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Find the volume of the box.
1 solutions
Answer 110872 by ankor@dixie-net.com(15746)   on 2008-08-05 15:43:26 (Show Source):
You can put this solution on YOUR website!An open-top box will be made from a square piece of cardboard of length 26-inch by cutting 2-inch squares from the corners and folding up the sides. Find the volume of the box.
:
After removing the 2" squares on the corners:
length and width = 26 - 4 = 22"
Height = 2"
;
vol = 22 * 22 * 2 = 968 cu/in
|
Rational-functions/150905: The sum of the ages of Art, Ben, and Cal is 59. Art is 1 year older than Cal, Cal is 1 year younger than Ben. Which of these people were teenagers 7 years ago?
1 solutions
Answer 110844 by ankor@dixie-net.com(15746) on 2008-08-05 14:18:54 (Show Source):
You can put this solution on YOUR website!Write an equation for each statement:
:
"The sum of the ages of Art, Ben, and Cal is 59."
a + b + c = 59
:
"Art is 1 year older than Cal,"
a = c + 1
:
"Cal is 1 year younger than Ben."
c = b - 1
or
b = c + 1
;
Substitute for a and b and find in the total age equation, find c
(c+1) + (c+1) + c = 59
3c + 2 = 59
3c = 59 - 2
c = 
c = 19 yrs
:
a = 20; b = 20
:
Which of these people were teenagers 7 years ago?
:
c would be 12, a & b would be teenagers
|
Quadratic_Equations/150893: 1. A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of rows and columns, found that 24 characters were left out. When he tried to add one more row and column, he found that he was short of 25 characters. Can you find the number of characters used by the designer?
1 solutions
Answer 110825 by ankor@dixie-net.com(15746) on 2008-08-05 12:21:41 (Show Source):
You can put this solution on YOUR website!"A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of row and columns, found that 24 characters were left out."
:
If x = number of characters in each row
we translate this statement as
x*x + 24
x^2 + 24 = total number of characters
:
"When he tried to add one more row and column, he found that he was short of 25 characters."
:
Now, the number of rows is "x + 1", and the number of columns is "x + 1", so we have
(x + 1)(x + 1) - 25
FOIL
x^2 + 2x + 1 - 25 = total number of charaters
:
an equation using both statement:
x^2 + 2x + 1 -25 = x^2 + 24
x^2 + 2x -24 = x^2 + 24
x^2 - x^2 + 2x - 24 - 24 = 0
2x - 48 = 0
2x = +48
x = 48/2
x = 24
:
Grid is 24 by 24 which contains 576 character + 24 left out = 600
Grid of 25 by 25 = 625 character so he would have 25 blanks
|
absolute-value/150824: Solve |-10x + 70| = |8x - 74|
I really have no idea as to how to go about starting this problem.... Please help!
1 solutions
Answer 110816 by ankor@dixie-net.com(15746) on 2008-08-05 11:35:16 (Show Source):
You can put this solution on YOUR website!Solve |-10x + 70| = |8x - 74|
:
Case 1:
-10x + 70 = +|8x - 74|
-10x + 70 = 8x - 74
-10x - 8x = -74 - 70
-18x = -144
x = 
x = +8
;
Case 2:
-10x + 70 = -|8x - 74|
-10x + 70 = -(8x - 74)
-10x + 70 = -8x + 74
-10x + 8x = 74 - 70
-2x = +4
x = 
x = -2
:
Prove that this is true by substituting both values in the original equation
x=8)
|-10(8) + 70| = |8(8) - 74|
|-80 + 70| = |64 - 74|
|-10| = |-10|
+10 = +10
:
x=-2
|-10(-2) + 70| = |8(-2) - 74|
|+20 + 70| = |-16 - 74|
|+90| = |-90|
+90 = +90
:
|
Mixture_Word_Problems/150850: Solve This Problem Interactively Customize This Problem
A mixture containing 6% salt is to be mixed with 2 ounces of a mixture which is 15% salt, in order to obtain a solution which is 12% salt. How much of the first solution must be used?
1 solutions
Answer 110806 by ankor@dixie-net.com(15746) on 2008-08-05 10:37:04 (Show Source):
You can put this solution on YOUR website!A mixture containing 6% salt is to be mixed with 2 ounces of a mixture which is 15% salt, in order to obtain a solution which is 12% salt. How much of the first solution must be used?
:
How do you solve a problem "Interactively"?
:
Anyway.
:
Let x = amt of 1st solution required
:
.06x + .15(2) = .12(x+2)
:
.06x + .3 = .12x + .24
:
.3 - .24 = .12x - .06x
:
.06 = .06x
:
x = 1 oz of the 1st solution required
:
:
Check solution:
.06(1) + .15(2) = .12(1+2)
.06 + .30 = .36
|
Rate-of-work-word-problems/150822: A tank can be filled by two pipes separately in 10 and 15 minutes respectively. When a third pipe is used simultaneously with the first two pipes, the tank can be filled in 4 minutes. How long would it take the third pipe alone to fill the tank?
1 solutions
Answer 110752 by ankor@dixie-net.com(15746) on 2008-08-04 22:07:03 (Show Source):
You can put this solution on YOUR website!A tank can be filled by two pipes separately in 10 and 15 minutes respectively. When a third pipe is used simultaneously with the first two pipes, the tank can be filled in 4 minutes. How long would it take the third pipe alone to fill the tank?
:
Let x = time (in min) required by the 3rd pipe alone:
Let the full tank = 1
:
 +  +  = 1
:
Multiply equation by 30x to eliminate the denominators, results
3x(4) + 2x(4) + 30(4) = 30x
:
12x + 8x + 120 = 30x
:
20x + 120 = 30x
:
120 = 30x - 20x
:
120 = 10x
x = 
x = 12 min for the third pipe to fill it alone
;
:
Check solution using a calc
(4/10) + (4/15) + (4/12) =
.4 + .267 + .333 = 1
|
Linear-systems/150807: Please help with this problem.
Z=sqrt((1000^2)+(1592^2))
It is my understanding that the square root of a "number" squared is the "number".
If this is true I would solve this as: Z=1000+1592 so Z=2592, but Im not sure this is correct
1 solutions
Answer 110731 by ankor@dixie-net.com(15746) on 2008-08-04 19:14:18 (Show Source):
You can put this solution on YOUR website!Z=sqrt((1000^2)+(1592^2))
No, if there were a * (multiply) between them it would be 1000*1592
but if there's a plus or a minus you have to do the math inside the radical
then find the square root of that
:
You can prove this to yourself with a calc: Enter  = 1880...
|
Points-lines-and-rays/150781: What is the slope of a line that is perpendicular to the line that passes through the points (4,7) and (9,3)?
A. -4/5 B. -5/4 C. 4/5 D. 5/4
1 solutions
Answer 110708 by ankor@dixie-net.com(15746) on 2008-08-04 16:24:10 (Show Source):
You can put this solution on YOUR website!What is the slope of a line that is perpendicular to the line that passes through the points (4,7) and (9,3)?
:
Use the slope formula to find the slope: m = 
:
Assign values: x1=4, y1=7; x2=9, y2=3
m1 =  =  = 
:
The relationship of slopes of perpendicular lines: m1*m2 = -1; find m2
* m2 = -1
m2 = -1 * 
m2 = +  slope of the perpendicular line
|
Radicals/150700: This question is from textbook
Can someone please help solve this problem 2/3=2-5x-3/x-1 thank you for your help.
1 solutions
Answer 110698 by ankor@dixie-net.com(15746) on 2008-08-04 15:17:32 (Show Source):
You can put this solution on YOUR website!Can someone please help solve this problem 2/3=2-5x-3/x-1:
:
Assume you mean:
;
Multiply equation by the common denominator: 3(x-1); results:
2(x-1) = 2(3(x-1)) - 3(5x - 3)
:
do the multiplying to get rid of the brackets
2x - 2 = 6x - 6 - 15x + 9
:
group like terms, x's on the left, no. on the right
2x - 6x + 15x = -6 + 9 + 2
:
11x = 5
x = 
;
I'll let you check the solution in the original equation
|
Mixture_Word_Problems/150710: a mixture of food a and b is to be made so that it contains at least 45 oz of nutrient N2. the cost per pound of a is $4 and each pound of A contains 1 oz of N1 and 2 oz of N2. Food b cost $8 per pound and each pound contains 1.5 oz of N1 and 0.5 of N2. if the weight of the mixture must not exceed 40lb, how many pound of each should be used so that the total cost is a minimum?
1 solutions
Answer 110687 by ankor@dixie-net.com(15746) on 2008-08-04 14:45:28 (Show Source):
You can put this solution on YOUR website!a mixture of food a and b is to be made so that it contains at least 45 oz of nutrient N2. the cost per pound of a is $4 and each pound of A contains 1 oz of N1 and 2 oz of N2. Food b cost $8 per pound and each pound contains 1.5 oz of N1 and 0.5 of N2. if the weight of the mixture must not exceed 40lb, how many pound of each should be used so that the total cost is a minimum?
;
Just get 23 lbs of Food a, that gives you 46 oz of N2, less than 40 lb, at 4$ a lb
;
There is no constraint on N1, so I quess we ignore that.
|
Numbers_Word_Problems/150667: This question is from textbook
The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is increased by 20 which is twice the original number. Find the original number.
1 solutions
Answer 110603 by ankor@dixie-net.com(15746) on 2008-08-03 18:26:46 (Show Source):
You can put this solution on YOUR website!Let x = the 10's digit
Let y = the units digit
:
the number = (10x + y)
the reversed number = (10y + x)
"
Write an equation for each statement:
"The sum of the digits of a two-digit number is 11."
x + y = 11
or
y = 11-x
:
"When the digits are reversed, the new number is increased by 20 which is twice the original number."
(10y+x) + 20 = 2(10x+y)
10y + x + 20 = 20x + 2y
10y - 2y + x - 20x = -20
8y - 19x = -20
:
Find the original number.
;
Substitute (11-x) for y in the above equation:
8(11-x) - 19x = -20
88 - 8x - 19x = -20
-8x - 19x = 20 - 88
-27x = -108
x = 
x = +4
:
y = 11-4
y = 7
:
original number: 47
;
:
Check solution in the statement;
"When the digits are reversed, the new number is increased by 20 which is twice the original number."
74 + 20 = 2(47); confirms our solutions
|
Length-and-distance/150629: This question is from textbook CPM Geometry
A 12 foot ladder is six feet from the wall. How high on the wall does the ladder touch??
1 solutions
Answer 110575 by ankor@dixie-net.com(15746) on 2008-08-03 14:52:28 (Show Source):
You can put this solution on YOUR website!A 12 foot ladder is six feet from the wall. How high on the wall does the ladder touch??
:
use Pythagorean here: a^2 + b^2 = c^2
;
a = height where the ladder touches
b = 6 ft;
c = the 12'ladder
:
a^2 + 6^2 = 12^2
:
a^2 + 36 = 144
:
a^2 = 144 - 36
:
a^2 = 108
a = 
a = 10.4 ft
|
Inequalities/150622: suoppose uyou want to cover the backyard with rocks and trees. I will need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees I can buy with a budget for rock and trees of $2,500. How do I write this as an inquality that illustrates the problem.
1 solutions
Answer 110574 by ankor@dixie-net.com(15746) on 2008-08-03 14:44:00 (Show Source):
You can put this solution on YOUR website!I will need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees I can buy with a budget for rock and trees of $2,500. How do I write this as an inequality that illustrates the problem.
:
Write an equation for the statement:
30 tons of rock + x trees =< 2500
:
(30*60) + 84x =< 2500
:
1800 + 84x =< 2500
:
84x =< 2500 - 1800
:
84x =< 700
x =< 
x =< 8.333
You can't buy a fractional tree, therefore max trees = 8
:
:
Check solution:
(30*60) + (8*84) =
1800 + 672 = 2472 which is < 2500
|
Polynomials-and-rational-expressions/150603: An astronaut on the moon tosses a ball upwards; by how much will the height of the ball exeed 100 feet if the ball's height follows:
h(t)= -2.6t(second power) +32.1t+5.5
1 solutions
Answer 110571 by ankor@dixie-net.com(15746) on 2008-08-03 14:28:19 (Show Source):
You can put this solution on YOUR website!An astronaut on the moon tosses a ball upwards; by how much will the height of the ball exceed 100 feet if the ball's height follows:
:
h(t)= -2.6t^2 + 32.1t + 5.5
:
Find the axis of symmetry x = 
a=-2.6; b=32.1
t = 
t = 
t = +6.173 sec
:
Find the vertex (max)
h(t) = -2.6(6.173^2) + 32.1(6.173) + 5.5
h(t) = -2.6(38.106) + 198.153 + 5.5
h(t) = -99.075 + 198.153 + 5.5
h(t) = +104.578 ft
:
Exceeds 100 ft by 4.578 ft
|
Finance/150616: If I have $1000 to invest for 2 yrs, which gives a higher yield, a CD or a money market account.
Please help me - Nancy
1 solutions
Answer 110566 by ankor@dixie-net.com(15746) on 2008-08-03 13:25:24 (Show Source):
You can put this solution on YOUR website!If I have $1000 to invest for 2 yrs, which gives a higher yield, a CD or a money market account.
:
A CD always has a higher yield, than a mm account for that amount
Check with your bank
:
The CD, however is locked in, and can't be withdrawn early without penalty
The mm account has less interest but will allow a limited number of withdrawals every month
|
Travel_Word_Problems/150630: 7) The path of a falling object is given by the function where represents the initial velocity in ft/sec and represents the initial height in feet. Also, s represents the height in feet of the object at any time, t, which is measured in seconds.
a) If a rock is thrown upward with an initial velocity of 40 feet per second from the top of a 30-foot building, write the height (s) equation using this information.
Typing hint: Type t-squared as t^2
Answer:
b) How high is the rock after 2 seconds?
Answer:
Show your work here:
c) After how many seconds will the graph reach maximum height? Show your work algebraically.
Answer:
Show your work here:
d) What is the maximum height?
Answer:
Show your work here:
I have tried numerous approaches but don't feel I have the right answer. If I use the #2 in place of x my solution comes out to s=46 which does not sound reasonable to me. Please help
1 solutions
Answer 110565 by ankor@dixie-net.com(15746) on 2008-08-03 13:16:44 (Show Source):
You can put this solution on YOUR website!The path of a falling object is given by the function where represents the initial velocity in ft/sec and represents the initial height in feet. Also, s represents the height in feet of the object at any time, t, which is measured in seconds.
a) If a rock is thrown upward with an initial velocity of 40 feet per second from the top of a 30-foot building, write the height (s) equation using this information.
Typing hint: Type t-squared as t^2
Answer:
:
The equation consists of three parts,
Gravity: -16t^2; negative because it's pulling down
Initial velocity: +40t; plus because it's thrown upward
Initial height: 30; from a 30 ft building
:
s(t) = -16t^2 + 40t + 30
;
:
b) How high is the rock after 2 seconds?
Answer:
:
Substitute 2 for t in the above equation:
h = -16(2^2) + 40(2) + 30
h = -64 + 80 + 30
h = +46 ft; so you're right!!
;
:
c) After how many seconds will the graph reach maximum height? Show your work algebraically.
:
The max height will occur at the axis of symmetry x =
In your equation a=-16 and b=40
:
t = 
t = 
t = 1.25 seconds it will be max height
:
:
d) What is the maximum height?
:
Substitute 1.25 for t and find the height
h = -16(1.25^2) + 40(1.25) + 30
h = -16(1.5625) + 50 + 30
h = -25
h = 55 ft is the max height
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Numbers_Word_Problems/150595: the units digit of a two-digit number is 3 less than its tens digit. if the number is divided by the sum of its digits, the quotient is 6 and the remainder is 8. find the number.
1 solutions
Answer 110556 by ankor@dixie-net.com(15746) on 2008-08-03 10:51:39 (Show Source):
You can put this solution on YOUR website!the units digit of a two-digit number is 3 less than its tens digit. if the number is divided by the sum of its digits, the quotient is 6 and the remainder is 8. find the number.
:
Let x = the 10's digit
then
(x-3) = the units digit
:
The number: 10x + (x-3) which can be written 11x-3
:
Write an equation for the statement:
"if the number is divided by the sum of its digits, the quotient is 6 and the remainder is 8."
(subtract the remainder to make it come out even)
 = 6
:
 = 6
:
Multiply both sides by (2x-3)
11x - 11 = 6(2x-3)
:
11x - 11 = 12x - 18
:
-11 + 18 = 12x - 11x
:
x = 7 is the 10's digit
then
7 - 3 = 4 is the units digit
:
Our number is 74
:
Check the solution by dividing it by the sum which is 11
That gives you 6 with a remainder of 8
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Rate-of-work-word-problems/150560: Janet and Carl decorate cakes in a bakery. Janet can decorate a cake every 0.24 hour and Carl can decorate a cake every 0.33 hour. If they work together, at what rate are they decorating cakes? Round to the nearest tenth of a cake per hour.
1 solutions
Answer 110523 by ankor@dixie-net.com(15746) on 2008-08-02 21:27:47 (Show Source):
You can put this solution on YOUR website!Janet and Carl decorate cakes in a bakery. Janet can decorate a cake every 0.24 hour and Carl can decorate a cake every 0.33 hour. If they work together, at what rate are they decorating cakes? Round to the nearest tenth of a cake per hour.
:
Let t = how long it take for them to decorate a cake together;
Let a completed cake = 1
 +  = 1
:
Multiply equation by .24*.33 which is .0792
.33t + .24t = .0792
:
.57t = .0792
t = 
t = .13895 hr per cake (both working)
;
That's a rate of  = 7.2 cakes per hour
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Geometry_Word_Problems/150562: THE WIDTH OF A RECTANGLE IS 3 FEET LESS THAN ITS LENGHTH .IF THE PERIMETER IS 22 FEET WHAT IS THE WIDTH?
1 solutions
Answer 110521 by ankor@dixie-net.com(15746) on 2008-08-02 21:08:56 (Show Source):
You can put this solution on YOUR website!THE WIDTH OF A RECTANGLE IS 3 FEET LESS THAN ITS LENGHTH .IF THE PERIMETER IS 22 FEET WHAT IS THE WIDTH?
:
Let x = the width
It says the length is 3 ft longer, therefore:
(x+3) = the length
:
Perimeter is 2L + 2W, therefore:
2(x+3) + 2x = 22
:
2x + 6 + 2x = 22
:
2x + 2x = 22 - 6
:
4x = 16
x = 
x = 4 ft is the width
and
4 + 3 = 7 ft is the length
:
:
Check using the given perimeter
2(7) + 2(4) = 22
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Rational-functions/150500: graph f(x) = 4^x and g(x)=log(base4)x in the same rectangular coordinate system
1 solutions
Answer 110509 by ankor@dixie-net.com(15746) on 2008-08-02 16:50:34 (Show Source):
You can put this solution on YOUR website!graph f(x) = 4^x and g(x)=log(base4)x in the same rectangular coordinate system
:
Plot y = 4^x; (purple)
x | y
-------
.5 | 2
1.0| 4
2.0|16
;
To plot y = logb4(x), change base to nat log: y = 
(so we can use a calc and I can graph it here.)
x | y
-------
.5 |-.5
1.0| 0
1.5|+.3
2.0|+.5
3.0|+.8
:
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Equations/150530: Hi, I'm having trouble understanding factoring and reducing algebraic equations. if you could explain this problem step by step i'd really appreciate it.
6w^3(w+1)^3÷10w^5(w+1)^3. Thanks!!
Sincerely,
Michelle van Humbeck
1 solutions
Answer 110495 by ankor@dixie-net.com(15746) on 2008-08-02 14:43:50 (Show Source):
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Quadratic_Equations/150318: This question is from textbook
The path of a falling object is given by the function s+-16t^2+vot + so where represents the initial velocity in ft/sec and represents the initial height in feet. Also, s o represents the height in feet of the object at any time, t, which is measured in seconds.
a) If a rock is thrown upward with an initial velocity of 40 feet per second from the top of a 30-foot building, write the height (s) equation using this information.
1 solutions
Answer 110492 by ankor@dixie-net.com(15746) on 2008-08-02 14:34:33 (Show Source):
You can put this solution on YOUR website!a) If a rock is thrown upward with an initial velocity of 40 feet per second from the top of a 30-foot building, write the height (s) equation using this information.
:
s = -16t^2 + 40t + 30
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Rate-of-work-word-problems/150509: This question is from textbook
working together, alice and betty can do a certain job in 4 1/3 days. but alice fell ill after 2 days of working and betty finished the job continuing to work alone in 6 3/4 more days. how long would it take each to do the job if each of them worked alone?
1 solutions
Answer 110489 by ankor@dixie-net.com(15746) on 2008-08-02 14:26:00 (Show Source):
You can put this solution on YOUR website!working together, alice and betty can do a certain job in 4 1/3 days. but alice fell ill after 2 days of working and betty finished the job continuing to work alone in 6 3/4 more days. how long would it take each to do the job if each of them worked alone?
:
Let a = time required by Alice working alone
Let b = time required by Betty alone
Let the completed job = 1
:
equation when they both work 4  day
 +  = 1
Multiply equation by 3 give us integers to work with
 +  = 3
:
Equation when one got sick; (b worked a total of 2+6.75 = 8.75
 +  = 1
Multiply equation by 6.5
+  = 6.5
:
Use elimination here:
+ = 6.5
+ = 3
-------------------------------subtraction eliminates a, find b
 = 3.5
3.5b = 43.875
b = 
b = 12.5357 days for Betty alone
:
Use + = 3, substitute for b and find a
+  = 3
+ 1.037 = 3
= 3 - 1.037
= 1.963
1.963a = 13
a = 
a = 6.6225 days for Alice alone
;
:
To check solutions, use + = 1, substituting for a and b:
 +  = 1
.302 + .698 = 1; confirms our solution
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Square-cubic-other-roots/150473: ______
√7x + 29 = x + 3
1 solutions
Answer 110444 by ankor@dixie-net.com(15746) on 2008-08-01 21:48:18 (Show Source):
You can put this solution on YOUR website! = x + 3
:
Square both sides, this gets rid of the radical on the left
7x + 29 = (x+3)^2
:
FOIL (x+3)(x+3)
7x + 29 = x^2 + 6x + 9
:
0 = x^2 + 6x - 7x + 9 - 29
:
A quadratic equation:
x^2 - x - 20 = 0
:
Factors to:
(x-5)(x+4) = 0
:
The positive solution
x = 5
:
Check in the original equation
 = 5 + 3
 = 8
:
The negative solution
x = -4
Check in original equation
 = -4 + 3
 = -1
 = -1
+1 does not = -1
:
Only x=5 is a solution
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Travel_Word_Problems/150471: Hello! Can you please help me with our homework? Please explain it thoroughly and show the solution step by step. Thanks!
Problem: RV and Pearl are 50 meters apart. After recognizing each other from a distance, they run towards each other along a straight path to give each other a hug. RV’s rate is 6 m/s while Pearl runs at 4 m/s. As they start to run, RV’s dog leaves him and run towards Pearl at 8 m/s. Upon reaching Pearl, the dog runs towards RV and continues to run back and forth until they meet. What is the distance traveled by the dog when the two finally hug each other?
My idea about the problem:
x=time
4x + 6x = 50
10 x =50
x = 5 seconds
So, the distance travelled by RV when they hug each other is 20 m and the distance travelled by Pearl is 30 m. I don't have any idea on how to get the total distance travelled by the dog.
1 solutions
Answer 110442 by ankor@dixie-net.com(15746) on 2008-08-01 21:27:47 (Show Source):
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Quadratic-relations-and-conic-sections/150467: A ball is thrown upward from a 100 foot tall building with an initial velocity of 14 feet per second. Its height s(t) in feet is given by the function s(t)= -16t^2+14t+100. Find the interval of time for which the height of the ball is greater than 103 feet.
I don't even know where to start.
1 solutions
Answer 110437 by ankor@dixie-net.com(15746) on 2008-08-01 20:40:40 (Show Source):
You can put this solution on YOUR website!A ball is thrown upward from a 100 foot tall building with an initial velocity of 14 feet per second. Its height s(t) in feet is given by the function s(t)= -16t^2+14t+100. Find the interval of time for which the height of the ball is greater than 103 feet.
:
Write the equation for s = 103 ft
-16t^2 + 14t + 100 = 103
:
-16t^2 + 14t + 100 - 103 = 0
;
-16t^2 + 14t - 3 = 0
:
Use the quadratic formula to find t:
In this problem a=-16, b=14; c=-3
:
:
Two solutions:
t = .375 sec; (passes 103 ft on the way up)
and
t = .5 sec; (passes 103 ft on the way down)
:
So the interval of time would be .5 - .375 = .125 sec above 103 ft
;
How about this? Does it make sense to you now?
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Volume/150283: the radius of a certain brand of lollipop is 12mm
the formula for the volume of a sphere is V=(4/3)(pie)(r)^3. what is the volume of the lollipop? if you are licking at a rate of 1 lick every 5 seconds, and each lick you take removes 40mm^3 from the volume of the lollipop. how many seconds does it take until the lollipop is consumed? how many licks? if you're dealing with a lollipop with bubble gum in the center, how many licks will it take to get to the center, if the gum has a radius of 5 mm. write an equation that tells you the volume of the lollipop in terms of L, the number of licks. write an equation that tells you the radius of the lollipop in terms of L.
1 solutions
Answer 110431 by ankor@dixie-net.com(15746) on 2008-08-01 19:35:28 (Show Source):
You can put this solution on YOUR website!the radius of a certain brand of lollipop is 12mm
the formula for the volume of a sphere is V=(4/3)(pie)(r)^3. what is the volume of the lollipop?
:
V = 
V = 
V = 7238.23 cu mm
;
:
if you are licking at a rate of 1 lick every 5 seconds, and each lick you take removes 40mm^3 from the volume of the lollipop. how many seconds does it take until the lollipop is consumed?
t =  * 5
t = 904.78 seconds
:
how many licks?
L =
L = 181 licks
:
if you're dealing with a lollipop with bubble gum in the center, how many licks will it take to get to the center, if the gum has a radius of 5 mm.
:
Find the volume of the gum center
V = 
V = 
V = 523.6 cu mm is the gum
:
L = 
L = 
L = 168 licks
;
write an equation that tells you the volume of the lollipop in terms of L, the number of licks.
:
Using the volume containing the gum
:
V = 6715 - 40L
:
write an equation that tells you the radius of the lollipop in terms of L.
:
Using the one containing the gum;
r = 12 - L 
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Mixture_Word_Problems/150331: Paul's Plumbing charges $35 for any service call plus an additional $40 an hour for labor. A service call from Robert's Rapid Repair Plumbing costs $45 plus and additional $40 and hour for labor. When is the total price for a service the same for both companies? when is it better to use Paul's Plumbing? explain your answer in terms of slopes and y-intercepts.
1 solutions
Answer 110427 by ankor@dixie-net.com(15746) on 2008-08-01 17:45:57 (Show Source):
You can put this solution on YOUR website!Paul's Plumbing charges $35 for any service call plus an additional $40 an hour for labor. A service call from Robert's Rapid Repair Plumbing costs $45 plus and additional $40 and hour for labor. When is the total price for a service the same for both companies? when is it better to use Paul's Plumbing? explain your answer in terms of slopes and y-intercepts.
:
Since they charge the same for labor ($40), Paul's is always $10 cheaper
:
In terms of graphs, they have the same slope (40x) so the lines are parallel and never intersect. the y intercepts will be different, 35 & 45
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Equations/150351: This question is from textbook
Maximum height. If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t) = -16t² + 32t where t is time in seconds. Graph this parabola for 0≤ t ≤ 2.
What is the maximum height reached by the ball?
1 solutions
Answer 110408 by ankor@dixie-net.com(15746) on 2008-08-01 14:06:31 (Show Source):
You can put this solution on YOUR website!Maximum height. If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t) = -16t² + 32t where t is time in seconds. Graph this parabola for 0≤ t ≤
:
y = s(t); x = t
Find y for x=0, x=.5, x=1, x=1.5, and x=2
:
2. What is the maximum height reached by the ball:
From the graph we can see max occurs when t = 1
Find s(1)
s(1) = -16(1^2) + 32(1)
s(1) = -16 + 32
s(1) = +16 ft max
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Graphs/150339: Write the equation of a line in standard form, passing through (-2,-3) and parallel to a line with the equation 3x-y=2
1 solutions
Answer 110406 by ankor@dixie-net.com(15746) on 2008-08-01 13:49:11 (Show Source):
You can put this solution on YOUR website!Write the equation of a line in standard form, passing through (-2,-3) and parallel to a line with the equation 3x-y=2
:
Since they are parallel both lines will have the same slope
Find the slope from the given equation, put it in the slope/intercept form
:
3x - y = 2
-y = -3x + 2
y = +3x - 2; y has to be positive, multiply by -1
the slope: m = 3
:
Find the line with coordinates -2,-3 and m=3;
use point slope formula y - y1 = m(x-x1)
:
y -(-3) = 3(x - (-2))
y + 3 = 3(x + 2)
y + 3 = 3x + 6
y = 3x + 6 - 3
y = 3x + 3
Standard form
-3x + y = 3
or
3x - y = -3
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