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# Recent problems solved by 'ichudov'

ichudov answered: 497 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

 Square-cubic-other-roots/196: is one a square number 1 solutions Answer 61 by ichudov(499)   (Show Source): You can put this solution on YOUR website!Sure, one is a square of one itself and also of -1: 1=1 x 1 1= -1 x -1
 Polynomials-and-rational-expressions/197: under what situation would one or more solutions of a rational equation be unacceptable?1 solutions Answer 62 by ichudov(499)   (Show Source): You can put this solution on YOUR website!Let's say a problem asks you to compute a length of something, or some other positive number. And let's say that the problem is expressed as a quadratic equation with one solution positive and one negative. In this instance, the negative solution is unacceptable.
 Quadratic_Equations/198: why are there usually two solutions in quadratic equations?1 solutions Answer 63 by ichudov(499)   (Show Source): You can put this solution on YOUR website!Good question. A graph of a quadratic equation is a parabola, and because it has two wings pointing inthe same direction, a parabola could cross the x axis twice. By the way, cubic equations can have up to 3 different solution, quartic (4th power) equations can have up to 4 solutions, etc.
 Money_Word_Problems/199: An airline has 2000 passengers each day paying \$100 each, and knows that for each \$10 increase in price they lose 50 passengers. What would be the equation that would determine their maximum revenue? 1 solutions Answer 64 by ichudov(499)   (Show Source): You can put this solution on YOUR website!Airline's revenue is: Number of passengers * ticket price. Number of passengers also depends on ticket price: Number of passengers = 2,000 - 50 * (ticket price - 100)/10 So, airline's revenue is: (2,000 - 50 * (ticket price - 100)/10)*ticket price Denote ticket price as x Revenue = (2000-50*(x-100)/10)*x When you simplify it, you get a quadratic expression, that you can plot on my site.
 Age_Word_Problems/200: what if the teacher asks what is the half of the sum of the brother of my cousin which is 12 and my sister which is 14 after 26 years from my birth... i am 8 years old...???1 solutions Answer 65 by ichudov(499)   (Show Source): You can put this solution on YOUR website!That's a tough problem for an 8 year old, I am rather impressed. After 26 years, the brother of your cousin will be 12+26 years old, and your sister will be 14 + 26. So, your cousin will be 38 and your sister will be 40 (which is VERY old). The sum of their ages will be 78, half of that sum will be 39.
 Rectangles/201: The length of a rectangular park is 4 m longer than the width. If the area of the park is 140 m^, find the length and the width.1 solutions Answer 66 by ichudov(499)   (Show Source): You can put this solution on YOUR website!We have length = width + 4. The area is length*width and is 140. Because length = width+4, we have (width+4)*width = 140, or . That's a simple quadratic equation that you can solve on my website. (10 seems to be the obvious root)
 Mixture_Word_Problems/202: How can you get 6 cups of a liquid using a container that holds 4 cups and another one that holds 9 cups?1 solutions Answer 67 by ichudov(499)   (Show Source): You can put this solution on YOUR website!If you fill a 9 cup container, and then pour off to fill a full 4 cup container, dump water from the 4 cup container and fill it again, you would be left with 9-4-4 = one cup of water in the big container. Pour that one cup of water into the 4 cup container and set it aside. Fill the 9 cup again, pour off 3 cups into the 4 cup container (which already holds one cup, so it has space for 3 more cups), you will end up with 6 cups in the big container.
 Numbers_Word_Problems/203: If the original number is 2400 and you need to find 3 numbers to equal that number, one being 25% higher than the remaining 2 which are equal...how do I calulate that and get the answer?1 solutions Answer 68 by ichudov(499)   (Show Source): You can put this solution on YOUR website!Your task here is mainly to write an equation. Write it in words first: number PLUS same number PLUS same 1.25 * number = 2400. Replace number with x: x + x + 1.25*x = 2400 3.25*x = 2400 this equation does not solve for a natural number x, the result is x = 738.461..., which makes me suspect that you either mis-stated the problem or I did not understand it.
 percentage/204: what percent of 1800 is 400? 1 solutions Answer 69 by ichudov(499)   (Show Source): You can put this solution on YOUR website!there is a calculator for this on my site.
 percentage/205: I would like to know how to convert percentages to degrees in order to make a pie chart. So what i would like to know is how to show my working out fully. It would be great if you could show me an example.1 solutions Answer 70 by ichudov(499)   (Show Source): You can put this solution on YOUR website!This is a great question. When you draw pie charts, you deal with numbers as percentages of the total. So, let's say some number is 10% of the total (0.1, or one tenth). What angle should it require in a pie chart? There are 360 degrees in the pie. The angle should be 0.1 times 360, or 36 degrees. This way, just as all numbers in a total add to 100% of the total, all angles in the pie chart will also add up to 360 degrees.
 Money_Word_Problems/206: A person invested \$2,000, part at 7% and part at 8% simple interest. If the total yearly interest from these investments was \$154, how much was vested at each rate? How many gallons of a 70% alcohol solution must be mixed with 30 gallons of a 15% alcohol solution to obtain a solution that is 60% alcohol?1 solutions Answer 71 by ichudov(499)   (Show Source): You can put this solution on YOUR website!You should ask two questions separately, but here goes. Denote the amount invested at 7% as x dollars. The remaining amount to be invested is, obviously, 2000-x. Amount of interest at 7% is x*0.07. Amount of interest invested at 8% is (2000-x)*0.08. So, we have x*0.07+(2000-x)*0.08 = 154. x*0.07+2000*0.08 - x*0.08 = 154 2000*0.08-154 + x*0.07 - x*0.08 = 0 160-154-0.01x = 0 6 = 0.01x x = 600, 2000-x = 1400 Answer: He invested \$600 at 7% and \$1,400 at 8%. Regarding your unhealthy interest in alcohol solutions :), I have a word problem solver for exactly this problem. Go to word problems from my home page.
 percentage/207: If there are 2,347,690 employees this year and it is a 43.7 percent increase from the previous year. What was the former number of employees?1 solutions Answer 72 by ichudov(499)   (Show Source): You can put this solution on YOUR website!43.7% increase means that the number of employees this year is 1.437 times the number of employees last year. That means that the number of employees last year was times the number of employees this year, or , or 1633744 employee.
 percentage/208: Can a percentage be more than 100?yes it can1 solutions Answer 73 by ichudov(499)   (Show Source): You can put this solution on YOUR website!A percentage is a ratio of one number to another, expressed in 's. So, if the first number is bigger than another, then the percentage would be above 100. For example, if your car can go 60 mph and you expected it to go only 50 mph, then it will go at 120% the expected speed.
 logarithm/209: When solving the equation e to the power of x = -2 can we write x = ln(-2) ?1 solutions Answer 74 by ichudov(499)   (Show Source): You can put this solution on YOUR website!If you are studying complex numbers (and know what is an imaginary number i), then we can write exponents of e that give negative results. If you are studying basic logarithms and exponents and do not know what i is, then the above equation makes no sense.
 Functions/210: given f(3)=7, find f-1(7). the negative one is the exponent.1 solutions Answer 75 by ichudov(499)   (Show Source): You can put this solution on YOUR website!My guess is that f-1(7) is the inverse function and -1 is not an exponent but a sign of inverse function. If so, then f-1(7) = 3.
 Polynomials-and-rational-expressions/211: 6X^6+x^3=15 solve for X1 solutions Answer 76 by ichudov(499)   (Show Source): You can put this solution on YOUR website!What this really is is a quadratic equation. Note that (see lesson on logarithms). So, replace with y. You will have: . Solve it for y, you can use my quadratic solver on this website which will show work. Once you get y, solve equation , which means take third root of y.
 logarithm/212: What is a logarithm of a negative number?1 solutions Answer 77 by ichudov(499)   (Show Source): You can put this solution on YOUR website!A logarithm is only defined for positive numbers. The reason is that for most negative numbers, powering then to, say, degree is impossible. Power of 1/2 means square root and, as we know, there is no real number representing a square root of a negative. So, non-integer powers and logarithms are defined only for positive numbers.