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# Recent problems solved by 'Alan3354'

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 Pythagorean-theorem/299766: What is the lengths of the hypoteneuse and the long leg in an 30-60-90 triangle when the short leg is 11 cm? I really hope this makes sense, but if not here's another question A person who is 2m tall casts a shadow that is 3m long. At the same time a flagpole casts a shadow 12m long. How tall is the flagpole?1 solutions Answer 215298 by Alan3354(31521)   on 2010-05-03 10:36:58 (Show Source): You can put this solution on YOUR website!What is the lengths of the hypoteneuse and the long leg in an 30-60-90 triangle when the short leg is 11 cm? Hypotenuse = 2*11 = 22 cm long leg = = ----------------------------- I really hope this makes sense, but if not here's another question A person who is 2m tall casts a shadow that is 3m long. At the same time a flagpole casts a shadow 12m long. How tall is the flagpole? The shadow is 4x as long, so it's 4x as high = 8 meters
 Equations/299783: findthe x- and y- intercepts of y=-5x-61 solutions Answer 215297 by Alan3354(31521)   on 2010-05-03 10:32:38 (Show Source): You can put this solution on YOUR website!findthe x- and y- intercepts of y=-5x-6 ------------- Set x = 0, find the y-int Set y = 0, find the x-int
 Square-cubic-other-roots/299784: what is the simplified radical of 1/2 square root of 112?1 solutions Answer 215296 by Alan3354(31521)   on 2010-05-03 10:31:28 (Show Source): You can put this solution on YOUR website!what is the simplified radical of 1/2 square root of 112? ---------- If you mean = = =
 Exponential-and-logarithmic-functions/299779: Rewrite each of the following as an equivalent exponential equation.Do not solve. loge 0.989 = -0.01111 solutions Answer 215295 by Alan3354(31521)   on 2010-05-03 10:29:15 (Show Source): You can put this solution on YOUR website!Rewrite each of the following as an equivalent exponential equation.Do not solve. loge 0.989 = -0.0111 ------------------ loge 0.989 = -0.0111 Logs base e are usually written as ln, natural logs There's nothing to solve anyway.
 Polynomials-and-rational-expressions/299770: common factor, set equal to o, then solve. (x+5)(x-3)=0 1 solutions Answer 215290 by Alan3354(31521)   on 2010-05-03 10:14:32 (Show Source): You can put this solution on YOUR website!What do you mean by "common factor?"
 Quadratic-relations-and-conic-sections/299760: If a right circular cone intersects a plane that runs perpendicular to the cone's axis (but does not pass through its vertex), the resulting curve will be a(n)1 solutions Answer 215278 by Alan3354(31521)   on 2010-05-03 09:45:23 (Show Source): You can put this solution on YOUR website!circle ----- If it does pass thru the vertex, it's still a circle of radius zero, which is a point.
 Trigonometry-basics/299753: vertical distance between a wave's high point and low point is 1.8 and they cycle is repeated every 4 seconds. determine a sinusoidal equation use your model to determine when the boat is 0.5 abovie its mean position 1 solutions Answer 215277 by Alan3354(31521)   on 2010-05-03 09:42:05 (Show Source): You can put this solution on YOUR website!vertical distance between a wave's high point and low point is 1.8 and they cycle is repeated every 4 seconds. determine a sinusoidal equation ------------------ h(t) = 0.9*sin(2pi*t/4) t in seconds, vertical units not specified h(t) = 0.9*sin(pi*t/2) ------------------------ use your model to determine when the boat is 0.5 abovie its mean position 0.5 = 0.9*sin(pi*t/2) sin(pi*t/2) = 5/9 =~ 0.55555 pi*t/2 = arcsin(0.55555) =~ 0.589, 2.5526 radians t = 0.589*2/pi t =~ 0.375 + 4n seconds, n = 0,1,2,3,... rising ----------------- t = 2.5526*2/pi t =~ 1.625 + 4n seconds, n = 0,1,2,3.... falling ---------------- Or, t = (1 +/- 0.625) + 4n seconds, n = 0,1,2,3,...
 Trigonometry-basics/299745: Given Θ = 30 degrees, and b = 2, c = ? A. 8 B. 6.5 C. 4.8 D. 6.9 E. 4 How do I go about solving this question?1 solutions Answer 215274 by Alan3354(31521)   on 2010-05-03 09:19:44 (Show Source): You can put this solution on YOUR website!Insufficient data. 3 elements are needed to solve for another element of a triangle.
 Exponents/299747: (3x to the 5th)3(2x to the 7th)21 solutions Answer 215273 by Alan3354(31521)   on 2010-05-03 09:15:56 (Show Source): You can put this solution on YOUR website!(3x to the 5th)3(2x to the 7th)2 ---------------- Like this? Expand each term = Multiply the coefficients and add the exponents =
 Equations/299630: I need to translate this verbal phrase into an algebraic expression or equation: Nine decreased by 5 times a number1 solutions Answer 215247 by Alan3354(31521)   on 2010-05-02 22:10:08 (Show Source): You can put this solution on YOUR website!9 - 5n
 Permutations/299623: Phone numbers are seven digits long and the digits an repeat themselves. Using this information, find the probability for when the phone number ends with an even digit. Thank you for your help.1 solutions Answer 215246 by Alan3354(31521)   on 2010-05-02 22:09:41 (Show Source): You can put this solution on YOUR website!Only the last digit matters. That's 5 out of 10, = 1/2
 logarithm/299542: Can someone solve this, 3logx=1/2log256-log21 solutions Answer 215233 by Alan3354(31521)   on 2010-05-02 21:28:42 (Show Source): You can put this solution on YOUR website!Can someone solve this, 3logx=1/2log256-log2 --------------- I suppose you want to solve for x? --> x = 2 (principal value)
 Radicals/299607: the weight of an object follows this equation: , where C is a constant, and r is the distance that the object is from the center of the earth. Solve the equation for r. 1 solutions Answer 215231 by Alan3354(31521)   on 2010-05-02 21:23:28 (Show Source): You can put this solution on YOUR website!r = distance from the center of the earth.
 Permutations/299611: how can i solve 26c14 when 26 is a very large number?1 solutions Answer 215230 by Alan3354(31521)   on 2010-05-02 21:22:34 (Show Source): You can put this solution on YOUR website!26 is never greater than 26.
 Average/299585: If i have an 86% in a class, what do i need on the final to keep a B.1 solutions Answer 215229 by Alan3354(31521)   on 2010-05-02 21:21:53 (Show Source): You can put this solution on YOUR website!Not enough info. How much does the final count? What % is needed for a B? What's the basis of the 86%?
 Radicals/299610: radical 100ab/ 5 radical 21 solutions Answer 215227 by Alan3354(31521)   on 2010-05-02 21:19:49 (Show Source): You can put this solution on YOUR website!What do you want to do?
 Equations/299609: radical 7a/6b1 solutions Answer 215226 by Alan3354(31521)   on 2010-05-02 21:19:29 (Show Source): You can put this solution on YOUR website!Do you have a question?
 Quadratic_Equations/299608: Find the distance between the pair of points. Express your answer in simplest radical form. (1,-3) and (9,-18)1 solutions Answer 215224 by Alan3354(31521)   on 2010-05-02 21:18:53 (Show Source):
 Angles/299588: Find the approximate value of the volume of the right circular cone with a circular base shown below. Approximate your solution to the nearest hundredth. cone is base is { 24cm 20cm { is the cone1 solutions Answer 215223 by Alan3354(31521)   on 2010-05-02 21:17:23 (Show Source): You can put this solution on YOUR website!Is the 24 cm base the radius, diameter, or circumference? Is 20 cm the height? ---------------------- The volume of a cone is: Put in the values for r and h, and calculate it.
Quadratic_Equations/299593: A baseball is thrown straight upwards with an initial velocity of 224 ft/s.
At what time(s) does the ball reach 832 feet?

1 solutions

Answer 215216 by Alan3354(31521)   on 2010-05-02 21:01:53 (Show Source):
You can put this solution on YOUR website!
A baseball is thrown straight upwards with an initial velocity of 224 ft/s.
At what time(s) does the ball reach 832 feet?
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h(t) = -16t^2 + 224t gives the height in feet as a function of t in seconds.
832 = -16t^2 + 224t
-t^2 + 14t - 52 = 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 -12 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 -12 is + or - . The solution is , or Here's your graph:

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Looks like it's on May 32nd.
It doesn't go that high, it's max height is 784 feet at 7 seconds.

Quadratic_Equations/299546: This is the exact equation she gave me: "A child tosses a ball upward with an initial velocity of 10 f/s at a height of 3 feet. If it is not caught, how long will it be in the air?"
The formula she gave us to use is h(t)=-16^2+vt+s
I tried setting it equal to zero but got lost after that.
1 solutions

Answer 215196 by Alan3354(31521)   on 2010-05-02 19:43:50 (Show Source):
You can put this solution on YOUR website!
This is the exact equation she gave me: "A child tosses a ball upward with an initial velocity of 10 f/s at a height of 3 feet. If it is not caught, how long will it be in the air?"
The formula she gave us to use is h(t)=-16^2+vt+s
I tried setting it equal to zero but got lost after that.
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If you set it to zero, you can find the time when it hits the ground, when h=0. That's how long it is in the air.
h(t)=-16^2+vt+s
Actually, it's h(t)=-16t^2+vt+s
h(t) = -16t^2 + 10t + 3
-16t^2 + 10t + 3 = 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 : . Discriminant d=292 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.221500234082346, 0.846500234082346. Here's your graph:

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Ignore the negative number.
t =~0.8465 seconds to impact
You were doing it right, setting it to zero.

 Linear-systems/299545: I need to find the particular solution and general solution for the following problem x-4y+z=3 x+8y-z=101 solutions Answer 215191 by Alan3354(31521)   on 2010-05-02 19:36:40 (Show Source): You can put this solution on YOUR website!There are 3 variables and 2 eqns.
Quadratic_Equations/299526: what is the exact and approximate solution to three decimal places x^2+5x-7=0
1 solutions

Answer 215188 by Alan3354(31521)   on 2010-05-02 19:17:51 (Show Source):
You can put this solution on YOUR website!
what is the exact and approximate solution to three decimal places x^2+5x-7=0
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 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=53 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.14005494464026, -6.14005494464026. Here's your graph:

 Linear-systems/299523: Find an equation of ther line that contains the point (1,0) and is perpendicular to 2x + y = -41 solutions Answer 215187 by Alan3354(31521)   on 2010-05-02 19:16:09 (Show Source): You can put this solution on YOUR website!A line and a point example. Write in standard form the eqation of a line that satisfies the given conditions. Perpendicular to 9x+3y=36, through (1,2) ----------------- Find the slope of the line. Do that by putting the equation in slope-intercept form, y = mx + b. That means solve for y. 9x+3y = 36 3y= - 9x + 36 y = -3x + 12 The slope, m = -3 ------------------ The slope of lines parallel is the same. The slope of lines perpendicular is the negative inverse, m = +1/3 ---------------- Use y = mx + b and the point (1,2) to find b. 2 = (1/3)*1 + b b = 5/3 The equation is y = (1/3)x + 5/3 (slope-intercept form) x - 3y = -5 (standard form) ------------------------ For further assistance, or to check your work, email me via the thank you note, or at Moral Loophole@aol.com
 Linear-equations/299525: Find an equation of a line that is perpendicular to the line that passes through the points (0,1) & (5, 6)?1 solutions Answer 215185 by Alan3354(31521)   on 2010-05-02 19:13:51 (Show Source): You can put this solution on YOUR website!Given 2 points example. Find the equation of the line thru the points (2,1) and (3,5) --------------------- This is a 2 step process. First find the slope of the line thru the points. slope, m = diffy/diffx m = (5-1)/(3-2) m = 4 --------- Now use y = mx + b with either point to find b, the y-intercept. y = mx + b 5 = 4*3 + b b = -7 ------- y = mx + b y = 4x - 7 is the answer. ------------------------ Another approach using determinants: |x y 1| |2 1 1| = 0 |3 5 1| -------- x(1-5) - y(2-3) + 1(10-3) = 0 -4x + y + 7 = 0 y = 4x - 7 --------- For further assistance, or to check your work, email me via the thank you note or at Moral Loophole@aol.com
 Linear-equations/299391: write an equation of the line containing the giving point and parallel to the givenline. express your answer in the form y=mx+b (-4,5);8x=9y+41 solutions Answer 215140 by Alan3354(31521)   on 2010-05-02 15:26:09 (Show Source): You can put this solution on YOUR website!A line and a point example. Write in standard form the eqation of a line that satisfies the given conditions. Perpendicular to 9x+3y=36, through (1,2) ----------------- Find the slope of the line. Do that by putting the equation in slope-intercept form, y = mx + b. That means solve for y. 9x+3y = 36 3y= - 9x + 36 y = -3x + 13 The slope, m = -3 ------------------ The slope of lines parallel is the same. The slope of lines perpendicular is the negative inverse, m = +1/3 ---------------- Use y = mx + b and the point (1,2) to find b. 2 = (1/3)*1 + b b = 5/3 The equation is y = (1/3)x + 5/3 (slope-intercept form) x - 3y = -5 (standard form) ------------------------ For further assistance, or to check your work, email me via the thank you note, or at MoralLoophole@aol.com
 logarithm/299402: x^=101 solutions Answer 215137 by Alan3354(31521)   on 2010-05-02 15:23:42 (Show Source): You can put this solution on YOUR website!What is the exponent of x?
 Probability-and-statistics/299382: lock combinations are made by using 4 digits. how many different lock combinations can be made if repetition of digits is allowed?1 solutions Answer 215128 by Alan3354(31521)   on 2010-05-02 14:08:30 (Show Source): You can put this solution on YOUR website!10*10*10*10 = 10000
 Linear-equations/299337: trying to do linear graphs. having trouble with y = 2x+5. can you help?1 solutions Answer 215120 by Alan3354(31521)   on 2010-05-02 12:03:49 (Show Source): You can put this solution on YOUR website!trying to do linear graphs. having trouble with y = 2x+5. can you help? -------------- I probably can. What sort of trouble?
 Linear-equations/299303: trying to do linear graphs. having trouble with x-y=10. can you help?1 solutions Answer 215110 by Alan3354(31521)   on 2010-05-02 11:02:22 (Show Source): You can put this solution on YOUR website!trying to do linear graphs. having trouble with x-y=10. can you help? --------------- It's a straight line, so you need 2 points. x-y = 10 y = x - 10 Pick values for x, find y x = 0, y = -10 --> (0,-10) x = 10, y = 0 --> (10,0) ------------- Plot them, draw a line thru them
 Equations/299199: An airplane took 4 hours to fly 1200 miles agianst a headwind.The return trip with the wind took 3 hours. Find the speed of the plane in still air and the speed of the wind. What is the speed of the wind in still air? What is the wind speed?1 solutions Answer 215093 by Alan3354(31521)   on 2010-05-02 09:10:24 (Show Source): You can put this solution on YOUR website!An airplane took 4 hours to fly 1200 miles agianst a headwind.The return trip with the wind took 3 hours. Find the speed of the plane in still air and the speed of the wind. What is the speed of the wind in still air? What is the wind speed? ---------------- 1200/4 = 300 mph groundspeed 1200/3 = 400 mph groundspeed The plane's airspeed is the average, = 350 mph ---------------- The windspeed is the difference, = 50 mph