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# Recent problems solved by 'Nate'

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 logarithm/39459: Tell whether the x-value is a soultion of the equation. 5e^x + 2 = 17, x = ln 31 solutions Answer 24906 by Nate(3500)   on 2006-05-25 20:46:25 (Show Source): You can put this solution on YOUR website!That answer is correct.
 logarithm/39467: Solve the logarithmic equation. Round the result to the three decimal places if necessary. -3 + ln x = 51 solutions Answer 24905 by Nate(3500)   on 2006-05-25 20:45:12 (Show Source):
 Functions/39471: f(x)=sqrt -5x+4 find the domain. 1 solutions Answer 24903 by Nate(3500)   on 2006-05-25 20:39:17 (Show Source): You can put this solution on YOUR website! The value in the square root sign has to be greater than or equal to zero: That is your domain.
f(x)= x2 - 1
f of X= x sqared minus one
Graph each function.
1 solutions

Answer 24902 by Nate(3500)   on 2006-05-25 20:36:50 (Show Source):
You can put this solution on YOUR website!

Should look like the parabola below:
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=4 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1, -1. Here's your graph:

 Linear-systems/39476: This question is from textbook Algebra 1 could you please help me with this problem .1x+2.3=.7x+.51 solutions Answer 24898 by Nate(3500)   on 2006-05-25 20:13:01 (Show Source):
 Equations/39477: World grain demand. Freeport McMoRan projects that in 2010 world grain supply will be 1.8 trillion metric tons and the supply will be only 3/4 of world grain demand. What will world grain demand be in 2010?1 solutions Answer 24896 by Nate(3500)   on 2006-05-25 20:09:04 (Show Source): You can put this solution on YOUR website!(3/4)x = 1.8 x = (4/3)1.8 The total demand will be 2.4 trillion metric tons.
 Radicals/39322: Hello, I need help I was told to simplify. 5 sqrt 12+6 sqrt 1/3 - 3 sqrt 48 Thank you 1 solutions Answer 24895 by Nate(3500)   on 2006-05-25 20:06:33 (Show Source):
 logarithm/39457: Tell whether the x-value is a soultion of the equation. ln 2x = 14, x = 2e^141 solutions Answer 24893 by Nate(3500)   on 2006-05-25 18:57:45 (Show Source):
 logarithm/39456: Tell whether the x-value is a soultion of the equation. ln x = 3, x = 3e 1 solutions Answer 24892 by Nate(3500)   on 2006-05-25 18:56:30 (Show Source): You can put this solution on YOUR website!No ....
 Quadratic-relations-and-conic-sections/39452: Describe in words the graph below. Include in your description the shape, along with other possible relevant information such as length, width, and center points. y = x^2 - x1 solutions Answer 24891 by Nate(3500)   on 2006-05-25 18:54:25 (Show Source): You can put this solution on YOUR website! We know that this is a parabola, so it is "U-shaped". The length and width will always increase as the x-values increase. The vertex is: (-b/2a , f(x)) = (1/2 , -1/2) Latus Rectum (the distance from one point on the parabola across the foci to another point on the parabola) = |1/a| = |1/1| So we know this parabola is skinny. The distance from the foci to the vertex (also known as the distance from the Directix to the vertex) = (1/(4a)) = (1/4)
 Expressions-with-variables/39432: The product of the first and third of three positive consecutive odd integers is 80 less then 23 times the second integer. find all three odd integers.1 solutions Answer 24889 by Nate(3500)   on 2006-05-25 18:35:42 (Show Source): You can put this solution on YOUR website!Variables: Equation: or Even though two is a possible answer, it is an even postive integer. Two is not the answer. Your answers are: 17,19,21
 Square-cubic-other-roots/39372: This question is from textbook College Algebra Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign.I am having a hard time coming up with an example for this problem. 1 solutions Answer 24808 by Nate(3500)   on 2006-05-24 23:22:42 (Show Source): You can put this solution on YOUR website!The advantage would be that if the number has a radical sign, you would have to convert in order to solve faster. Also, its a faster way to multiply or add exponents. Faster way: or or
 Radicals/39373: This question is from textbook Rationalize the denominator of each radical expression. Assume all variables represent nonnegative numbers and that no denominitors are 0. 1 + Square root 3 __________________ 3 Square root of 5 + 2 Square Root 31 solutions Answer 24807 by Nate(3500)   on 2006-05-24 23:16:09 (Show Source): You can put this solution on YOUR website! After simplifying, you get:
Linear_Equations_And_Systems_Word_Problems/39353: Hello,
First and foremost I would like to thank you for your assistance. I am a parent of a high school student and have not taken Alegbra in a years. I would appreciate any assistance you can provide.
Thanks,
Steve
Problem 1:

Use the table shown below. Assume the data can be represented as a linear relationship.

a) Using the two points defined by data from 2000 and 2005, develop a linear equation for the data.

b) Using the equation found in a), predict the tax revenue for 2006.

c) Use the calculator to determine the "best fit" equation for the data.

d) Using the equation found in c), predict the tax revenue for 2006.

e) Using the equation found in c), estimate tax revenue for the missing 2002 data

Year Sales Tax Revenue
2000 \$19500
2001 \$21000
2003 \$24000
2004 \$27300
2005 \$31000

Note: data is missing for 2002, the county clerk embezzled the funds for that year.

__________________________________________________________________________

Problem #2

A rocket is shot from the top of an oceanside cliff that is 60ft high. The original angle is 45 degrees and the original velocity is 50ft per sec. The formula for the rocket's motion is:

y = f(x) = -0.0128x(squared) + x + 60

The variables x and y are both measured in feet. The variable x represents horizontal displacement (distance from the base of the cliff), and y represents the height of the rocket above the ground.

a) What is the maximum height attained by the rocket? How far has the rocket travelled horizontally at this point?

b) At waht point(s) (after launch) is the rocket 70 feet high? (Horizontal displacement)

c) How far away from the base of the cliff does the rocket land?
1 solutions

Answer 24805 by Nate(3500)   on 2006-05-24 23:07:03 (Show Source):
You can put this solution on YOUR website!
Year Sales Tax Revenue
2000 \$19500
2001 \$21000
2003 \$24000
2004 \$27300
2005 \$31000
a) Using the two points defined by data from 2000 and 2005, develop a linear equation for the data.
2000 \$19500 at this time (0 years from 2000)
2005 \$31000 at this time (5 years from 2000)
y = ((31000-19500)/5)x + 19500
y = 2300x + 19500
b) Using the equation found in a), predict the tax revenue for 2006.
y = 2300(6) + 19500
y = 13800 + 19500 = 33300
c) Use the calculator to determine the "best fit" equation for the data.
I haven't done any equations dealing with the "best fit" line, but I will try my best. It seems right.
y = (31000-((19500 + 21000 + 24000 + 27300 + 31000)/5))x + 19500
y = 2205x + 19500
d) Using the equation found in c), predict the tax revenue for 2006.
y = 2205(6) + 19500 = 32730
e) Using the equation found in c), estimate tax revenue for the missing 2002 data
y = 2205x(2) + 19500 = 23910
.............................................................................

a) What is the maximum height attained by the rocket? How far has the rocket travelled horizontally at this point?
The highest point would be at the vertex.
((-b/2a),f(x))
10000/256 = 5000/128 = 2500/64 = 1250/32 = 625/16
f(x) = -0.0128(625/16)^2 + (625/16) + 60
v(39.0625,79.53125) Max height: 39.0625ft. Distance traveled: 79.53125ft.
b) At waht point(s) (after launch) is the rocket 70 feet high? (Horizontal displacement)

Use the quadratic formula to determine the root.
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=0.488 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 11.7746106303547, 66.3503893696453. Here's your graph:

c) How far away from the base of the cliff does the rocket land?
Again, use quadratic formula to determine the roots.
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=4.072 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -39.762489097684, 117.887489097684. Here's your graph:

Graphs/39370: This question is from textbook algebra 1
graph . what are the roots of
1 solutions

Answer 24800 by Nate(3500)   on 2006-05-24 22:29:39 (Show Source):
You can put this solution on YOUR website!

The zeros are and
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=4 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, 2. Here's your graph:

 Divisibility_and_Prime_Numbers/39369: Can someone help me with this problem? Subtract: 4 7/9 - 2 11/18 Thanks!1 solutions Answer 24799 by Nate(3500)   on 2006-05-24 22:26:21 (Show Source): You can put this solution on YOUR website!4 7/9 - 2 11/18 4 14/18 - 2 11/18 86/18 - 47/18 39/18
 Inequalities/39368: x+33/x+3 is greater than or equal to 7....could you please solve this and show how to work it out1 solutions Answer 24798 by Nate(3500)   on 2006-05-24 22:21:36 (Show Source): You can put this solution on YOUR website! Since any number cannot equal zero, cannot equal . <------ {2} ========= (-3) -------> The shaded region (=======) is the location of the answers. (-3) means not equal to while {2} means equal to.
 Numeric_Fractions/39367: Could you please help me solve this problem? Three drill bits are marked 3/8, 5/16, and 11/32. Which drill bit is larger? Thanks, Sher1 solutions Answer 24795 by Nate(3500)   on 2006-05-24 22:06:17 (Show Source): You can put this solution on YOUR website!3/8, 5/16, and 11/32 3(4)/8(4), 5(2)/16(2), and 11/32 12/32, 10/32, and 11/32 (3/8) is the largest drill bit
 Miscellaneous_Word_Problems/39302: A rectangle is 4 times as long as it is wide. A second rectangle is 5 centimenters longer and 2 centimeters wider than the first. The area of the second rectangle is 270 square centimeters greater than the first. What are the dimensions of the original rectangle?1 solutions Answer 24792 by Nate(3500)   on 2006-05-24 21:52:31 (Show Source): You can put this solution on YOUR website!Original: length = 4w width = w Second rectangle: length: 5 + 4w width = 2 + w Equations: First triangle: Second triangle:
 Radicals/39329: I posted this earlier incorrectly! Find the perimeter of the triangle if one side is 4, one side is sqrt 5 + sqrt 3, and the third side is sqrt 5 - sqrt 3. Thanks again!1 solutions Answer 24787 by Nate(3500)   on 2006-05-24 21:44:07 (Show Source): You can put this solution on YOUR website!The perimeter is the sum of all the sides.
 Problems-with-consecutive-odd-even-integers/39337: Find three consecutive integers such that -4 times the sum of the first and third is 13 less then 7 times the opposite of the second1 solutions Answer 24782 by Nate(3500)   on 2006-05-24 21:38:33 (Show Source): You can put this solution on YOUR website!Integers: Equation: The numbers are: 11,13,15
 logarithm/39360: This question is from textbook Could you help me with this problem, please. 3^x2 =81 solutions Answer 24778 by Nate(3500)   on 2006-05-24 21:28:52 (Show Source):
 Evaluation_Word_Problems/39359: A cube measures 3 inches on all sides.what is it's voulme in inches? What is the perimeter of a triangle which sides measure 6,8,and 10?1 solutions Answer 24774 by Nate(3500)   on 2006-05-24 21:17:05 (Show Source): You can put this solution on YOUR website!The volume for a cube is: where is length, is width, and is height The volume is 27 inches cubed. The perimeter is the sum of all the sides: The perimeter is 24 units.
 logarithm/39340: This question is from textbook How do I do the following problem? log 81=4 b^ Thank you for your help1 solutions Answer 24773 by Nate(3500)   on 2006-05-24 21:13:30 (Show Source): You can put this solution on YOUR website! or
 test/39355: rationalize the denominator and 1 solutions Answer 24771 by Nate(3500)   on 2006-05-24 21:09:25 (Show Source): You can put this solution on YOUR website! and
 Quadratic_Equations/39352: assume variables are nonnegative and 1 solutions Answer 24770 by Nate(3500)   on 2006-05-24 21:05:57 (Show Source): You can put this solution on YOUR website! ------------------------------------------------------------------------
 Probability-and-statistics/39272: A pair of 8 sided dice have sides numbered 1 through 8. Each side has the same probability of landing face up. Find the probability that the product of the 2 numbers on the sides that land face up exceeds 36.1 solutions Answer 24709 by Nate(3500)   on 2006-05-24 14:35:51 (Show Source): You can put this solution on YOUR website!Number of Ways to Get More than 36: 5:8 6:7 6:8 7:6 7:7 7:8 8:5 8:6 8:7 8:8 There are eight different ways to achieve this: 10/(8*8) (5/32)
 Functions/39258: What is the domain of function Show your answers in 2 different ways: a) by algebraic solution. b) by graphical solution. DO NOT USE CIRCLE. SOMEBODY PLEASE HELP ME WITH THIS QUESTION! THANKS.1 solutions Answer 24707 by Nate(3500)   on 2006-05-24 14:15:24 (Show Source): You can put this solution on YOUR website! The values in the square root sign have to be greater than or equal to zero: or Domain: (x| or ) Range: {y|y >= 0} Since you are not adding any numbers to your function, your range is equal or greater than zero. I am sorry; I do not know how to graph using programs available to this web.
 Polynomials-and-rational-expressions/39259: Square lot. Sam lives on a lot that he thought was a square, 157 feet by 157 feet. When he had it surveyed, he discovered that one side was actually 2 feet longer than he thought and the other was actually 2 feet shorter than he thought. How much less area does he have than he thought he had? 1 solutions Answer 24706 by Nate(3500)   on 2006-05-24 14:04:44 (Show Source): You can put this solution on YOUR website!(ideal area) - (real area) = (difference of area) (157*157) - (159*155) = (difference of area) (24649) - (24645) = 4ft. less than what he thought he originally had
test/39260: Assume that a ball is thrown vertically upward with initial velocity of 96ft per second. The distance s(t) (in feet) of the ball from the ground after t seconds is .
a) at what instant will it be back at the ground level?
b) for what time interval is the ball more than 384ft above the ground?

1 solutions

Answer 24705 by Nate(3500)   on 2006-05-24 14:00:05 (Show Source):
You can put this solution on YOUR website!
a) at what instant will it be back at the ground level?
Use quadratic formula to determine zeros.
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=9216 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0, 6. Here's your graph:

At 6 seconds, the ball will hit the ground.
b) for what time interval is the ball more than 384ft above the ground?

If you try to work this out, you will get an imaginery number. The ball will not reach this height. The highest the ball will go is about 144ft.