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# Recent problems solved by 'Alan3354'

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 Rectangles/673114: A carpenter is building a rectangular room with a fixed perimeter of 420 ft. What are the dimensions of the largest room that can be built? What is its area? 1 solutions Answer 418487 by Alan3354(30993)   on 2012-10-28 23:09:34 (Show Source): You can put this solution on YOUR website!A carpenter is building a rectangular room with a fixed perimeter of 420 ft. What are the dimensions of the largest room that can be built? What is its area? ---------- A square, 105 by 105.
 Exponential-and-logarithmic-functions/673067: How do I solve the equation 4^2X=64? The teacher gave us the answer, 3/2, but I don't know the steps to get to that answer.1 solutions Answer 418468 by Alan3354(30993)   on 2012-10-28 21:33:54 (Show Source): You can put this solution on YOUR website!How do I solve the equation 4^2X=64? The teacher gave us the answer, 3/2, but I don't know the steps to get to that answer. ----------- 4x = 6 x = 3/2 That's one way. ============== 2x = 3, etc ============== 2x*log(4) = log(64) x = 3/2
 Graphs/672927: what is the slop of this equation y=0.15x-28?1 solutions Answer 418402 by Alan3354(30993)   on 2012-10-28 15:52:05 (Show Source): You can put this solution on YOUR website!what is the slop [sic] of this equation y=0.15x-28? ---------- Slope = 0.15
 Angles/672932: if a triangle is 93 by 49 ?1 solutions Answer 418400 by Alan3354(30993)   on 2012-10-28 15:42:03 (Show Source): You can put this solution on YOUR website!if a triangle is 93 by 49 ? ------------- What about it? triangles have 3 sides.
 Rectangles/672907: If a rectangle is 29 inches diagnally, what is the height and width of the rectangle1 solutions Answer 418399 by Alan3354(30993)   on 2012-10-28 15:41:12 (Show Source): You can put this solution on YOUR website!If a rectangle is 29 inches diagnally, what is the height and width of the rectangle ------------ An infinite # of solutions
 Travel_Word_Problems/672925: Suppose a bike rider climbs a mountain at 10km/hr and decends the mountain at 50km/hr. Find the distance traveled if he were on the mountain for 3hrs. So I get that distance = rate * time. I just can't seem to wrap my head around how to set up this equation to find the answer which I know is 50km.1 solutions Answer 418398 by Alan3354(30993)   on 2012-10-28 15:39:27 (Show Source): You can put this solution on YOUR website!Suppose a bike rider climbs a mountain at 10km/hr and decends the mountain at 50km/hr. Find the distance traveled if he were on the mountain for 3hrs. -------- d = r*t t = d/r d = one-way distance ----- d/10 + d/50 = 3 5d + d = 150 d = 25 km each way
 Quadratic_Equations/672813: y=-0.015x^2=+0.975x where x is the distance the bird is from the slingshot and y is the height of the bird... How far can this slingshot launch the bird?1 solutions Answer 418356 by Alan3354(30993)   on 2012-10-28 13:18:12 (Show Source): You can put this solution on YOUR website!y=-0.015x^2=+0.975x ----------- Too many equal signs.
 Linear-equations/672831: Graphing functions. All of them are based off of the basic slope equation: y = mx +b y = -3/4x + 4 y = 3x - 5 1 solutions Answer 418346 by Alan3354(30993)   on 2012-10-28 12:45:34 (Show Source): You can put this solution on YOUR website!Do it like this one: ----------- Solving systems of equations by graphing Y=3x-1 Y=5-1/2x ----------- The 2 equations are linear, so the graph is a straight line. You need 2 points. Pick 2 values for x, find y. Plot the 2 points. Draw a line thru them ------------- The intersection of the lines is the solution of the system.
 test/672846: Solve system of equations by graphing Y=3/2x 2y=-x+81 solutions Answer 418344 by Alan3354(30993)   on 2012-10-28 12:44:51 (Show Source): You can put this solution on YOUR website!Do it like this one: ----------- Solving systems of equations by graphing Y=3x-1 Y=5-1/2x ----------- The 2 equations are linear, so the graph is a straight line. You need 2 points. Pick 2 values for x, find y. Plot the 2 points. Draw a line thru them ------------- The intersection of the lines is the solution of the system.
 test/672852: Solving systems of equations by graphing Y=3x-1 Y=5-1/2x1 solutions Answer 418343 by Alan3354(30993)   on 2012-10-28 12:44:06 (Show Source): You can put this solution on YOUR website!Do it like this one: ----------- Solving systems of equations by graphing Y=3x-1 Y=5-1/2x ----------- The 2 equations are linear, so the graph is a straight line. You need 2 points. Pick 2 values for x, find y. Plot the 2 points. Draw a line thru them ------------- The intersection of the lines is the solution of the system.
 test/672850: Solving systems of equations by graphing Y=1 X-y=41 solutions Answer 418341 by Alan3354(30993)   on 2012-10-28 12:43:40 (Show Source): You can put this solution on YOUR website!Do it like this one: ----------- Solving systems of equations by graphing Y=3x-1 Y=5-1/2x ----------- The 2 equations are linear, so the graph is a straight line. You need 2 points. Pick 2 values for x, find y. Plot the 2 points. Draw a line thru them ------------- The intersection of the lines is the solution of the system.
 test/672849: Solving system of equations by graphing Y=1/4x-3 Y=2x-31 solutions Answer 418340 by Alan3354(30993)   on 2012-10-28 12:43:21 (Show Source): You can put this solution on YOUR website!Do it like this one: ----------- Solving systems of equations by graphing Y=3x-1 Y=5-1/2x ----------- The 2 equations are linear, so the graph is a straight line. You need 2 points. Pick 2 values for x, find y. Plot the 2 points. Draw a line thru them ------------- The intersection of the lines is the solution of the system.
 test/672847: solving systems of equations by graphing Y=1 X-y=41 solutions Answer 418339 by Alan3354(30993)   on 2012-10-28 12:42:58 (Show Source): You can put this solution on YOUR website!Do it like this one: ----------- Solving systems of equations by graphing Y=3x-1 Y=5-1/2x ----------- The 2 equations are linear, so the graph is a straight line. You need 2 points. Pick 2 values for x, find y. Plot the 2 points. Draw a line thru them ------------- The intersection of the lines is the solution of the system.
 test/672848: Solving systems of equations by graphing Y=3x-1 Y=5-1/2x1 solutions Answer 418338 by Alan3354(30993)   on 2012-10-28 12:42:19 (Show Source): You can put this solution on YOUR website!Solving systems of equations by graphing Y=3x-1 Y=5-1/2x ----------- The 2 equations are linear, so the graph is a straight line. You need 2 points. Pick 2 values for x, find y. Plot the 2 points. Draw a line thru them ------------- The intersection of the lines is the solution of the system.
 Miscellaneous_Word_Problems/672857: What two positive numbers when multiplied together also equal the sum of the same two numbers?1 solutions Answer 418337 by Alan3354(30993)   on 2012-10-28 12:36:18 (Show Source): You can put this solution on YOUR website!duplicate
 Expressions-with-variables/672834: hello:)im not all that good at math its a subsitution problem and i need help! please. y=x-1 3x+4y=171 solutions Answer 418331 by Alan3354(30993)   on 2012-10-28 11:36:04 (Show Source): You can put this solution on YOUR website!y=x-1 3x+4y=17 ----------- y is solved for in the 1st eqn, so sub for y in the 2nd. ----- 3x+4y=17 3x + 4(x-1) = 17 3x + 4x-4 = 17 7x = 21 x = 3 ----- y = x-1 y = 2 ------- Nothing to it.
 Linear-equations/672815: LEASE HELP I HAVE A QUIZ ON TUESDAY Okay, so lately I've been having trouble in Algebra. We're doing slopes and graphing them, and I get the basics. It's the more complicated stuff I get confused on. y = mx+b 1.) y = x^2 - 1 2.) y = 5/2x - 3 3.) 2y = 4x + 8 4.) y = 2x^2 - 6 These are all graphing equations. If you could please explain how to tackle these problems and do them successfully, I'd be really happy! Thanks!1 solutions Answer 418328 by Alan3354(30993)   on 2012-10-28 11:25:55 (Show Source): You can put this solution on YOUR website!1.) y = x^2 - 1 2.) y = 5/2x - 3 3.) 2y = 4x + 8 4.) y = 2x^2 - 6 These are all graphing equations. ---------------- #2 & #3 are linear, so you need 2 points. --------- y = 5/2x - 3 Pick 2 values for x and find y Plot the 2 points, draw a line thru them. ================= 3.) 2y = 4x + 8 y = 2x+4 Same as #2 -------------- The other 2 are 2nd order. Plot as many points as you like, then draw a smooth curve thru them.
 Trigonometry-basics/672828: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. Round your answers to three decimal places where appropriate.) sin 2θ + sin θ = 0 1 solutions Answer 418326 by Alan3354(30993)   on 2012-10-28 11:22:14 (Show Source): You can put this solution on YOUR website!sin(2t) + sin(t) = 0 2sin(t)cos(t) + sin(t) = 0 sin*(2cos + 1) = 0 sin(t) = 0 t = 0, pi ----------- cos = -1/2 t = 2p/3, 4pi/3
 Expressions-with-variables/672799: What two positive numbers when multiplied together also equal the sum of the same two numbers? what I have tried so far: xy=a x+y=a xy=x+y x(y-1)=y x=y/y-1 I know the answer is 2 but how do I show that?1 solutions Answer 418320 by Alan3354(30993)   on 2012-10-28 10:55:51 (Show Source): You can put this solution on YOUR website!What two positive numbers when multiplied together also equal the sum of the same two numbers? what I have tried so far: xy=a x+y=a xy=x+y x(y-1)=y x=y/y-1 I know the answer is 2 but how do I show that? ---------- xy = x+y xy - y = x y*(x-1) = x y = x/(x-1) ------------ Same as what you did. There are an infinite number of solutions. Pick any x and find y. eg, 2 ----- x = 3 --> y = 3/2 x = 4 --> y = 4/3 etc
 test/672817: Explain how to factor (and then factor) the difference of squares: (x+y)^2-25z^21 solutions Answer 418318 by Alan3354(30993)   on 2012-10-28 10:42:51 (Show Source): You can put this solution on YOUR website!Explain how to factor (and then factor) the difference of squares: (x+y)^2-25z^2 -----------
 test/672816: Explain how to factor (and then factor) the difference of cubes: 64x^3-8y^31 solutions Answer 418317 by Alan3354(30993)   on 2012-10-28 10:41:54 (Show Source): You can put this solution on YOUR website!Explain how to factor (and then factor) the difference of cubes: 64x^3-8y^3 ------------
Equations/672756: Find an equation(s) of the line(s) containing (5,4) and at a distance 2 from (-1,-3).
1 solutions

Answer 418308 by Alan3354(30993)   on 2012-10-28 09:36:45 (Show Source):
You can put this solution on YOUR website!
Find an equation(s) of the line(s) containing (5,4) and at a distance 2 from (-1,-3).
-----------
The lines are tangents to a circle of radius 2 centered at (-1,-3)
The distance from (5,4) to the center (-1,-3) = sqrt(85).
Right angles are formed at the tangent points.
----
The distance from (5,4) to the tangent points = 9.
The tangent points are the intersection of the circle above and a circle of radius 9 centered at (5,4).
----------

---

----------------------------------- Subtract
12x + 14y = -46
6x + 7y = -23 is an equation of the line thru the 2 tangent points.
y = (-6x - 23)/7
Sub for y in one of the circles

 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=63504 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.764705882352941, -2.2. Here's your graph:

==========================
x = -2.2 --> y = (-6*-2.2 - 23)/7 = -1.4
Tangent point at (-2.2,-1.4)
Equation of the line thru (-2.2,-1.4) and (5,4) is
3x - 4y = -1
==============================================
x = 0.7647 --> y = -3.94117 --> tangent point at (0.7647,-3.84117)
Equation of line thru the 2 points is
7.94x - 4.2353y = 22.7588 (approximation)

 Inequalities/672652: How would I divide this problem? 72x^6-72x^5+40x/8x1 solutions Answer 418246 by Alan3354(30993)   on 2012-10-27 18:37:52 (Show Source): You can put this solution on YOUR website!How would I divide this problem? 72x^6-72x^5+40x/8x ------------ You don't divide problems, unless you're giving some problems to different people. --------------- You might mean, "How do I do this division problem?", a different situation. ---------- Then I have a question. Is it Or is it ? It's your job to eliminate ambiguities, and make it clear what the problem is.
 Polynomials-and-rational-expressions/672651: x^3-y^4=30 find yprime1 solutions Answer 418245 by Alan3354(30993)   on 2012-10-27 18:26:59 (Show Source): You can put this solution on YOUR website!x^3-y^4=30 find yprime ---------------- Differentiate implicitly
 Problems-with-consecutive-odd-even-integers/672647: If four consecutive odd integers had a sum of 96, what would be the largest integer? Please show how to do it!!1 solutions Answer 418243 by Alan3354(30993)   on 2012-10-27 18:03:12 (Show Source): You can put this solution on YOUR website!If four consecutive odd integers had a sum of 96, what would be the largest integer? ----------- The hard way: n + n+2 + n+4 + n+6 = 96 4n+12 = 96 n = 21 =========== Better way: 96/4 = 24, the center. 2 below & 2 above --> 21, 23, 25 & 27
 Equations/672611: write equation that passes through the oints 2 -6 and is parallel to x axis1 solutions Answer 418232 by Alan3354(30993)   on 2012-10-27 17:28:03 (Show Source): You can put this solution on YOUR website!write equation that passes through the oints [sic] 2 -6 and is parallel to x axis --------- Clarify the points. Use (x,y) format. 2 -6 is not a point. (2,-6) is a point.
 Quadratic_Equations/672613: Find the polynomial which has the binomial (2b-3) as a facor1 solutions Answer 418227 by Alan3354(30993)   on 2012-10-27 17:16:44 (Show Source): You can put this solution on YOUR website!Find the polynomial which has the binomial (2b-3) as a facor ------------ There's an infinite number of them. (2b-3) times anything except zero or 1/(2b-3) times 2 times (2b-3) times 7 times -99 times x times x^2 times abcdefg times (m+n+o+p)
 Rectangles/672625: the area of a parallelogram increased from 28 square centimeters to 126 square centimeter. Find the percent increase in area. Can you help me 1 solutions Answer 418226 by Alan3354(30993)   on 2012-10-27 17:14:17 (Show Source): You can put this solution on YOUR website!the area of a parallelogram increased from 28 square centimeters to 126 square centimeter. Find the percent increase in area. ----------- An increase of 98 98/28 = 3.5 = 350% increase
 Mixture_Word_Problems/672631: If copper is worth \$8 per kilogram, what is the value of the copper in 10 cubic kilometers of seawater? 1 solutions Answer 418220 by Alan3354(30993)   on 2012-10-27 16:47:35 (Show Source): You can put this solution on YOUR website!If copper is worth \$8 per kilogram, what is the value of the copper in 10 cubic kilometers of seawater? ============== How much copper is that?
Complex_Numbers/672619: how to we solve the following equation to find the complex number/roots?
x^2-8x+30=0
I was sick and was absent when my class went over complex numbers and roots so Im not familiar with it.
Thanks(:

1 solutions

Answer 418204 by Alan3354(30993)   on 2012-10-27 14:47:10 (Show Source):
You can put this solution on YOUR website!
how to we solve the following equation to find the complex number/roots?
x^2-8x+30=0
-------------
 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -56 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -56 is + or - . The solution is , or Here's your graph:

===================
If you want to know the number and type of roots, look at what it says about the Discriminant.
-----------------
For these [real] solutions to exist, the discriminant should not be a negative number.

Trigonometry-basics/672584: Here is an example of a Trig function we are working on that I HAVE been able to solve, I think:
solve trig equations algrebraically; sin^2(t)=2sin(t)+1
first set everything to zero; sin^2(t)-2sin(t)-1=0
then in this case I can use the foil method; (sin(t)-1)(sin(t)-1=0
then solve for (t); t=4.7+l(2pi) and t=pi-4.7i(2pi)
I know to set everything equal to zero. sec(t)-tan(t)=0
I know sec=1/cos, but not sure if that would apply here....
1 solutions

Answer 418203 by Alan3354(30993)   on 2012-10-27 14:37:42 (Show Source):
You can put this solution on YOUR website!
Here is an example of a Trig function we are working on that I HAVE been able to solve, I think:
solve trig equations algrebraically; sin^2(t)=2sin(t)+1
first set everything to zero; sin^2(t)-2sin(t)-1=0
then in this case I can use the foil method; (sin(t)-1)(sin(t)-1=0
then solve for (t); t=4.7+l(2pi) and t=pi-4.7i(2pi)

---------------------------
first set everything to zero; sin^2(t)-2sin(t)-1=0
then in this case I can use the foil method; (sin(t)-1)(sin(t)-1=0
(sin(t)-1)(sin(t)-1=0
**** That doesn't factor
---------------------
Sub x for sin(t) to save typing.

 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=8 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2.41421356237309, -0.414213562373095. Here's your graph:

=======================
Ignore the 1st solution, it's > 1 --> no real solution.
x = 1 - sqrt(2)
sin(t) =~ -0.41421
t = 204.47, 335.53 + n*360 degs, n = -,1,2,3...