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Recent problems solved by 'stanbon'
stanbon answered: 57288 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299, >>Next
logarithm/698510: How do I solve the following logarithm for x?
The base of the following logs is 2.
log(x-1) - log(x+3) = log(1/x)
1 solutions
Answer 430741 by stanbon(57361)   on 2013-01-04 22:23:47 (Show Source):
You can put this solution on YOUR website!The base of the following logs is 2.
log2(x-1) - log2(x+3) = log2(1/x)
-----
log2[(x-1)/(x+3)] = log2(1/x)
------
Take the antilog of both sides:
(x-1)/(x+3) = 1/x
----
Cross-multiply:
x^2-x = x+3
------
x^2 -2x - 3 = 0
---
Factor:
(x-3)(x+1) = 0
Positive solution:
x = 3
============
Cheers,
Stan H.
===================
|
logarithm/698511: How do I solve the following logarithmic equation for x?
The base of the following log is x.
log64 = 3/2
1 solutions
Answer 430739 by stanbon(57361) on 2013-01-04 22:16:40 (Show Source):
You can put this solution on YOUR website!The base of the following log is x.
logx(64) = 3/2
----
base = x
log = exponent = 3/2
result = 64
-----
x^(3/2) = 64
----
x = (64)^(2/3)
-----
x = 4^2
---
x = 16
------------------
Cheers,
Stan H.
|
Rectangles/698507: The diagonal of a rectangle is 13 cm. How long is its width if its length is 10 cm?
1 solutions
Answer 430738 by stanbon(57361) on 2013-01-04 22:12:01 (Show Source):
You can put this solution on YOUR website!The diagonal of a rectangle is 13 cm. How long
is its width if its length is 10 cm?
---------------------
Draw the picture:
You have a right triangle with hypotenuse = 13 and one side is 10
=====
Equation:
Let the length be "x":
13^2 = 10^2 + x^2
-----
169 = 100 + x^2
------
x^2 = 69
----
length = sqrt(69)
=======================
Cheers,
Stan H.
======================
|
Probability-and-statistics/698348: Error Analysis.The error in measuring the diameter of a large tree in inches is normal(-0.25,0.5).Find the probability that the error is between -1 and 1 inches.
1 solutions
Answer 430734 by stanbon(57361) on 2013-01-04 21:35:58 (Show Source):
You can put this solution on YOUR website!Error Analysis.The error in measuring the diameter of a large tree in inches is normal(-0.25,0.5).Find the probability that the error is between -1 and 1 inches.
------
z(-1) = (-1--0.25)/0.5 = -0.75/0.5 = -1.5
---
z(1) = (1--0.25)/0.5 = 1.25/0.5 = 2.5
----
P(-1< x <1) = P(-1.5< z < 2.5) = normalcdf(-1.5,2.5) = 0.9270
=========
Cheers,
Stan H.
=========
|
Probability-and-statistics/698392: Two number cubes are rolled three times in a row. What is the probability of rolling a sum of 10 all three times?
1 solutions
Answer 430733 by stanbon(57361) on 2013-01-04 21:28:31 (Show Source):
You can put this solution on YOUR website!Two number cubes are rolled three times in a row. What is the probability of rolling a sum of 10 all three times?
------
Sum of 10: 4/6 ; 5/5 ; 6/4 ----- 3 ways
--------
P(sum of 10 on one roll) = 3/36 = 1/12
----
P(sum of 10 on 3 rolls) (1/12)^3
=========
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/698485: The Sum of two numbers is 9 . the difference between five times of the first and four times of the seconds is 9 .what are the numbers ?
1 solutions
Answer 430732 by stanbon(57361) on 2013-01-04 21:22:14 (Show Source):
You can put this solution on YOUR website!The Sum of two numbers is 9 . the difference between five times of the first and four times of the seconds is 9 .what are the numbers ?
--------
Equations:
x + y = 9
5x-4y = 9
------
Multiply thru the top equation by 5:
5x + 5y = 45
5x - 4y = 9
--------
Subtract and solve for "y":
9y = 36
y = 4
------
Solve for "x":
x + y = 9
x + 4 = 9
x = 5
=========
Cheers,
Stan H.
|
Metalworking/698492: What is the answer for "u" is this equation:
5.1u-6.6=2.4-0.9u
At first I remembered like families so 5.1u and 0.9u will be together I dont know if Im correct so it will be:
5.1u + or - 0.9 I am always getting confused can you explain the steps for me.
1 solutions
Answer 430730 by stanbon(57361) on 2013-01-04 21:07:31 (Show Source):
You can put this solution on YOUR website!5.1u -6.6 = 2.4 -0.9u
----
Add 0.9u to both sides:
6u - 6.6 = 2.4
-----
Add 6.6 to both sides:
6u = 9
----
Divide both sides by 6 to get:
u = 3/2
================
Cheers,
Stan H.
|
Mixture_Word_Problems/698489: You answered one question for me, and I have another just so I get the hang of how to set it up. if 8 oz of chili has 17 grams of protein how many protein in 1 oz?
Thank you
Shelley
1 solutions
Answer 430725 by stanbon(57361) on 2013-01-04 20:57:55 (Show Source):
You can put this solution on YOUR website!if 8 oz of chili has 17 grams of protein how many protein in 1 oz
-------------
Proportion:
protein/weight = protein/weight
----------------------------
x/1oz = 17/8oz
------
x = 1(17/8)
----
x = 2 1/8 grams of protein
===============================
Cheers,
Stan H.
============
|
Angles/698470: find m of angle a(6x+7) and m of angle B(3x+20) if m of angle A+m of angle B+360
1 solutions
Answer 430719 by stanbon(57361) on 2013-01-04 20:08:39 (Show Source):
You can put this solution on YOUR website!find m of angle a(6x+7) and m of angle B(3x+20) if m of angle A+m of angle B+360
-------
Equation:
6x+7 + 3x+20 = 360
-----
9x + 27 = 360
-----
9x = 333
----
x = 37
-----------
A = 6x+7 = 229 degrees
----
B = 3x+20 = 131 degrees
==============
Cheers,
Stan H.
|
test/698479: Four times a number is less than or equal to the sum of 3 times the number and-2
1 solutions
Answer 430716 by stanbon(57361) on 2013-01-04 19:58:20 (Show Source):
You can put this solution on YOUR website!Four times a number is less than or equal to the sum of 3 times the number and-2
----
Equation:
4x <= 3x -2
----
x <= -2
-------------
Cheers,
Stan H.
|
Numbers_Word_Problems/698471: In Exercises 2-6, find two positive numbers that satisfy the given requirements.
The second number is the reciprocal of the first and their sum is minimum.
1 solutions
Answer 430715 by stanbon(57361) on 2013-01-04 19:55:35 (Show Source):
You can put this solution on YOUR website!find two positive numbers that satisfy the given requirements.
The second number is the reciprocal of the first and their sum is minimum.
-----
1st; x
2nd: 1/x
----
Equation:
S(x) = x + (1/x)
----
S(x) = (x^2+1)/x
----
Take the derivative:
S'(x) = [x(2x)- (x^2+1)]/x^2
-----
Find the zeroes:
[2x^2 - x^2 - 1] / x^2 = 0
----
(x^2-1) = 0
x = 1 or x = -1
----
Max = 1+(1/1) = 2
Min = -1+ (1/-1) = -1-1 = -2
=========
Cheers,
Stan H.
=============
|
Trigonometry-basics/697939: If a building casts a shadow of 150' from its base, and a yardstick casts a shadow of 2' , how tall is the building?
1 solutions
Answer 430711 by stanbon(57361) on 2013-01-04 19:11:45 (Show Source):
You can put this solution on YOUR website!If a building casts a shadow of 150' from its base, and a yardstick casts a shadow of 2' , how tall is the building?
-----
Note: a yardstick is 3 feet long.
-----
Proportion:
x/150 = 3/2
----
x = 150(3/2)
-----
x = 225 feet (height of the building)
=================
Cheers,
Stan H.
|
Trigonometry-basics/697952: solve the equation for 0 ≤ theta ≥ 2pi. write your answer as multiple of pi, if possible
2sin theta (cos theta) + cos theta=0
1 solutions
Answer 430708 by stanbon(57361) on 2013-01-04 19:06:52 (Show Source):
You can put this solution on YOUR website!solve the equation for 0 <= theta <= 2pi.
write your answer as a multiple of pi, if possible
-------
2sin(theta)*cos (theta) + cos(theta) = 0
------------------
Factor:
cos(theta)[2sin(theta)+1] = 0
-------
cos(theta) = 0 or sin(theta) = -1/2
-------
theta = pi/2 or (3/2)pi or (7/6)pi or (11/6)pi
===================
Cheers,
Stan H.
===================
|
Graphs/698466: solve 5x + 3y > -6 and 2y + x < 6 (inequalities)
1 solutions
Answer 430692 by stanbon(57361) on 2013-01-04 18:09:22 (Show Source):
You can put this solution on YOUR website!solve
5x + 3y > -6
Solve for "y":
y > (-5/3)x - 2
---
Graph the boundry line as a dashed line:
y = (-5/3)x - 2
Shade the half-plane ABOVE the boundary because you want
y to be greater than (-5/3)x-2:::
---------------------------------------------------
and 2y + x < 6
y < (-1/2)x + 3
----
Boundary y = (-1/2)x + 3
Shade the half-plance BELOW te boundary:
-------
The intersection of the two half-planes is the solution
set for the system on inequalities.
===================
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/698265: How do i graph y=2x^2+4 what are the steps in solving to get the vertex and the axis of symmetry and then find the parabula?
1 solutions
Answer 430562 by stanbon(57361) on 2013-01-03 20:14:35 (Show Source):
You can put this solution on YOUR website!How do i graph y=2x^2+4 what are the steps in solving to get the vertex and the axis of symmetry and then find the parabula?
-----
Vertex occurs where x = -b/(2a) = -0/(2*2) = 0
---
The y-coordinate of the vertex is f(0) = 4
----
Vertex: (0,4)
------
The axis of symmetry is a vertical line thru the axis:
Its equatiion is x = 0
==================
Cheers,
Stan H.
==================
|
Trigonometry-basics/698164: If x is not equal to 0, then u/x+5u/x-u/5x
1 solutions
Answer 430525 by stanbon(57361) on 2013-01-03 17:26:53 (Show Source):
You can put this solution on YOUR website!If x is not equal to 0, then
u/x+5u/x-u/5x
----
least common denominator: 5x
====
Rewrite each fraction with the lcd as its denominator to get:
-----
= 5u/5x + 25u/5x - u/5x
-----
= (5u + 25u - u)/5x
----
= 24u/5x
----------------
Cheers,
Stan H.
================
|
Trigonometry-basics/698003: hello. i would really appreciate your help with the following question.
i need to find the range of the following function: f(x)=(x+6)^2
if you can provide a step by step explanation, that would be really helpful.
thank you.
1 solutions
Answer 430521 by stanbon(57361) on 2013-01-03 17:16:56 (Show Source):
You can put this solution on YOUR website!find the range of the following function: f(x)=(x+6)^2
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Since y = (x+6)^2 it cannot be negative.
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The smallest value it can have is zero; that occurs when x = -6.
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So the Range is ALL Real Numbers greater than or equal to zero.
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Cheers,
Stan H.
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Inequalities/698206: Can you please help with 7x+2y=-13
-3x-8y=-23 I am suppose to solve the system by substitution and tell whether it has one no or infinitly solution but I don't understand how do you solve with all those x and y and how can you tell how many solutins it has
1 solutions
Answer 430518 by stanbon(57361) on 2013-01-03 17:06:34 (Show Source):
You can put this solution on YOUR website!7x+2y=-13
-3x-8y=-23 I am suppose to solve the system by substitution and tell whether it has one no or infinitly solution
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7x+2y=-13
-3x-8y=-23
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Solve the top equation for "y":
y = (-7x - 13)/2
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Substitute for "y" and solve for "x":
-3x - 8(-7x-13)/2 = -23
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-3x + (56x+104)/2 = -23
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-3x + 28x + 52 = -23
25x = -75
x = -3
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Solve for "y":
y = (-7x-13)/2
y = (-7*-3-13)/2
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y = 4
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Ans: one solution
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Cheers,
Stan H.
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Equations/698202: Peter took a 1,500 mile trip in 5 days. Each day, he drove 30 miles more than the day before. How many miles did he cover on the first day?
x+x+30+x+30+x+30+x+30=1500
5x+120=1500
5x=1380
x=276
The answer is not correct. What am I doing wrong?
1 solutions
Answer 430511 by stanbon(57361) on 2013-01-03 16:50:33 (Show Source):
You can put this solution on YOUR website!Peter took a 1,500 mile trip in 5 days. Each day, he drove 30 miles more than the day before. How many miles did he cover on the first day?
x+(x+30)+(x+2*30)+(x+3*30)+(x+4*30) = 1500
Now you can solve it.
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Cheers,
Stan H>
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