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# Recent problems solved by 'richard1234'

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 Graphs/397729: can you graph y=+2+x1 solutions Answer 281804 by richard1234(5390)   on 2011-01-20 23:31:22 (Show Source):
 Travel_Word_Problems/397717: A driver leaves on a road trip at 8:00am. The function v(t) is the speed he is traveling t hours after the start of the trip. What value of t should be used so that v(t) will represent the driver's speed at 9:40 am? (three decimal places)1 solutions Answer 281802 by richard1234(5390)   on 2011-01-20 23:25:34 (Show Source): You can put this solution on YOUR website!At 9:40, t = 1 hour 40 minutes = 5/3 hours, so use t = 5/3 or 1.667.
 Expressions-with-variables/397724: Please help me solve this practice test question: If ab=10, and a-squared + b-squared = 30, solve for y in the equation, y=(a+b)squared. Can you explain it also? Many thanks! a. 40 b. 45 c. 50 d. 551 solutions Answer 281801 by richard1234(5390)   on 2011-01-20 23:23:41 (Show Source): You can put this solution on YOUR website!We have and . Since , we can substitute and to obtain so choice C is correct.
 Triangles/397725: How could I find the altitude of the triangle with only two sides given?1 solutions Answer 281800 by richard1234(5390)   on 2011-01-20 23:13:26 (Show Source): You can put this solution on YOUR website!It's impossible. Two sides alone cannot uniquely determine a triangle.
 Polynomials-and-rational-expressions/397710: Here is a word problem I am having difficulty getting started on. I don't have an example in my book to help. A population of deer in a state forest was rapidly decreasing due to over-hunting. To prevent further population decline, lawmakers enacted hunting restrictions. A biologist studying the deer found that, with the hunting restrictions in effect,t he growth of the deer population could be modeled by N= 0.6x^4-20x^3+225x^2-950x+2300 where N represents the number of deer and x represents the number of years the restrictions are in effect. Using this model, estimate what the deer population would be if the hunting restrictions were kept in effect for 15 years.1 solutions Answer 281793 by richard1234(5390)   on 2011-01-20 22:12:05 (Show Source): You can put this solution on YOUR website!It's a little difficult to estimate with x = 15 because of those nasty coefficients in the other terms. It's much better just plugging x = 15 into a calculator, or on paper.
 Complex_Numbers/397698: How do i solve the equation _ What is the square root of 4-7i?1 solutions Answer 281790 by richard1234(5390)   on 2011-01-20 22:08:06 (Show Source): You can put this solution on YOUR website!It is indeed possible to solve it using Euler's formula, by multiplying/dividing by to obtain a unit vector and obtaining: where and . However, the easiest way is probably to assume that the square root of is for real numbers a,b. Squaring both sides, Equating the real and imaginary parts, we get the system of equations --> ab = -7/2. Using the substitution b = -7/2a, Use the quadratic formula to solve for then take the square root. Note that must be positive based on our assumption that a and b are real numbers. After that, the rest is just arithmetic.
 Miscellaneous_Word_Problems/397649: Using four 4s and any mathematical operation (+, -, X, /, Sq. root, Exponents, i, etc.), complete an operation that equals 37. Example 44 / 4 - 4 = 7.1 solutions Answer 281776 by richard1234(5390)   on 2011-01-20 21:46:34 (Show Source): You can put this solution on YOUR website!Eh, closest I got was , or . This is probably cheating, but...
 Miscellaneous_Word_Problems/397536: What is the distance from Langhorne to Newtown if the car is traveling 35miles/hr up Rt.413 for 0.12seconds.... this is a sience problem. i am have terrible troble not because i can't find the answer more because i dont under stant why i could travel from one city to another in .12 sesonds PLESE HELP!!!1 solutions Answer 281764 by richard1234(5390)   on 2011-01-20 21:33:06 (Show Source): You can put this solution on YOUR website!Maybe the two cities are that close together. I have no idea...did you write the problem correctly?
 Radicals/397677: I'm stuck could you please help me here. Find f(2a) if f(x) =2-x^3 + 2x-5. I'm reviewing for a test tomorrow. thanks, Pete1 solutions Answer 281758 by richard1234(5390)   on 2011-01-20 21:28:01 (Show Source): You can put this solution on YOUR website!Replace all occurrences of x with 2a, and simplify.
 test/397646: 6 years ago bob was 4 times as old as Mary. In 4 years he will be twice as old as Mary. How old are they?1 solutions Answer 281756 by richard1234(5390)   on 2011-01-20 21:26:14 (Show Source): You can put this solution on YOUR website!Let b and m be Bob's and Mary's ages. Then, b-6 = 4(m-6) --> b-6 = 4m - 24 b+4 = 2(m+4) --> b+4 = 2m + 8 This is essentially a system of equations that can be solved for b and m. Solving using any method (I used substitution), we get m = 11, b = 26, so Mary is 11 and Bob is 26.
 Polynomials-and-rational-expressions/397683: How Can I find the quotient and the residue by using synthetic division?? / I have tried but I cant figure out a way x^2 can go into x^5.... Please help!1 solutions Answer 281753 by richard1234(5390)   on 2011-01-20 21:18:31 (Show Source): You can put this solution on YOUR website!Synthetic division only works when you're dividing by a polynomial of degree 1. Try dividing by x-1 then by x+1...or use long division. Btw x^2 goes into x^5 a total of x^3 times.
 Square-cubic-other-roots/397608: What is the square root of 1491 solutions Answer 281742 by richard1234(5390)   on 2011-01-20 20:39:06 (Show Source): You can put this solution on YOUR website!Roughly 12.2065556.
 Miscellaneous_Word_Problems/397447: If 5 to the n power is > than 10,000 and n is an integer, what is the smallest possible value of n? The answer is 6 but how is that figured?1 solutions Answer 281739 by richard1234(5390)   on 2011-01-20 20:34:56 (Show Source): You can put this solution on YOUR website!This is because 5^5 = 3125, and 5^6 = 15625, which is greater than 10000.
 Numbers_Word_Problems/397591: The sum of the digits of a two-digit number is 13. Twice the first digit is 1 less than the second digit. What is the two-digit number?1 solutions Answer 281734 by richard1234(5390)   on 2011-01-20 20:29:08 (Show Source): You can put this solution on YOUR website!Suppose the digits are d and 13-d. Then, 2d = (13-d)-1 = 12-d Solving, d = 4, 13-d = 9. If 4 is the first digit (which satisfies the statement), then the number is 49.
 Rectangles/397638: the perimeter of a rectangle is 100 ft. if its width is four times the length, then what is the area?1 solutions Answer 281731 by richard1234(5390)   on 2011-01-20 20:27:07 (Show Source): You can put this solution on YOUR website!If the length is L and the width is 4L, then 2(L + 4L) = 100 --> L + 4L = 50 --> L = 10, 4L = 40 The dimensions are 10 and 40, so the area is 400.
 Points-lines-and-rays/397519: I am doing something in math and I need the definition of "point." I looked in my math book, and there is no definition! I looked EVERYWHERE! Please can I have a good definition?1 solutions Answer 281729 by richard1234(5390)   on 2011-01-20 20:21:39 (Show Source): You can put this solution on YOUR website!I would do exactly what the other tutor did...just Google it. In fact, over 1.2 billion results showed up on my browser in .16 seconds.
 test/397578: What is the slope intercept form of this equation 5x+y=61 solutions Answer 281727 by richard1234(5390)   on 2011-01-20 20:19:22 (Show Source): You can put this solution on YOUR website!y = -5x + 6
 Expressions-with-variables/397642: 8. Write the expression using exponents. Do not solve. b ∙ b ∙ b ∙ b ∙ b ∙ b ∙ b 1 solutions Answer 281726 by richard1234(5390)   on 2011-01-20 20:17:30 (Show Source): You can put this solution on YOUR website!b is multiplied seven times. So the exponent is .
 Square-cubic-other-roots/397611: How do you simplify complex Radical numbers ? ex: 3(squareroot of 3) - 1 ----------------------- 3(squareroot of 2) - 11 solutions Answer 281724 by richard1234(5390)   on 2011-01-20 20:12:56 (Show Source): You can put this solution on YOUR website!Btw, these do not involve complex numbers so I have changed the subject. However, some of these techniques can be used to simplify complex number expressions. Multiply both sides by the conjugate of the denominator, i.e. to produce A consequence of the difference of two squares theorem, this ensures the denominator will be an integer.
 Equations/397630: (x-4)^4= 811 solutions Answer 281722 by richard1234(5390)   on 2011-01-20 20:07:21 (Show Source): You can put this solution on YOUR website!81 has four roots of unity: 3, 3i, -3, -3i. We have the equations x-4 = 3 x-4 = 3i x-4 = -3 x-4 = -3i all of which can easily be solved for x.
 Complex_Numbers/396778: How do I use a graph to demonstrate the operation of these complex numbers? 1. (7-6i)+(-5-2i) 2. (5-9i)-(-3-12i) Thank you for your help!1 solutions Answer 281530 by richard1234(5390)   on 2011-01-19 22:41:58 (Show Source): You can put this solution on YOUR website!Complex numbers add exactly like vectors do. For example, on the first question, you have the complex number , which is equivalent to a vector with an x-component of 7 and a y-component of -6. You're adding which is another vector. To add them graphically, you could use the parallelogram rule or the head-to-tail method. The second one is similar, but you have to subtract the vectors instead. (Hint: vectors follow the commutative properties and other arithmetic properties as real numbers do!)
 Linear-systems/396878: Please solve this for me, this is on Graph of Linear Equations. Please tell me how you arrived at the answer. y-x +11 solutions Answer 281525 by richard1234(5390)   on 2011-01-19 22:34:04 (Show Source): You can put this solution on YOUR website!There's nothing to solve for.
 Functions/396562: f(x)=3x^2-2x f(0)=3(0)^2-2(0)=0 likewise for f-(-1), let x=-1 f(-1)=5 i don't undestand how they came up with 5 finally (2)=2(2)^2-2(2)=81 solutions Answer 281523 by richard1234(5390)   on 2011-01-19 22:33:19 (Show Source): You can put this solution on YOUR website!f(-1) = 5 because f(-1) = 3(-1)^2 - 2(-1) = 3 + 2 = 5.
 Probability-and-statistics/397124: Hello, I have this math brain teaser that is killing me. Can you help please? In a dark room, a boxed is filled with different colored balls there are 14 blue, 13 red, 22 black and 18 green. What is the smallest number of balls you need to select to get at least 4 of the same color. Kindest regards, Candy1 solutions Answer 281520 by richard1234(5390)   on 2011-01-19 22:24:40 (Show Source): You can put this solution on YOUR website!Note that the Pigeonhole Principle says that if there if we have kn + 1 pigeons distributed into n holes, then there is at least one hole with k+1 pigeons. In this case, n = 4 (there are four colors, or "holes"), and we want to guarantee that one of these "holes" has four "pigeons." Therefore, letting k = 3, we see that if we draw 3(4) + 1 or 13 balls, we are guaranteed to have four of the same color. If there are 12 balls, then it is possible to draw three of each color.
 Evaluation_Word_Problems/397119: Please help me solve this question! "Determine the equation of the tangent to the circle (x-2)^2+(y+3)^2=13 at the point (5,-5)"1 solutions Answer 281516 by richard1234(5390)   on 2011-01-19 22:19:52 (Show Source): You can put this solution on YOUR website!Right away, we can tell that the center of the circle is at (2, -3). It suffices to find the slope of the line between (2, -3) and (5, -5). This is because the radius of a circle is perpendicular to the line tangent to the circle at that point (5, -5). The slope of the line is . Therefore the slope of the line tangent to the circle is 3/2 (since these two lines are perpendicular). Since it runs through the point (5, -5) we can find the y-intercept: -5 = 5(3/2) + b, where b is the y-intercept. Solving, we get b = -25/2, so the equation is .
 Rectangles/397112: if they give me the measurement of one line, how do i find the measurement of the rest of the lines?1 solutions Answer 281512 by richard1234(5390)   on 2011-01-19 22:10:38 (Show Source): You can put this solution on YOUR website!Use your amazing geometry and measurement skills.
 Length-and-distance/397114: I'm so stuck on this question! I don't even know where to start! please help! "Use Coordinate geometry to verify that the triangle formed by the points (3,5) , (7,3) and (-5,4) is isosceles "1 solutions Answer 281510 by richard1234(5390)   on 2011-01-19 22:09:24 (Show Source): You can put this solution on YOUR website!The triangle can't be isosceles...this is because the distance between each pair of points is different: (3,5), (7,3) (3,5), (-5,4) (7,3), (-5,4)
 Complex_Numbers/396764: Hello, how do I figure out this complex numbers problem? Any help is greatly appreciated! The point (-4+bi)has been plotted on the complex plane and r=8. If 0°≤θ≤180° find the value of b. Leave answer as a radical. Thank you. 1 solutions Answer 281507 by richard1234(5390)   on 2011-01-19 22:04:32 (Show Source): You can put this solution on YOUR website!The magnitude of the complex number is . Simplifying, . Note that b must be positive since the angle is between 0 and 180, so .
 test/397025: Is 3.14 a rational number?1 solutions Answer 281498 by richard1234(5390)   on 2011-01-19 21:50:01 (Show Source): You can put this solution on YOUR website!Yes. 3.14 = 314/100, which is a ratio of two integers (we don't need to worry about simplifying the fraction, all we care about is that it's a ratio of two integers).
 Probability-and-statistics/397044: what are the odds that the card is not the ace of spades?1 solutions Answer 281496 by richard1234(5390)   on 2011-01-19 21:47:33 (Show Source): You can put this solution on YOUR website!There is one ace of spades in the deck, out of 52 cards. The probability of drawing a card that is not the ace of spades is 1 - (1/52) = 51/52.
 Quadratic_Equations/396941: Find the largest integral value of k such that the roots of 2x^2-5x+k are real.1 solutions Answer 281485 by richard1234(5390)   on 2011-01-19 21:37:45 (Show Source): You can put this solution on YOUR website!We want the discriminant of the equation to be nonnegative. This means, The largest integral value is 3.