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# Recent problems solved by 'ewatrrr'

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 Functions/637406: Good day tutors, I need your help with this function How do I calculate the slope of f(x) = -3x² + 5x at the point P(-1,-8) ?1 solutions Answer 401641 by ewatrrr(10682)   on 2012-08-14 14:47:23 (Show Source): You can put this solution on YOUR website! ``` Hi, f(x)= -3x^2 + 5x f '(x) = -6x + 5, when x = -1 ⇒ f '(-1) = y = mx + b (representing the Line tangent to the curve at x = -1) y = 11x + b |Using Pt(-1,-8) to solve for b -8 = 11 + b 3 = b y = 11x + 3 is the line tangent ro the cureve at (-1,-8) ```
 Circles/637413: Use the Factor Theorem to determine whether (x-3) is a factor of f(x)=x^4+12x^3+6x+2 ? Please help!1 solutions Answer 401639 by ewatrrr(10682)   on 2012-08-14 14:23:57 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: if (x-3) is a factor, then the Factor Theorem states: F(3) = 0 f(x)=x^4+12x^3+6x+2 ≠ 0, (x-3) NOT a factor ```
 Functions/637403: Derivative of this function please h( x) = -2x^2/x-1 Thanks 1 solutions Answer 401632 by ewatrrr(10682)   on 2012-08-14 13:04:53 (Show Source): You can put this solution on YOUR website! ``` Hi, h(x) = ||using the Quotient Rule h '(x) = h '(x) = h '(x) = ```
 Evaluation_Word_Problems/637396: a rocket is launched from atop a 102-foot cliff with an initial velocity of 158ft/s. substitute the values into the vertical motion formula h=-16t^2+vt+c. let h=0.use the quadratic formula to find out how long after the rocket is launched it will hit the ground. round to the nearest tenth of a second. show work.1 solutions Answer 401625 by ewatrrr(10682)   on 2012-08-14 12:47:47 (Show Source): You can put this solution on YOUR website! ``` Hi, h= -16t^2+vt+c Question states***initial velocity of 158ft/s,launched from atop a 102-foot cliff -16t^2+ 158t + 102 = 0 || ax^2 + bx + c = 0 x = 10.5 sec ```
 Numbers_Word_Problems/637389: 7) When I divided number A by number B, the answer is 6 1/4. If number A is less than 30 and number B is less than 10, what are numbers A and B?1 solutions Answer 401618 by ewatrrr(10682)   on 2012-08-14 12:34:15 (Show Source): You can put this solution on YOUR website! ``` Hi, ```
 Bodies-in-space/637373: A right circular cylinder has height 6 and volume 54pie . What is the circumference of its base?1 solutions Answer 401605 by ewatrrr(10682)   on 2012-08-14 11:14:27 (Show Source): You can put this solution on YOUR website! ``` Hi, A right circular cylinder has height 6 and volume 54pie r^2 = 9, r = 3 and ```
 Numbers_Word_Problems/637371: what is the sum of all integers between -25 and +26 1 solutions Answer 401602 by ewatrrr(10682)   on 2012-08-14 11:08:53 (Show Source): You can put this solution on YOUR website! ``` Hi, {-25, ...26} Arithemetic Sequence, d = 1 and , n = 52 0r ```
 Functions/637331: The calculation of lim 5x + 5h + 1 - (5x + 1)/h h -> 01 solutions Answer 401597 by ewatrrr(10682)   on 2012-08-14 10:33:07 (Show Source): You can put this solution on YOUR website! ``` Hi, Curious to know where the 5x + 5h + 1 - (5x + 1) came from. If You meant: ```
 Permutations/637329: On a shelf of 24 books how many combinations of arrangement are possible1 solutions Answer 401595 by ewatrrr(10682)   on 2012-08-14 10:31:16 (Show Source): You can put this solution on YOUR website! ``` Hi, On a shelf of 24 books how many combinations of arrangement are possible: 24! ```
 Exponents-negative-and-fractional/637367: How do you solve 2^(5/2) - 2^(3/2)? The fractions are fractional exponents (not mixed numbers). I submitted this question yesterday but I apologize it was in the wrong form (I did not include parentheses.)The answer is supposed to be 2^3/2 according to the answer key. I need to see it worked out line by line. Thanks so much!1 solutions Answer 401594 by ewatrrr(10682)   on 2012-08-14 10:26:39 (Show Source): You can put this solution on YOUR website! ``` Hi, Yes, parenthesis so important 2^(5/2) - 2^(3/2) 2^(3/2)[2^(2/2) - 1] 2^(3/2)[2 - 1] 2^(3/2) ```
 Matrices-and-determiminant/637361: 2xa-3xb=1.313 4xb-3xc=1.906 xa-xc=3.784 use cramer's rule to determine the value of Xa, Xb and Xc1 solutions Answer 401591 by ewatrrr(10682)   on 2012-08-14 10:22:14 (Show Source): You can put this solution on YOUR website! ``` Hi, (23.086, 14.953, 19.302) D = 1, = 23.086, = 14.953, = 19.302 Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 3 variables First let . This is the matrix formed by the coefficients of the given system of equations. Take note that the right hand values of the system are , , and and they are highlighted here: These values are important as they will be used to replace the columns of the matrix A. Now let's calculate the the determinant of the matrix A to get . To save space, I'm not showing the calculations for the determinant. However, if you need help with calculating the determinant of the matrix A, check out this solver. Notation note: denotes the determinant of the matrix A. --------------------------------------------------------- Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'x' column so to speak). Now compute the determinant of to get . Again, as a space saver, I didn't include the calculations of the determinant. Check out this solver to see how to find this determinant. To find the first solution, simply divide the determinant of by the determinant of to get: So the first solution is --------------------------------------------------------- We'll follow the same basic idea to find the other two solutions. Let's reset by letting again (this is the coefficient matrix). Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'y' column in a way). Now compute the determinant of to get . To find the second solution, divide the determinant of by the determinant of to get: So the second solution is --------------------------------------------------------- Let's reset again by letting which is the coefficient matrix. Replace the third column of A (that corresponds to the variable 'z') with the values that form the right hand side of the system of equations. We will denote this new matrix Now compute the determinant of to get . To find the third solution, divide the determinant of by the determinant of to get: So the third solution is ==================================================================================== Final Answer: So the three solutions are , , and giving the ordered triple (23.086, 14.953, 19.302) Note: there is a lot of work that is hidden in finding the determinants. Take a look at this 3x3 Determinant Solver to see how to get each determinant. ```
 Functions/637360: which is the derivative of this function 4x^3/2 i want to be sure i have the correct result1 solutions Answer 401584 by ewatrrr(10682)   on 2012-08-14 09:37:12 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: Power rule: If f(x) = ⇒ f '(x) = Be confident and work carefully, my recommendation. f(x) = f '(x) = f '(x) = 6x^(1/2) ```
 Quadratic-relations-and-conic-sections/637355: In a quadratic equations why does the y value for subsequent x values increase or decrease in a pattern. For example, in the equation x^2 -2x -3, the y value when x is 1(vertex), 2, 3, and 4 is -4(vertex), -3, 0, and 5 respectively. Every time the y value is increasing by 1, then 3, then 5, then 7, then 9, and so on. Please explain this!1 solutions Answer 401579 by ewatrrr(10682)   on 2012-08-14 09:28:58 (Show Source): You can put this solution on YOUR website! ``` Hi, y = x^2 -2x -3 | y = ax^2 + bx + c and y = |completing the Square to find Vertex form y = (x-1)^2 - 4 , , the vertex form of a parabola, where(h,k) is the vertex The pattern You are seeing is the result of the (x-1)^2 pattern x (x-1)^2 y 1 0 -4 2 1 -3 3 4 0 4 9 5 5 16 12 ```
 Quadratic-relations-and-conic-sections/637352: Why does the x^2 coefficient of the equation of a parabola determine the direction it opens?1 solutions Answer 401574 by ewatrrr(10682)   on 2012-08-14 09:02:31 (Show Source): You can put this solution on YOUR website! ``` Hi, , the vertex form of a Parabola opening up(a>0) or down(a<0), where(h,k) is the vertex and x = h is the Line of Symmetry Why does the x^2 coefficient of the equation of a parabola determine the direction it opens... As the value of the 'squared' term (which is always positve) ->infinity, that coefficient will determine which direction the parabloa heads (to +infinity or -infinity) Same Idea applies to a parabola open right or left ,the vertex form of a Parabola opening right(a>0) or left(a<0), where(h,k) is the vertex and y = k is the Line of Symmetry ```
 Probability-and-statistics/637335: in how many ways can 3 boys and 2 girls sit in a row? 1 solutions Answer 401573 by ewatrrr(10682)   on 2012-08-14 08:47:31 (Show Source): You can put this solution on YOUR website! ``` Hi, in how many ways can 3 boys and 2 girls sit in a row? Thinking of the boys and girs being 1 unit: 2! Girls themselves can be arranged in 2 ways Boys themselves can be arranged in 3! ways in how many ways can 3 boys and 2 girls sit in a row? ```
 Functions/637344: What is the value of the slope of the tangent to the curve f (x) = x ^ 3 - x ^ 2 - 2x at x = +2 Thanks is advance1 solutions Answer 401572 by ewatrrr(10682)   on 2012-08-14 08:41:09 (Show Source): You can put this solution on YOUR website! ``` Hi, What is the value of the slope of the tangent to the curve at x = +2 f (x) = x ^ 3 - x ^ 2 - 2x | Taking the 1st Derivative f '(x) = f '(2) = , the slope-value y = mx + b |Using (x,y) coordinate (2,0) to solve for b, 0 = 12 + b -12 = b EQ of the tangent line at x = 2 is y = 6x-12 ```
 Expressions-with-variables/637162: Can you please write out how to do 1/2y+6=2y+21 Thank you.1 solutions Answer 401473 by ewatrrr(10682)   on 2012-08-13 17:33:43 (Show Source): You can put this solution on YOUR website! ``` Hi, |Multiplying thru by 2 so as all denominators = 1 y + 12 = 4y + 42 -30 = 3y -10 = y and... ```
 Numbers_Word_Problems/637130: 1 1/3 times a number is equal to 6, then a =?1 solutions Answer 401472 by ewatrrr(10682)   on 2012-08-13 17:29:24 (Show Source): You can put this solution on YOUR website! ``` Hi, 1 1/3 times a number is equal to 6 a = 18/4 = 9/2 or ```
 Exponential-and-logarithmic-functions/637160: log 12x^2 - log 3x = 31 solutions Answer 401469 by ewatrrr(10682)   on 2012-08-13 17:25:23 (Show Source): You can put this solution on YOUR website! ``` Hi, log 12x^2 - log 3x = 3 0r log 12x^2/3x = 3 10^3 = 4x 1000/4 = x ```
 Geometry_Word_Problems/637148: a dog walks 32 meters completely around the perimeter of his yard. What are the possible dimensions of his rectangular yard?1 solutions Answer 401468 by ewatrrr(10682)   on 2012-08-13 17:23:12 (Show Source): You can put this solution on YOUR website! ``` Hi, 0r 8m by 8m 10m by 6m etc ```
 Percentage-and-ratio-word-problems/637134: 2 + 3 1/7 equals what and why when adding mixed numbers1 solutions Answer 401450 by ewatrrr(10682)   on 2012-08-13 16:28:04 (Show Source): You can put this solution on YOUR website! ``` Hi, 0r starting at adding 2, lands one on ```
 Linear-equations/637127: Each of the following is a system of equations that is NOT linear. Each is linear in form because an appropriate substitution (say 'u' for 1/x and 'v' for 1/y) yields a linear system. Solve for the new variable, and then solve for the original variable. 2/x + 1/y = 0 5/x + 2/y = -5 I would highly appreciate it if you could help.1 solutions Answer 401448 by ewatrrr(10682)   on 2012-08-13 16:05:32 (Show Source): You can put this solution on YOUR website! ``` Hi, 2/x + 1/y = 0 5/x + 2/y = -5 'u' = 1/x and 'v' = 1/y **** 2u + v = 0 |multiplying thru by -2 to eliminate the v variable 5u + 2v = -5 u = -5 and v = 10 x = 1/-5 and v = 1/10 and... ```
 Finance/637110: Good day Can someone help me with this problem If a construction company purchased a machine in 2010, for the value of USD 150 000. And we know also that the machine has a constant annual depreciation of USD 5500. Which is the value of the parameter m (slope) THANKS1 solutions Answer 401446 by ewatrrr(10682)   on 2012-08-13 15:56:49 (Show Source): You can put this solution on YOUR website! ``` Hi, (1, 9500) (0, 15000) m = (9500-15000)/1 = -5500 Value = -5500x + 15000 , where x is the number of years from 2010. ```
 Polynomials-and-rational-expressions/637123: Please help me solve this problem: (x^3 - 13x^2 - 41x + 4) / (x - 7) Right now I have the answer as x^2 -6x + 48 I don't think what I have so far is right, and I don't know how to finish it. Please help, thank you.1 solutions Answer 401444 by ewatrrr(10682)   on 2012-08-13 15:49:02 (Show Source): You can put this solution on YOUR website! ``` Hi, (x^3 - 13x^2 - 41x + 4) / (x - 7) may use Synthetic Divsion for this ex. 7 1 -13 -41 4 7 -42 -581 1 -6 -83 -577 Yields x^2 - 6x - 83 R = -577 ```
 Mixture_Word_Problems/637105: the cost of producing x units of a product is C=0.4x^2+16x+10 and therefore the average cost per unit is C=C/x=(0.4x^2+16x+10)/x, 0< x Sketch the graph of the average cost function and use it to estimate the number of units that should be produced to minimize the average cost per unit.1 solutions Answer 401433 by ewatrrr(10682)   on 2012-08-13 14:56:19 (Show Source): You can put this solution on YOUR website! ``` Hi, C=0.4x^2+16x+10 x > 0 C = .4x + 16 + 10/x C' = .4 - 10/x^2 .4 - 10/x^2 = 0 x^2 = 10/.4 = 25 x = 5, units that should be produced to minimize the average cost per unit ```
 Linear-systems/637104: Using the addition method, how do I solve for 1/4x+1/3Y=5 and x-y=6?1 solutions Answer 401427 by ewatrrr(10682)   on 2012-08-13 14:29:36 (Show Source): You can put this solution on YOUR website! ``` Hi, 1/4x+1/3y= 5 || |multiplying thru by 3 to eliminate the y variable x - y= 6 x = x = 12 and y = 6 and ```
 Miscellaneous_Word_Problems/637069: In the following sum the same two numbers are needed. When they are added or mutliplied together, they form the answers for (a) and (b). I need to work out what theose numbers are (a) ............+........... = 2.7 (b) ............x........... = 1.8 Can anone help me with the following I just cnat seem to get it thanks I have already submitted this question but my email address was wrong1 solutions Answer 401415 by ewatrrr(10682)   on 2012-08-13 13:49:43 (Show Source): You can put this solution on YOUR website! ``` Hi, The 'clue' to the problem is the numbers must end with something that results in a zero in the hundredths place when multiplied: x + y = 2.7 x^2 - 2.7x + 1.8 = 0 | x = 1.5 0r x = 1.2 ```
 test/637036: X^2 sqr of x^2+9 dx integrate from 0 to 21 solutions Answer 401394 by ewatrrr(10682)   on 2012-08-13 12:59:27 (Show Source): You can put this solution on YOUR website! ``` Hi, x= 2 ⇒ (15.32 -17.45) x = 0 ⇒ -11.12 (15.32 -17.45) + 11.12 = 8.99 ```
 Functions/637034: Good day can someone help me with this function g(x)= x^2 + x -7/3 Which is the domain?1 solutions Answer 401369 by ewatrrr(10682)   on 2012-08-13 09:53:28 (Show Source): You can put this solution on YOUR website! ``` Hi, g(x)= x^2 + x -7/3 = (x+1/2)^2 - 1/4 - 7/3 =(x+1/2)^2 - 31/12 domain: all real numbers. range: g(x) ≥ - 31/12 ```
 Quadratic_Equations/637033: I believe this is a Quadratic Equation... I need to solve the equation graphically by finding x-intercepts. Confirm by using factoring to solve the equation. 4x^2-8x+3=0 Please help!1 solutions Answer 401368 by ewatrrr(10682)   on 2012-08-13 09:47:46 (Show Source): You can put this solution on YOUR website! ``` Hi, 4x^2-8x+3=0 (2x-1)(2x-3) = 0 x=intercepts are 1/2, 3/2 vertex form of a Parabola opening up(a>0) or down(a<0), where(h,k) is the vertex and x = h is the Line of Symmetry 4x^2-8x+3= 4(x-1)^2 -4 + 3 = 4(x-1)^2 -1 V(1,-1), parabola opens Upward, x= 1 the line of symmetry ```
 Expressions-with-variables/637032: solve for x and y by using elimination. 3x+5y=-1 4x+7y=41 solutions Answer 401367 by ewatrrr(10682)   on 2012-08-13 09:37:48 (Show Source): You can put this solution on YOUR website! ``` Hi, solve for x and y by using elimination. 3x+5y=-1 |Multiplying 1st EQ by 4, 2nd by 3 and subtracting to eliminate x 4x+7y=4 -y = -16 y = 16 and x = -27 and... ```