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Recent problems solved by 'stanbon'
stanbon answered: 57911 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 , 57300..57329 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899 , 57900..57929, >>Next
Quadratic_Equations/77444: Can someone please help me with this? Thanks
Graph the following equations and find:
The y-intercept.
The x-intercepts, if any.
The vertex.
The line of symmetry.
Solve for the y-intercept, x-intercepts (if any), the coordinates of the vertex, and the line of symmetry using the methods shown in the lesson.
y = x2 + 7x + 12
y = x2 - 8x + 6
y = - x2 + 6x - 5
1 solutions
Answer 55549 by stanbon(57984)   on 2007-04-08 09:43:32 (Show Source):
You can put this solution on YOUR website!Graph the following equations and find:
The y-intercept.
The x-intercepts, if any.
The vertex.
The line of symmetry.
Solve for the y-intercept, x-intercepts (if any), the coordinates of the vertex, and the line of symmetry using the methods shown in the lesson.
y = x^2 + 7x + 12
-------------------
y-intercept: let x=0, then y=12
x-interdept: let y=0
(x+4)(x+3)=0
x=-4 or x=-3
--------------
Vertex:
y-12+? = x^2+7x+?
y-12+(7/2)^2 = x^2+7x+(7/2)^2
y-(1/4) = (x+(7/2))
Vertex at (-7/2,1/4)
--------
Line of symmetry:
x=-7/2
==========
Cheers,
Stan H.
|
Radicals/77139: table: x -2 -1 0 1 2
y .111 .333 1 3 9
Given the table above, graph the function, identify the graph of the function (line, parabola,hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function.
Graph:
Graph Type:
Explanation:
Domain:
Range:
1 solutions
Answer 55522 by stanbon(57984) on 2007-04-07 19:47:39 (Show Source):
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Quadratic_Equations/77398: it is estimated that the earth is losing 4000 species of plant and animals every year if s represents the number of species living last year how many species are on eath this year
1 solutions
Answer 55514 by stanbon(57984) on 2007-04-07 19:29:05 (Show Source):
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Polynomials-and-rational-expressions/77376: Solve the problem. Answer could be rational expression.
Henry sold 120 magazine subscriptions in x+2 days. If he sold at the same rate for another week, then how many magazines did he sell in the extra week?
1 solutions
Answer 55512 by stanbon(57984) on 2007-04-07 19:22:06 (Show Source):
You can put this solution on YOUR website!Henry sold 120 magazine subscriptions in x+2 days. If he sold at the same rate for another week, then how many magazines did he sell in the extra week?
----------------
120/(x+2) mags/day
Another week is 7 days:
In that week he will sell
7(120/(x+2) = 840/(x+2) mags/week
===========
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/77388: Find a ratio for the following, and write it as a ratio of integers in lowest terms.
Among 100 coffee drinkers, 36 said that they preferred their coffee black and the rest did not prefer their coffee black. Find the ratio of those who prefer black coffee to those who prefer nonblack coffee.
1 solutions
Answer 55510 by stanbon(57984) on 2007-04-07 19:14:49 (Show Source):
You can put this solution on YOUR website!Find a ratio for the following, and write it as a ratio of integers in lowest terms.
Among 100 coffee drinkers, 36 said that they preferred their coffee black and the rest did not prefer their coffee black. Find the ratio of those who prefer black coffee to those who prefer nonblack coffee.
--------
36 prefer black coffee
100-36 = 64 prefer nonblack coffee
--------
Ratio of prefer black to prefer nonblack = 36/64 = 9/16
==============
Cheers,
Stan H.
|
Exponents/77396: Convert 71 to base 3
1 solutions
Answer 55507 by stanbon(57984) on 2007-04-07 19:07:59 (Show Source):
You can put this solution on YOUR website!Convert 71 to base 3
---------
You need to keep track of the remainders under successive divisions by 3.
71/3 = 23; remainder 2
23/3=7 ; remainder 2
7/3=2 ; remainder 1
2 is the surviving 1st digit:
71(base 3) = 2122
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/77390: To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population?
1 solutions
Answer 55505 by stanbon(57984) on 2007-04-07 19:03:18 (Show Source):
You can put this solution on YOUR website!To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population?
----------
Let "x" be the number in the population.
real population/sample caught = released population/sample caught
x/100=50/2
x=2500 bears
===============
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/77394: End behavior of of each graph of the polynomial..
-6d^3 -4d^2 +2d -1
I got.. a<0 n odd.. because the function d has odd degree and a negative dominating term.
is that correct?
1 solutions
Answer 55503 by stanbon(57984) on 2007-04-07 18:57:00 (Show Source):
You can put this solution on YOUR website!End behavior of of each graph of the polynomial..
-6d^3 -4d^2 +2d -1
--------
You may be right but that is not the way it is normally stated.
The graph goes to negative infinity as d goes to positive infinity because of
the -6d^3 term.
-------
The graph goes to + infinity as d goes to negative infinity for the
same reason.
--------
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/77368: can i please get help with this?
x^2+2x-15
over
4x^2
divided by
x^2-25
over
2x-10
1 solutions
Answer 55492 by stanbon(57984) on 2007-04-07 17:28:37 (Show Source):
You can put this solution on YOUR website!x^2+2x-15
over
4x^2
divided by
x^2-25
over
2x-10
-----------
Factor where you can to get:
(x+5)(x-3)
over
4x^2
divided by
(x+5)(x-5)
over
2(x-5)
--------------
Invert the denominator and change to multiplication.
(x+5)(x-3)
over
4x^2
muliplied by
2(x-5)
over
(x=5)(x+5)
-------------
Cancel any factors common to a numerator and a denominator to get:
(x-3)
over
2x^2
============
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/77349: A bridge is built in the shape of a semielliptical arch. It has a span of 94 feet. The height of the arch 28 feet from the center is to be 6 feet. Find the height of the arch at its center.
1 solutions
Answer 55482 by stanbon(57984) on 2007-04-07 16:51:12 (Show Source):
You can put this solution on YOUR website!A bridge is built in the shape of a semielliptical arch. It has a span of 94 feet. The height of the arch 28 feet from the center is to be 6 feet. Find the height of the arch at its center.
---------
Draw the picture putting the width of 94 on the x-axis centered
at the origin.
The vertices are then (-47,0) and (47,0)------
Then x^2/47^2 + y^2/b^2 = 1
The ellipse passes thru the point (28,6)
Substitute those values in the equation to solve for "b".
--------
28^2/47^2 + 6^2/b^2 = 1
0.3549117248 + 36/b^2 = 1
36/b^2 = 0.6450882752..
b^2/36=1.550175439
b^2=55.806
------
At the center the height is b=7.47 feet
===========
EQUATION of the ellipse
x^2/47^2 + y^2/55.806 = 1
==========
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/77348: A searchlight is shaped like a paraboloid of revelution. If the light source is located 3 feet from the base along the axis of symmetry and the opening is 12 feet across, how deep should the searchlight be? Assume the light source is at the parabola's focus.
1 solutions
Answer 55468 by stanbon(57984) on 2007-04-07 12:46:31 (Show Source):
You can put this solution on YOUR website!A searchlight is shaped like a paraboloid of revelution. If the light source is located 3 feet from the base along the axis of symmetry and the opening is 12 feet across, how deep should the searchlight be? Assume the light source is at the parabola's focus.
--------
Draw the picture of the parbola opening upward with vertex at (0,0)
and focus at (0,3).
---------
Form: x^2=4py
Distance from vertex to focus = p=3
--------
Equation: 12y=x^2
y=(1/12)x^2
---------
If the opening is 12 feet across it intersects the parabola at (-6,y) and (6,y)
Need to find y to get the depth of the light.
y=(1/12)(6^2)=3
So the depth is 3 ft.
============
Cheers,
Stan H.
|
Circles/77341: The price a flower shop charges for roses is inversely proportional to the number of days before Valentine's Day that the order is placed. A dozen roses ordered ten days before valentine's Day costs $12.00 while the same order placed five days before Valentine's Day costs $24.00. What is the cost of a dozen roses ordered one day before Valentine's day?
1 solutions
Answer 55467 by stanbon(57984) on 2007-04-07 12:30:50 (Show Source):
You can put this solution on YOUR website!The price a flower shop charges for roses is inversely proportional to the number of days before Valentine's Day that the order is placed.
P = k/d
-------
A dozen roses ordered ten days before valentine's Day costs $12.00 while the same order placed five days before Valentine's Day costs $24.00.
12 = k/10
k=120
Therefore, Formula: P=120/d
--------
What is the cost of a dozen roses ordered one day before Valentine's day?
p=120/1 = $120
=======
Cheers,
Stan H.
|
Circles/77340: if point a(-1,0) is rotated 60degree, the coordinates of point a would be
1 solutions
Answer 55458 by stanbon(57984) on 2007-04-07 10:40:01 (Show Source):
You can put this solution on YOUR website!Draw the picture.
Comment:I assumed you were rotating into the 3rd quadrant.
Let the new point be P(x,y)
Draw a segment from P to the x axis; that has length y
You now have a right triangle with a 60 degree angle at the origin.
The 3rd angle, at point P, is a 30 degree angle.
x=1cos(240)=-1/2
y=1sin(240)= (-sqrt3)/2
======
Cheers,
Stan H.
|
Travel_Word_Problems/77326: Problem #36(this problem is driving me crazy among two other ones more)
A ball is thrown upward from the roof of a building 100m tall with an initial velocity of 20m/s. Use this information for exercises 35 to 38.Please show all your steps and the answer in radical form.
The equation for the hieght of the ball is: h = -5t^2+20t+100
When will the ball reach a height of 80m?
1 solutions
Answer 55454 by stanbon(57984) on 2007-04-07 09:38:32 (Show Source):
You can put this solution on YOUR website!h = -5t^2+20t+100
When will the ball reach a height of 80m?
-------------
80 = -5t^2+20t+100
-5t^2+20t+20=0
t^2-4t-4=0
t=[4+sqrt(16-4*-4]/2
t=[4+sqrt(32)]/2
t=[4+4sqrt2]/2
t=2+2sqrt2 seconds
=========
Cheers,
Stan H.
|
logarithm/77329: If Log of 32.5_to the base 10 is 1.5118834 than the number whose log to the
same base is 3.5118834 is
a) 0.00325
b) 0.000325
c) 0.0000325
d) none
1 solutions
Answer 55452 by stanbon(57984) on 2007-04-07 09:25:05 (Show Source):
You can put this solution on YOUR website!If Log of 32.5_to the base 10 is 1.5118834 than the number whose log to the
same base is 3.5118834 is
a) 0.00325
b) 0.000325
c) 0.0000325
d) none
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Log32.5 = 1.5118814 means the following:
10^1.5118814 = 32.5
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So 10^3.5118814= 10^2*10^1.5118814= 100(32.5)=3250
Therefore log3250=3.5118834
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Cheers,
Stan H.
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Quadratic-relations-and-conic-sections/77260: Given a parabola whose axis of symmetry is the y-axis. The point (1,5)lies on the parabola. which point also lies on the parabola?
1 solutions
Answer 55424 by stanbon(57984) on 2007-04-06 22:17:10 (Show Source):
You can put this solution on YOUR website!Given a parabola whose axis of symmetry is the y-axis. The point (1,5)lies on the parabola. which point also lies on the parabola?
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Form: y=ax^2+bx+c
If passes thru (1,5) it passes thru (-1,5) because of symmetry.
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Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/77281: This question is from textbook Algebra:Structure and Method
Solve, using two equations in two variables: This year, the total number of dogs and cats sold by the Animal Adoption Agency was 1216. Last year, 420 more cats and double the number of dogs were sold for a total of 2024. How many of each were sold this year?
1 solutions
Answer 55418 by stanbon(57984) on 2007-04-06 22:06:16 (Show Source):
You can put this solution on YOUR website!This year, the total number of dogs and cats sold by the Animal Adoption Agency was 1216. Last year, 420 more cats and double the number of dogs were sold for a total of 2024. How many of each were sold this year?
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Let number of dogs be "d" ; Let number of cats be "c"
EQUATIONS:
d + c = 1216
2d+c+420 = 2024
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c=1216-d
Substitute to get:
2d+1216-d+420=2024
d = 388 dogs
c=1216-d = 828 cats
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Cheers,
Stan H.
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