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Volume/626398: Hi, My husband needs to build a fuel/chemical tank for work out of a cylinder pipe. It needs to hold 15 gallons but he isn't sure what length and diameter the pipe needs to be (in inches/feet) to achieve his goal. I am stumped on how to even find an equation for something such as this. ANY help would be greatly appreciated!! Thank you!
1 solutions
Answer 394136 by solver91311(16868)   on 2012-07-07 02:32:43 (Show Source):
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Quadratic_Equations/626391: Give exact and approximate solutions to three decimal places
y^2-20y+100=16
What are the exact solutions?
y=?
(Type an exact answer as needed)
(Rationalize all denominators)
(express complex numbers in terms of I)
(use a comma to separate answers as needed)
There are no approximate solutions since the solutions are integers
Does this mean that:
1)y^2 is the ^2 of y
2)+100=10^2
3)ignoring the sign (-) on -20, the product of square roots of 1st and 3rd term = 2*y*10 (20y)
4)y = (y-10)^2=16
y-10= ±4
y = 10 ±5
Am I doing this right?
1 solutions
Answer 394134 by solver91311(16868) on 2012-07-07 02:05:47 (Show Source):
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Percentage-and-ratio-word-problems/626319: if a company ownership is divided in the ratio of 3:2:1 what is the percentage of each ownership? Three owners I thought it would be 50%,33%,17% but I am not sure that it shouldn't be 50,30,20
1 solutions
Answer 394104 by solver91311(16868) on 2012-07-06 18:03:34 (Show Source):
You can put this solution on YOUR website!
Since the ownership is in the ratio 3:2:1, there are 3 + 2 + 1 = 6 shares and one guy has 3 out of 6 or 50%, the next has 2 out of 6 or 1/3, which is approximately 33%, and the last has 1 out of 6, or 1/6, which is slightly less than 17%.
Notice that 50% is roughly 3 times 17% and 33 percent is roughly 2 times 17%. But if your 50 30 20 were correct, then three times 20 would equal 50 and two times 20 would equal 30. Not even close.
John
My calculator said it, I believe it, that settles it
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Polynomials-and-rational-expressions/626175: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function.
f(x)=3x^2-12x+3
1. What is the vertex
2. What is the equation of the line of symmetry
3. What is the maximum/minimum of F(x)
4. Is the value, f(x)= -9 a minimum or a maximum?
Please graph. Thank you very much up front.
1 solutions
Answer 394019 by solver91311(16868) on 2012-07-06 01:27:02 (Show Source):
You can put this solution on YOUR website!
The vertex of the parabola defined by \ =\ ax^2\ +\ bx\ +\ c) is the point ) where  and ) .
The equation of the axis of symmetry is 
The maximum or minimum of ) is  . If the lead coefficient is positive, i.e.  , then the parabola opens upward and the vertex is a minimum. If the lead coefficient is negative, i.e.  , the parabola opens downward and the vertex is a maximum.
Graph: Plot the vertex. Plot the point ) which is the  -intercept. Then by symmetry, ) is also on the graph. Set the function equal to zero and solve for the two roots  and  (use the quadratic formula or complete the square since your example doesn't factor). Plot the two points, ) and ) . That gives you 5 points through which you can draw a smooth curve.
If you want more points, pick a convenient distance  from the vertex. Then calculate the value of the function ) , then plot the point \right)) . Then, by symmetry you can also plot \right)) . You can repeat this process with as many different values of as you like.
John
My calculator said it, I believe it, that settles it
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Permutations/626170: A class is working on finding patterns among the counting numbers. A student noticed an interesting pattern. She said that if you take 3 consecutive counting numbers (e.g. 7,8&9) and square the middle number (8 squared) then the resulting number (64) is one larger than the product of the two other numbers (i.e 64 is one greater that 7 x 9 = 63). Is this true for all sets of three consecutive numbers?
1 solutions
Answer 394015 by solver91311(16868) on 2012-07-06 00:38:39 (Show Source):
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Problems-with-consecutive-odd-even-integers/625788: Given A = {2, 4, 6}. B = {1, 3, 5}, and C = {1, 2, 3, 4, 5, 6, 7}
Evaluate each set:
A). A ∩ B
B). A ᴜ C
C). B ᴜ C
D). (A ᴜ B) ∩ C
E). A ᴜ ( B ᴜ C )
F). ( A ∩ B ) ∩ C
G). ( A ∩ B) ᴜ C
1 solutions
Answer 393787 by solver91311(16868) on 2012-07-04 00:16:27 (Show Source):
You can put this solution on YOUR website!
A). A ∩ B. Means the intersection of set A and set B which is the set of all elements that are in both A and B.
Since none of the elements of A are in B (and vice versa, of course), there are no elements in the set A ∩ B.
Therefore A ∩ B = 
John
My calculator said it, I believe it, that settles it
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Expressions-with-variables/625721: Write an algebraic expression to answer the question below.
A board is cut into two pieces. One piece has a length of 47 inches. If the other piece has a length of v inches, what was the total length of the board, in inches, before it was cut?
1 solutions
Answer 393746 by solver91311(16868) on 2012-07-03 17:59:19 (Show Source):
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Triangles/625736: Which of the following is the closest approximation of the perimeter of triangle PQR given P(4, 5), Q(-4, 2), and R(10, 13)?
a.37.38
b.36.35
c.22.14
d.30
*HELP NEEDEDDDD!!!!*******
♥Thanks!
1 solutions
Answer 393739 by solver91311(16868) on 2012-07-03 17:42:40 (Show Source):
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Human-and-algebraic-language/625738: I keep getting different answers so I thought I would ask this again.
Find the volume of a cone, in terms of pi, with a radius of 3 inches and a height of 6 inches. If the radius of the cone is doubled while the height remains constant, what is the volume of the cone? What happens to the volume of a cone if it’s radius is doubled?
1 solutions
Answer 393738 by solver91311(16868) on 2012-07-03 17:39:28 (Show Source):
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Equations/625691: Enclose in parentheses the expressions you need to do first.Then evaluate each expression.
1. 15+30divide6+8=______
2. 20-9+7X3=______
3. ___=5X9-5+3
4. ____=42divide6X7+3
5.48divide6-4X2+35=____
1 solutions
Answer 393710 by solver91311(16868) on 2012-07-03 14:21:54 (Show Source):
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Graphs/625671: Please Help!!
Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale).
tickets = -0.3x^2+6x+22
a. Does the graph of this equation open up or down? How did you determine this?
b. Describe what happens to the tickets sales as time passes.
c.Use the quadratic equation to determine the last day that tickets will be sold.
Note. Write your answer in terms of the number of days after ticket sales begin.
d. Will tickets peak or be at a low during the middle of the sale? How do you know?
e. After how many days will the peak or low occur?
f. How many tickets will be sold on the day when the peak or low occurs?
g. What is the point of the vertex? How does this number relate to your answers in parts e. and f?
h. How many solutions are there to the equation? How do you know?
i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
1 solutions
Answer 393708 by solver91311(16868) on 2012-07-03 14:16:47 (Show Source):
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Coordinate-system/625686: please help me with this question it says i have to solve the system below graphically and indicate the method i use to plot the lines and show my work.... a. y=2x 2x+y=4 b. check by substituting the answer back into the orginal equations. thank you...
1 solutions
Answer 393706 by solver91311(16868) on 2012-07-03 14:13:22 (Show Source):
You can put this solution on YOUR website!
Start with either one of your equations.
Step 1. Pick a value for x. It can be anything you like, but 0, 1, or some other small integer usually works well and makes the arithmetic easier.
Step 2. Substitute that value in place of x in your equation. Do the arithmetic and determine the value of y that results.
Step 3. Take the value of x that you selected for step 1 and the value of y that you calculated in step 2 and form an ordered pair (x,y).
Step 4. Plot the ordered pair from Step 3 on your graph. Remember that the x value is the distance right or left along the horizontal axis and the y value is the distance up or down along the vertical axis.
Step 5. Repeat steps 1 through 4 with a different value for x.
Step 6. Draw a line across your graph that passes through the two points that you plotted.
Step 7. Repeat steps 1 through 6 using the other equation.
The point where the lines intersect is the solution, because the coordinates of that point will satisfy (read: make true) both of your equations. You need to determine, by inspection of the graph, what the coordinates of that point are and report your answer as an ordered pair, (x,y), using those coordinates. To check your answer, you should substitute this set of coordinates into each of your original equations and verify that you have a true statement for each of the equations.
If both lines graph to the same line, then the solution set is infinite, i.e. every ordered pair that satisfies one equation will satisfy the other. If the lines are parallel, then the solution set is empty.
A consistent system has at least one solution.
An inconsistent system has no solutions.
An independent system has exactly one solution.
A dependent system has infinitely many solutions.
Therefore a system can be either consistent and independent, consistent and dependent, or inconsistent.
To check, take the  -coordinate of your solution point and substitute for in either one of your equations, then take the -coordinate of your solution point and substitute for in that same equation. Do the arithmetic. If the result is a true statement, then the point is a solution of that equation. Repeat the process with the other equation.
If the point is a solution of BOTH equations, then it is a solution of the system of equations.
John
My calculator said it, I believe it, that settles it
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