y =10 Do not understand how to work it. thank you , connie1 solutions Answer 6839 by ntnk(54)   on 2005-10-02 22:13:37 (Show Source): You can put this solution on YOUR website! is a linear equation written in standard form: But normally when solving linear equations, it is easier in slope-intercept form: To graph your equation, first change it to slope intercept form: Add 2x to both sides: Reduce: Divide both sides by 5: Reduce: Now you can graph it: Solved By: NtNk
 Equations/13575: Solve for X 2x - (2x)/7 = x/2 + 17/21 solutions Answer 6836 by ntnk(54)   on 2005-10-02 21:58:43 (Show Source): You can put this solution on YOUR website! Multiply both sides by the LCD, in this case, 14. Use the distributive property and reduce: Subtract 7x from both sides. Reduce. Divide both sides by 17. Reduce Check: Solved By: NtNk
 Linear-systems/13577: x + y = -6 11x - y = 42 Many solutions or no solutions?1 solutions Answer 6833 by ntnk(54)   on 2005-10-02 21:48:32 (Show Source): You can put this solution on YOUR website!To solve a system of equations, you can either graph, substitute, or use elimination. The easiest method for this problem will be elimination: Add the two equations together to eliminate y: x + y = -6 11x - y = 42 ------------ 12x + 0 = 36 Now solve like a one step equation. Divide both sides by 12. Reduce. Now plug in this value of x to one of the equations: Subtract 3 from each side. Reduce. x = 3 y = -9 Remember to check: ... ... Solved by: NtNk
 Quadratic_Equations/3607: how do you graph f(x)=-2x^21 solutions Answer 2022 by ntnk(54)   on 2005-07-05 19:44:55 (Show Source): You can put this solution on YOUR website!Solved By: NtNk
 Volume/3789: Sheri's freezer is 2 feet wide, 6 feet long, and 2 feet deep. What is the volume of her freezer? a- 10 cubic feet b- 12 cubic feet c- 24 cubic feet d- 4 cubic feet1 solutions Answer 2021 by ntnk(54)   on 2005-07-05 19:38:10 (Show Source): You can put this solution on YOUR website!The formula for finding the volume of a rectangular prism, such as a freezer, is , length times width times height (or depth). When you multiply, the product is 24 cubic feet. Check: 2 * 6 * 2 = 24Solved By: NtNk
 Rectangles/3701: The area of a gymnasium floor is 264 square yards. The floor is 11 yards wide. How long is the floor? a)253 yards b)24 yards c)11 yards d) 242 yards1 solutions Answer 2008 by ntnk(54)   on 2005-07-04 15:47:52 (Show Source): You can put this solution on YOUR website!The floor is B. 24 yards long. This can be found out by using the formula for area of a rectangle , or area equals length times width. The inverse of this formula is , and since you know the area and width, just divide: Check: Solved By: NtNk