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# Recent problems solved by 'Earlsdon'

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 Exponents/34745: How would you apply a factoring formula to completely factor the expression "x4 - 1"? 1 solutions Answer 21019 by Earlsdon(6291)   on 2006-04-24 11:33:36 (Show Source): You can put this solution on YOUR website!Can you see this expression as the difference of two squares? The difference of two squares is factorable thus: Apply this to your problem. Notice that the second parentheses is again the difference of two squares and can be factored as before. Putting it all together, we have:
 Polynomials-and-rational-expressions/34750: I need to find the value of f(-4).1 solutions Answer 21013 by Earlsdon(6291)   on 2006-04-24 11:15:32 (Show Source): You can put this solution on YOUR website!It would be of great help if you were to provide the function: f(x) = ???
 real-numbers/34749: The quotient of two fractions is equal to the product of the first and the reciprical of the second. Why? a/b/c/d=a/bx1/c/d=a/bxd/c ?1 solutions Answer 21012 by Earlsdon(6291)   on 2006-04-24 11:13:36 (Show Source): You can put this solution on YOUR website!I would say...because multiplication is the inverse operation of division, so the quotient of two numbers (not just fractions) is the same as the product of the first and the inverse (reciprocal) of the second. You have really done a double-inverse here so the result is the same.
 Equations/34717: I cant figure out how to solve this equation. 2(2x+9)=-16 Can you please help me?1 solutions Answer 20967 by Earlsdon(6291)   on 2006-04-23 22:25:02 (Show Source): You can put this solution on YOUR website!Solve for x: Divide both sides of the equation by 2.. Subtract 9 from both sides. Finally, divide both sides by 2. x = -8.5
 Equations/34639: Hi, I would appreciate your help simplifying this. Please show me how this is a hard one! 4xy^3/16x^2y Thank you1 solutions Answer 20911 by Earlsdon(6291)   on 2006-04-23 12:25:55 (Show Source): You can put this solution on YOUR website!Simplify: = Cancel the common factor:4xy
 Linear-systems/34580: please help me solve this.. i don't even know where to begin. :( 1 solutions Answer 20865 by Earlsdon(6291)   on 2006-04-22 17:10:51 (Show Source): You can put this solution on YOUR website!Solve: First add d to both sides of the equation. Now add 7 to both sides. Finally, divide both sides by 7.
 Polynomials-and-rational-expressions/34577: please help me with this problem solve for x x=3/x+1 this is what i have so far x(x+1)=3 (x+3)(x-1)=0 ?1 solutions Answer 20864 by Earlsdon(6291)   on 2006-04-22 17:08:03 (Show Source): You can put this solution on YOUR website!Solve for x: Your first step is correct. Multiply both sides by (x+1) Simplify...here's where you erred! Subtract 3 from both sides. Solve this quadratic equation using the quadratic formula:.
 Miscellaneous_Word_Problems/34543: A Square with and area of 16 is partitioned into four congruent small squares. What is the area of the cirle that passes through the centers of the four similar squares?1 solutions Answer 20843 by Earlsdon(6291)   on 2006-04-22 10:26:08 (Show Source): You can put this solution on YOUR website!1) A square whose area is 16 has sides of 4. 2) If partitioned into four congruent squares, the smaller squares will have sides of 2. 3) The center of the smaller squares will be at a distance of from the center of the parent square. 4) The radius of the circle whose circumference contains the centers of the four smaller squares will be. 5) The area of the circle is: If statement 3) is not obvious, here's how I determined that. From the center of one of the smaller squares, drop a perpendicular to one of its sides thus bisecting that side. You will have formed a right triangle whose legs are 1 each and whose hypotenuse is (See Pythagorean theorem). The hypotenuse is the radius of the circle.
 logarithm/34520: solve this exponential equation to the nearest hundreth 2e^4x=8 help :(1 solutions Answer 20792 by Earlsdon(6291)   on 2006-04-21 21:47:23 (Show Source): You can put this solution on YOUR website!Solve for x: Divide both sides by 2. Take the natural log (ln) of both sides. Simplify. But ln(e) = 1
 Numeric_Fractions/34439: This question is from textbook Modern Mathematics for Elementary Educators Find a fraction equivalent to 1/2 such that the product of the numerator and the denominator is 72.1 solutions Answer 20788 by Earlsdon(6291)   on 2006-04-21 21:38:30 (Show Source): You can put this solution on YOUR website!Try this: Let x = the numerator and y = the denominator. Rewrite this as: and substitute below. Solve for x. Divide both sides buy 2. Take the square root of both sides. x = +or-6 y = 2x y = +or-12 There are two answers: In both of these fractions, the product of the numerator (6 or -6) and the denominator (12 or -12) = 72
 Polynomials-and-rational-expressions/34494: Find the quotient: 12x^8 y^8/-3x^5 y^31 solutions Answer 20769 by Earlsdon(6291)   on 2006-04-21 15:53:28 (Show Source): You can put this solution on YOUR website!Find the quotient: Recall: When dividing monomials with the same base, you just subtract their exponents. Example: = and = so:
 Graphs/34493: This question is from textbook College algebra Thank you so much for taking the time to help students like me that are in way over thier heads. I am that is for sure. I really appericate it. Thanks again. First heres the directions; for the points P and Q, find (a)the distance d(P,Q) and (b) the coordinates for the midpoint of the segment PQ. #10 P(-4,3), Q(2,-5) This is what I did... d(P,R)= (under the radical sign) (2-(-4)squared + (-5-3)squared =(2+4) squared + (-5-3)squared =2Squared + 4squared + -5squared -3squared =6squared + -8squared =36+64= 100 under radical sign Heres the midpoint; -4+2/2squared, 3+-5/2squared = -1 and -2/5 I hope you were able to figure out what I did. I am pretty sure I got @ least part of it right. Thanks again. Have a great day. 1 solutions Answer 20767 by Earlsdon(6291)   on 2006-04-21 15:42:29 (Show Source): You can put this solution on YOUR website!It looks like you will have the right distance when you take the square root of 100. For the distance between P(-4, 3) and Q(2, -5): For the coordinates (x, y) of the midpoint of PQ: and and and and The coordinates of the midpoint are: (-1, -1)
 Equations/34490: Hello! Thank you for your time. I've been trying to solve this for a week now. Solve for y. X=51n(7+3y)for y. 1 solutions Answer 20765 by Earlsdon(6291)   on 2006-04-21 15:19:05 (Show Source): You can put this solution on YOUR website!Solve for y: First divide both sides by 5. Convert to exponential form: means so for your problem: means: Subtract 7 from both sides. Finally, divide both sides by 3. ...and there you have it!
 Mixture_Word_Problems/34435: I am trying to work a problem that my teacher gave me on a worksheet. We have worked other problems but none like this one. Could you please help. thanks!! An industrial chemist has a solution that is 60% alcohol. After she draws off 5L and replaces it with 5L of alcohol the resulting solution is 85% alcohol. How many liters does she have?1 solutions Answer 20692 by Earlsdon(6291)   on 2006-04-20 23:56:21 (Show Source): You can put this solution on YOUR website!A little common sense will reveal that if you remove 5 liters of the original liquid and replace it with 5 liters of another liquid, you have exactly the same amount you started with.
 test/34445: When using the quadratic formula to solve , what is the value of A?1 solutions Answer 20689 by Earlsdon(6291)   on 2006-04-20 23:47:40 (Show Source): You can put this solution on YOUR website!The general form for the quadratic equation is: Compare this with your equation:
 Trigonometry-basics/34342: Find the area of a segment of a circle if the diameter is 12 inches and the central angle is pi/4 radians? 1 solutions Answer 20603 by Earlsdon(6291)   on 2006-04-20 10:32:57 (Show Source): You can put this solution on YOUR website!First find out how much of the whole circle is radians. There are radians in a complete circle, so you need to divide by The segment is of the entire cicle, so the area of the segment will be the area of the entire circle. But = This is the area of the entire circle. Divide by 8 the get the area of the segment. Area of the segment is: Square inches.
 Exponential-and-logarithmic-functions/34349: This question is from textbook advanced algebra what is log3 + log51 solutions Answer 20600 by Earlsdon(6291)   on 2006-04-20 10:13:07 (Show Source): You can put this solution on YOUR website!Use the "Product Rule" for logarithms: =
 Rational-functions/34348: I am having difficulty with inverses of functions: What is the inverse of the following function: Heres what I did: When it is checked however, it does not work: This check works, but... This doesn't, I found the graph of the inverse of the function, but I need the equation. Please help! Thank you, Sally Mat 1 solutions Answer 20597 by Earlsdon(6291)   on 2006-04-20 10:02:04 (Show Source): You can put this solution on YOUR website!Well, you have the right idea but your algebra was a little off! Exchange the x and y and solve for x. Subtract 1 from both sides. Multiply both sides by y. Finally, divide both sides by x-1 Note! x = 1 not allowed.
 Linear_Equations_And_Systems_Word_Problems/33976: A cashier at Apex Parts received a check for \$2380 for 59 parts. The parts cost \$20 and \$50 but the number wanted of each wasn't given. How many of each can be bought with that amount?1 solutions Answer 20344 by Earlsdon(6291)   on 2006-04-17 23:14:23 (Show Source): You can put this solution on YOUR website!Let x = the number that can be bought for \$20.00 each, then (59-x) = the number that can be bought for \$50.00 each. You can write: \$20(x) + \$50(59-x) = \$2380 Simplify and solve for x. \$20(x) + \$2950 - \$50x = \$2380 -\$30(x) + \$2950 = \$2380 Subtract \$2950 from both sides. -\$30(x) = -\$570 Divide both sides by -\$30. x = 19 59-x = 40 19 can be bought at \$20.00 each 40 can be bought at \$50.00 each.
 Percentage-and-ratio-word-problems/33981: The ratio of the measures of the three sides of a triangle is 3:4:6. If the perimeter is 91, find the measure of the longest side.1 solutions Answer 20343 by Earlsdon(6291)   on 2006-04-17 22:58:19 (Show Source): You can put this solution on YOUR website!Try this: Simplify and solve for x. Divide by 13. 3x = 3(7) = 21 4x = 4(7) = 28 6x = 6(7) = 42 This is the measure of the longest side.
 Polygons/33843: find the no of sides of regular convex polygon whose angle is 40 deg? 1 solutions Answer 20242 by Earlsdon(6291)   on 2006-04-17 10:52:23 (Show Source): You can put this solution on YOUR website!The measure of one vertex angle of a regular polygon is given by: where n is the number of sides of the regular polygon...and, of course, it goes without saying, that n must be an integer >2(i.e, 3, 4, 5, 6, ...). If the measure of one vertex angle of a regular polygon is 40 degrees, then we can write: Simplify and solve for n. Multiply both sides by n. Add 360 to both sides. Subtract 40n from both sides. Divide both sides by 140. This is not possible since a regular polygon must have an integral numer of sides. Conclusion: There is no regular polygon whose vertex angle is 40 degrees.
 Polynomials-and-rational-expressions/33809: Please help me solve this equation by factoring:1 solutions Answer 20204 by Earlsdon(6291)   on 2006-04-16 22:14:50 (Show Source): You can put this solution on YOUR website!Solve by factoring: Factor. Apply the zero products principle. and/or If then and If then The roots are:
 Polynomials-and-rational-expressions/33693: I need help on this: Find a polynomial equation of lowest degree with integer coefficients and has 0,3, and also plus/minus square root of 2 as zeros.1 solutions Answer 20109 by Earlsdon(6291)   on 2006-04-15 14:11:33 (Show Source): You can put this solution on YOUR website!Since the required polynomial has 4 zeros (roots) it has to be a 4th degree polynomial. If x = 0 is a root, then x is a factor. If x = 3 is a root, then x - 3 is a factor. If x = (+-) are roots, then and is a factor. Now we can get the equation by multiplying the known factors.
 Surface-area/33541: This question is from textbook Addison-Wesley Geometry May you please help me with this question??: If the volume of a right cone is 72p(72 PI, can't put the sign on, srry), find the surface area if its height and radius are equal. Thank you.1 solutions Answer 20108 by Earlsdon(6291)   on 2006-04-15 13:07:35 (Show Source): You can put this solution on YOUR website!Let's first find the radius of the right circular cone from the given information. The volume of a right circular cone is given by: = but since r = h we can rewrite this and simplify it. Divide both sides by and multiply both sides by 3. Take the cube-root of both sides. So the radius, r = 6 The surface (lateral) area of a right circular cone is given by: but since r = h, we can rewrite this and simplify it. Now substitute r = 6. This is the surface area of the cone.
 Quadratic_Equations/33680: The height of a triangle is 2 millimeters less than the base. If the area is 60 square millimeters, find the base.1 solutions Answer 20105 by Earlsdon(6291)   on 2006-04-15 11:32:02 (Show Source): You can put this solution on YOUR website!Start with the formula for the area of a triangle: Where: A = 60, h = b-2 Simplify and solve for b. Multiply both sides by 2. Subtract 120 from both sides of the equation. Solve this quadratic for b by factoring. Apply the zero products principle. and/or If then Discard this solution as b can only be a positive value. If then This solution is acceptable. The length of the base is 12 mm. The height would be 10 mm Check: sq.mm.
 Linear_Algebra/33689: THe instructions say divide. The problem itself is (4x-4 / x) / (10x-10 / 7x^2). I have come up with 28x^2(x-1) / 10x(x-1). Can anyone please tell me if this is the correct answer. Thanks in advance. 1 solutions Answer 20102 by Earlsdon(6291)   on 2006-04-15 11:03:52 (Show Source): You can put this solution on YOUR website!Divide: Recall..."invert the 2nd fraction and multiply"? Simplify. Cancel the common factors: (x) and (x-1) Simplify.
 Human-and-algebraic-language/33687: This question is from textbook Algebra 1 It takes 10 hours to fill a pool with water, and 20 hours to drain it. If the pool is empty and the drain is open, how long will it take to fill the pool?1 solutions Answer 20101 by Earlsdon(6291)   on 2006-04-15 10:50:12 (Show Source): You can put this solution on YOUR website!In 1 hour, you can fill 1/10 of the pool and in 1 hour you can empty 1/20 of the pool. If the two events occur simultaneously, then in 1 hour you can fill 1/10 - 1/20 = 1/20 of the pool. So, at this rate, it will take 20 hours to fill the pool with the drain open.
 Quadratic_Equations/33685: I don't know how to solve x(to the fourth) minus (five x squared) plus four. In school we did something called a diamond formula or something with a diamond and it makes everything easier but i don't understand. Can you explain to me how to solve this by the diamond formula. Thank you.1 solutions Answer 20100 by Earlsdon(6291)   on 2006-04-15 10:41:06 (Show Source): You can put this solution on YOUR website!Well, I don't believe I've heard of the "diamond formula" for solving 4th-degree polynomials. But try this method: Solve: Rewrite this as: Temporarily set Solve this quadratic equation in y by factoring. Apply the zero products principle. and/or If then If then But, , so: Take the square root of both sides. or and: Take the square root of both sides. or The roots are: x = 1 x = -1 x = 2 x = -2
 Square-cubic-other-roots/33668: Express irrational solutions in simplest radical form. N^2-6=0 Would this be (+-)Sqrt 5? (n-5)^2=20 Would this be (+-)2*Sqrt 5?1 solutions Answer 20072 by Earlsdon(6291)   on 2006-04-14 20:54:38 (Show Source): You can put this solution on YOUR website!Solve: Add 6 to both sides. Take the square root of both sides. N = (+-) Take the square root of both sides. n-5 = (+-) Simplify the right side and add 5 to both sides. n = 5(+-)
 real-numbers/33667: A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Brown insisted on giving the man an award for his heroism. So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies.” As he’d been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved. a)How much money would Mr. Brown have to put on the 32nd square? b)How much would the traveling salesman receive if the checkerboard only had 32 squares? c)Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How much money would the farmer need to give the salesman? 1 solutions Answer 20071 by Earlsdon(6291)   on 2006-04-14 20:43:01 (Show Source): You can put this solution on YOUR website!This question has been answered. See my response # 19996 but if you are looking for a second opinion, then I appologise for responding.