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Linear_Algebra/262916: what is the value of the determinant? 3 6 8 2 4 0 3 6 8 1 solutions Answer 193701 by jim_thompson5910(28696)   on 2010-01-29 22:26:52 (Show Source): You can put this solution on YOUR website! Take note that two rows are identical. This means that the determinant must be zero. However, let's use another method. Solved by pluggable solver: Finding the Determinant of a 3x3 Matrix If you have the general 3x3 matrix: the determinant is: Which further breaks down to: Note: , and are determinants themselves. If you need help finding the determinant of 2x2 matrices (which is required to find the determinant of 3x3 matrices), check out this solver -------------------------------------------------------------- From the matrix , we can see that , , , , , , , , and Start with the general 3x3 determinant. Plug in the given values (see above) Multiply Subtract Multiply Combine like terms. ====================================================================== Answer: So , which means that the determinant of the matrix is

Linear_Algebra/262917: PLease find the inverse of the matrix -9 5 6 -3 1 solutions Answer 193700 by jim_thompson5910(28696)   on 2010-01-29 22:25:24 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Finding the Inverse of a 2x2 Matrix To find the inverse of the matrix , we can follow these steps: Step 1) Find the determinant The determinant of is . So this means that Step 2) Swap the values Now switch the highlighted values to get Step 3) Change the sign Now change the sign of the highlighted values to get Step 4) Multiply by the inverse of the determinant Multiply by to get Plug in to get Step 5) Multiply by every element in the matrix (simplify and reduce if possible) Multiply by EVERY element to get Multiply to get Reduce each element: ================================================================= Answer: So the inverse of is This means that if then

test/262835: If y=5^(x^3-2), then dy/dx= (A) (x^3-2)5^(x^3-2) (B) 3x^2(ln5)5^(x^3-2) (C) (3x^2)5^(x^3-2) (D) (ln5)5^(x^3-2) (E) x^3(ln5)5^(x^3-2) 1 solutions Answer 193611 by jim_thompson5910(28696)   on 2010-01-29 16:25:39 (Show Source): You can put this solution on YOUR website! Let to get . Derive both sides to get where is the derivative of 'u' with respect to 'x'. I'll let you take it from here.

Equations/262653: x^2+6x+5=0 1 solutions Answer 193463 by jim_thompson5910(28696)   on 2010-01-29 00:07:04 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Square to get . Multiply to get Subtract from to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the solutions are or

Parallelograms/262659: Which is a subset of the set of rectangles? 1 solutions Answer 193462 by jim_thompson5910(28696)   on 2010-01-29 00:06:17 (Show Source): You can put this solution on YOUR website! You can think of the set of squares as a subset of the set of rectangles since all squares are rectangles. Recall that rectangles are quadrilaterals with four right angles. Also, remember that a square is equilateral quadrilateral with four right angles.

Miscellaneous_Word_Problems/262664: what is the formula on how to answer this word problem? A computer with an old processor locks up if more than 4 applications are running simultaneously. If the owner has 20 applications stored in his program file, how many different sets of 4 can he run, so his computer does not lock up? a formula would be great, thank you. 1 solutions Answer 193461 by jim_thompson5910(28696)   on 2010-01-29 00:04:22 (Show Source): You can put this solution on YOUR website! Hint: Use the combination formula (since order doesn't matter) In this case, (he has 20 to choose from) and (but in the end he can only pick 4) which means that Note: computing 20! isn't practical. Try to see if you can think of a way to simplify it first before plugging it into your calculator.

Miscellaneous_Word_Problems/262660: five computers are to be wired linear network. How many permutations of the five computers are possible? please help, I have no idea on how to solve this, thank you. 1 solutions Answer 193460 by jim_thompson5910(28696)   on 2010-01-29 00:00:06 (Show Source): You can put this solution on YOUR website! The basic format is this: Number of permutations = # of choices for first slot * # of choices for second slot * # of choices for third slot * # of choices for fourth slot * # of choices for fifth slot Since we have 5 choices for the first position, 4 for the second (since 1 computer can't take up two spots), 3 for the third, 2 for the fourth, and 1 for the fifth, we get Number of permutations = 5*4*3*2*1 = 120 So there are 120 different permutations. You can choose to use the permutation formula, but you'll basically use this idea.

Graphs/262601: y=-3x+1 1 solutions Answer 193429 by jim_thompson5910(28696)   on 2010-01-28 21:43:54 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is -3 and the run is 1. This means that to go from point to point, we can go down 3 and over 1 So starting at , go down 3 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and

Distributive-associative-commutative-properties/262440: use distributive property to expand 5(4x-9) 1 solutions Answer 193352 by jim_thompson5910(28696)   on 2010-01-28 18:02:11 (Show Source): You can put this solution on YOUR website! So

Radicals/262443: Write the radical expression ^5sqroot(2^3) using exponents. ^5root(2^3) (2^3) is under the radical with a 5 in superscript above the radical 1 solutions Answer 193351 by jim_thompson5910(28696)   on 2010-01-28 18:01:30 (Show Source): You can put this solution on YOUR website! So

Quadratic_Equations/262441: I have tried this question many time but was unsuccessful in getting the right answer :( Please help me!! The solution set of the equation 2x^2-6x+3=0 is ?? 1 solutions Answer 193348 by jim_thompson5910(28696)   on 2010-01-28 18:00:10 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) or Break up the expression. or Reduce. So the solutions are or

Trigonometry-basics/262433: I am having a problem with this question...please don't just give me the answer, I would really like to know how to do it. Thanks f(theta)=3tan(theta)+sin2(theta), find f(pi/6) 1 solutions Answer 193347 by jim_thompson5910(28696)   on 2010-01-28 17:58:45 (Show Source): You can put this solution on YOUR website! Hint: Plug in and use the unit circle to determine that and . Let me know if this helps you get started.

Exponents-negative-and-fractional/262392: I need help with this problem: Write with positive exponents (3^-2 a^-2 b^5)over (c^-3 d^-4). Thanks 1 solutions Answer 193312 by jim_thompson5910(28696)   on 2010-01-28 17:02:45 (Show Source): You can put this solution on YOUR website! Let's break this up: ----------------------------------- So and Altogether, Now multiply by the reciprocal of the second fraction and simplify to get the final answer of So simplifies to where none of the variables can be equal to zero. In other words,

Linear-equations/262370: 3(2x-2)-4(x-6)=3x+8+x 1 solutions Answer 193291 by jim_thompson5910(28696)   on 2010-01-28 16:24:33 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Conjunction/262147: 8. Determine which, if any, of the three statements are equivalent. Give a reason for your conclusion. Show complete work. I) If the dog licks her nose, then the dog is not happy. II) If the dog licks her nose, then the dog is happy. III) If the dog is not happy, then the dog does not lick her nose. a. I, II, and III are equivalent b. I and II are equivalent c. II and III are equivalent d. I and III are equivalent e. None are equivalent How do I show work on this? I don't get it? 1 solutions Answer 193118 by jim_thompson5910(28696)   on 2010-01-28 01:24:42 (Show Source): You can put this solution on YOUR website! Here's the basic outline to solving this problem Step 1) Assign p: the dog licks her nose and q: the dog is happy Step 2) Translate each statement into symbolic form. Step 3) Create a table for each symbolic statement. Any tables which have equivalent final columns will be equivalent expressions. For example, translate "If the dog licks her nose, then the dog is not happy. " into p -> ~q and set up the following table p q ~q p -> ~q T T F F T F T T F T F T F F F T Do the same for the 2 other statements and compare the last columns in the table. Let me know if this helps.

Points-lines-and-rays/262023: Problem: SLTM is a rhombus measure of angle LST=11x-24 measure of angle TSM=3x+8 find x and the measure of each of the angles above I don't understand how this can work because these angles are on the diagonal inside the rhombus not on one of the vertices. 1 solutions Answer 193075 by jim_thompson5910(28696)   on 2010-01-27 20:51:55 (Show Source): You can put this solution on YOUR website! Hint: if you draw the rhombus, you'll see that the angles LST and TSM are adjacent angles (ie they are next to one another). Recall that adjacent angles of any parallelogram are supplementary which means that the two angles add to 180 degrees. So add up the angles and set them equal to 180 to get and solve for 'x'. Then use the solution to find the individual angles.

Miscellaneous_Word_Problems/262010: One and only one of five statements referring to our esteemed President is true. Assume that he either likes or dislikes any vegetable. Because of logical consistency, you should be able to infer which is the true statement. The statement are: a) President Obama likes broccoli, spinach, and beets. b) As regards beets and asparagus, President Obama likes one and dislikes the other. c) President Obama likes beets. d) President Obama likes asparagus e) President Obama likes both broccoli and spinach. Which is the true statement? Which of these vegetables does our Chief Executive dislikes? (Use deductive reasoning to decide.) 1 solutions Answer 193073 by jim_thompson5910(28696)   on 2010-01-27 20:28:35 (Show Source): You can put this solution on YOUR website! If a) is true, then certainly e) is true. But we only want one true statement. So a) cannot be true. If b) is true, then either c) or d) is true. Either way, we have 2 possible scenarios with 2 true statements, but we only want one true statement. So b) cannot be true. Here's where things get a bit tricky, but try to follow as close as you can. If c) is true, and d) is false (since we only want one true statement), then this automatically makes b) true. On the flip side, if d) is true, and c) is false, then b) is again automatically true. In either case, if c) or d) are true, then b) is true. But we only want one true statement. So c) and d) cannot be true. By process of elimination, every statement was shown to be false. So the only remaining statement e) must be true in order to satisfy the problem's requirements.

Numbers_Word_Problems/262000: Please give me a hint on the following word problem. Because Stephine wanted to win the Berryville bicycle race, she trained hard for a week, including the weekend. Each day, she rode 3 miles farther then she had the day before. If she rode a total of 126 miles, how far did she ride on the last day before the race? (create and equation using one variable and solve with proper work steps) M, T, W, T, F, S, S 108,111,114,117,120,123,126 I figure she started at 108 miles adding 3 miles per day. Just need a hint on the equation. Thanks Ray 1 solutions Answer 193069 by jim_thompson5910(28696)   on 2010-01-27 20:09:49 (Show Source): You can put this solution on YOUR website! Let x=number of miles that she rode for on the first day So on the second day, she rode x+3 miles. On the 3rd day, she rode (x+3)+3=x+6 miles. On the fourth day, she rode (x+6)+3=x+9 miles. This pattern continues. So we have the table Day of Week: Mon Tues Wed Thurs Fri Sat Sun Miles Traveled x x+3 x+6 x+9 x+12 x+15 x+18 Now just add up the number of miles and set them equal to 126 like so: From here, solve for 'x' to find the amount of miles she traveled on the first day. Use the table to find the amount of miles traveled on the last day.

Quadratic_Equations/261964: Jim, I have tried to follow and plug in the equation but it is not working. I have been at this for over an hour and my brain is fried. Help!! Bayside Insurance offers two health plans. Under plan A Giselle would have to pay the first $140 of her bills and 25% of the rest. Under plan B she would have to pay the first $160 of her bills and 20% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $160 in bills. Giselle would save with plan B if she had more than $_________in bills? When it says assume she has over $160 in bills, does that mean you can use any number higher than 160? Please help, Thank you Deborah 1 solutions Answer 193054 by jim_thompson5910(28696)   on 2010-01-27 19:09:45 (Show Source): You can put this solution on YOUR website! The reason why we're assuming that she has over $160 in medical bills is if she had less than $160 in bills, then she would be clearly paying more for plan B. For instance, if she has $159 in bills, then she pays almost $15 more for plan B. Let x = amount Giselle has to pay (ie her bill) Under plan A, she has to pay the first $140 and then 25% of the rest. So if we assume that she has over $160 in bills, this means that . After she pays the initial $140, then she has 25% of in bills left over. So this means that under plan A, the cost is Similarly, under plan B, because "she would have to pay the first $160 of her bills and 20% of the rest", this means that the cost for plan B is So to figure out when plan B will save her money, simply set the plan B expression less than the plan A expression Substitute the given cost equations. Distribute Combine like terms Subtract 0.25x from both sides. Subtract 128 from both sides. Combine like terms Divide both sides by -0.05. Remember that dividing both sides by a negative number will flip the inequality sign. So if she has any bills over $460, then Plan B will cost less than Plan A. If you're skeptical, try some values of 'x' that are around $460. Try x=400, x=450, x=500 (and maybe more) and you'll notice that plan B will become cheaper after you pass x=450. Note: the plans cost the same when the bill is $460. This is cross over point when the plans switch in cost.

Quadratic_Equations/261941: Bayside Insurance offers two health plans. Under plan A Giselle would have to pay the first $140 of her bills and 25% of the rest. Under plan B Giselle would pay the first $160, but only 20% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $160 in bills. Giselle would save with plan B if she had more than $____ in bills? Please help I have been working on this for over an hour. Deborah 1 solutions Answer 193037 by jim_thompson5910(28696)   on 2010-01-27 18:29:11 (Show Source): You can put this solution on YOUR website! Hi Deborah, Check out this similar solution (the values are just different) and let me know if this helps at all. If not, then let me know or repost.

Subset/261923: what are the subsets of a = {p,q,r,s,t}. I know there should be 32 subsets but I can only find 26 of them. 1 solutions Answer 193034 by jim_thompson5910(28696)   on 2010-01-27 18:24:19 (Show Source): You can put this solution on YOUR website! Here are all of the subsets of {p,q,r,s,t} {p,q,r,s,t}, {p,q,r,s}, {p,q,r,t}, {p,q,s,t}, {p,r,s,t}, {q,r,s,t}, {p,q,r}, {p,q,s}, {p,q,t}, {p,r,s}, {p,r,t}, {p,s,t}, {q,r,s}, {q,r,t}, {q,s,t}, {r,s,t}, {p,q}, {p,r}, {p,s}, {p,t}, {q,r}, {q,s}, {q,t}, {r,s}, {r,t}, {s,t}, {p}, {q}, {r}, {s}, {t}, {} Note: {} denotes the empty set

Conjunction/261773: In this exercise, construct a truth table for the statement ~p --> ~q 1 solutions Answer 192889 by jim_thompson5910(28696)   on 2010-01-27 11:46:51 (Show Source): You can put this solution on YOUR website! Hint: Recall that p -> q is only false when p is true and q is false. Here's the truth table for p -> q. p q p -> q T T T T F F F T T F F T Use this idea to find the table for ~p -> ~q

Coordinate-system/261769: find the slope of the line, if possible (if the line is undefined, enter undefined) the graph of x=13 1 solutions Answer 192882 by jim_thompson5910(28696)   on 2010-01-27 11:37:37 (Show Source): You can put this solution on YOUR website! Hint: Locate two points on the line (graph the equation if necessary) and use the slope formula to find the slope 'm'. If the denominator turns out to be zero, then the slope is undefined (since division by zero is not allowed).

Circles/261768: When Cammie finished making a friendship bracelet, it was 7.9 inches long. What was the diameter of the bracelet? What formula would or should I use for this? Do not understand. 1 solutions Answer 192880 by jim_thompson5910(28696)   on 2010-01-27 11:35:44 (Show Source): You can put this solution on YOUR website! I'm assuming that the bracelet forms a circle. If you were to cut the bracelet at one point and lay it out as long as you can (without breaking it further), then the bracelet would be 7.9 inches long. Since the circumference is simply the distance out the circle, this means that the circumference is 7.9 inches. You can use the circumference formula where (approximately) and 'd' is the diameter. So just plug in and to get . Now just solve for 'd' in the equation to find the diameter.

test/261766: The equation of the tangent line to the curve y=x^3-6x^2 at its point of inflection is (A) y= -12x+8 (B) y= -12x+40 (C) y= 12x-8 (D) y= -12x+12 (E) y= 12x-40 I know that the point of inflection relates to the second derivative, so do I just take the double derivative of the given equation? 1 solutions Answer 192874 by jim_thompson5910(28696)   on 2010-01-27 11:31:05 (Show Source): You can put this solution on YOUR website! First, derive to get . Derive to get the second derivative . Recall that the point of inflection occurs when the second derivative is zero. So set the second derivative equal to zero to get the equation . Solve for 'x' and use this 'x' value to find the corresponding 'y' value of the point of inflection. Then use the 'x' value and plug it into to find the slope of the tangent line at that x value. Since you have the slope of the line (ie the slope of the tangent) and the point that the line goes through (the inflection point), you can the formula , where 'm' is the slope and is the given point the line goes through, to find the equation of the tangent line.

decimal-numbers/261762: how do you wrote four hundredths in a decimal form? 1 solutions Answer 192869 by jim_thompson5910(28696)   on 2010-01-27 11:20:02 (Show Source): You can put this solution on YOUR website! Either use a calculator or long division to get

test/261640: If y=5^(x^3-2), then dy/dx= (A) (x^3-2)5^(x^3-2) (B) 3x^2(ln5)5^(x^3-2) (C) (3x^2)5^(x^3-2) (D) (ln5)5^(x^3-2) (E) x^3(ln5)5^(x^3-2) 1 solutions Answer 192865 by jim_thompson5910(28696)   on 2010-01-27 11:15:54 (Show Source): You can put this solution on YOUR website! Let to get . Derive both sides to get where is the derivative of 'u' with respect to 'x'. I'll let you take it from here.

Circles/261758: If the tires on a car each have a diameter of 25 inches, how far will the car travel in 100 rotations of its tires? 1 solutions Answer 192864 by jim_thompson5910(28696)   on 2010-01-27 11:12:20 (Show Source): You can put this solution on YOUR website! Simply find the circumference of the tire and multiply that figure by 100 to find out how far it will travel in 100 rotations.

Polynomials-and-rational-expressions/261678: Factor by grouping 6x^3-15x^2+14x-35 1 solutions Answer 192862 by jim_thompson5910(28696)   on 2010-01-27 11:10:51 (Show Source): You can put this solution on YOUR website! Start with the given expression. Pair up the terms. Factor out the GCF from the first group Factor out the GCF from the second group Factor out the common term So factors to In other words,

Rational-functions/261746: (2x^3+x^2-3x)/(x^3-x^2) 1 solutions Answer 192860 by jim_thompson5910(28696)   on 2010-01-27 11:05:50 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor the numerator. Factor the denominator. Break up to get . Highlight the common terms. Cancel out the common terms. Simplify So simplifies to . In other words,

test/261485: The equation of the line tangent to the curve y=kx+8/k+x at x=-2 is y=x+4. What is the value of k? (A) -3 (B) -1 (C) 1 (D) 3 (E) 4 1 solutions Answer 192669 by jim_thompson5910(28696)   on 2010-01-26 18:49:07 (Show Source): You can put this solution on YOUR website! Because the curve has a tangent line of at , this means that the curve intersects the line at and they intersect at the same 'y' value. In other words, the curve and the line intersect at the point (-2, y). Because these y values are the same, we can plug into to get . Now plug in (since they intersect at x=-2) to get and simplify to get . From here, it's just a simple matter of solving for k which I'll let you do.