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Quadratic_Equations/80501: help me someone please!!
The length of a rectangle is 1 cm longer than its width. If the diagonal
of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?
1 solutions
Answer 57743 by checkley75(3666)   on 2007-05-02 20:35:19 (Show Source):
You can put this solution on YOUR website!X^2+(X+1)^2=4^2 X=WIDTH + (X+1)=LENGTH.
X^2+X^2+2X+1=16
2X^2+2X+1-16=0
2X^2+2X-15=0
using the quadratic equation we get:
x=(-2+-sqrt[2^2-4*2*-15])/2*2
x=(-2+-sqrt[4+120])/4
x=(-2+-sqrt124)/4
x=(-2+-11.1355)/4
x=(-2+11.1355)/4
x=9.1355/4
x=2.284 answer.
x=(-2-11.1355)/4
x=-13.1355/4
x=-3.2839 answer.
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Quadratic_Equations/80487: you have at least $30 in change in your drawer, consisting of dimes and quarters. write and inequality that shows the different number of coins in yur drawer. Can some one please help me with this?
1 solutions
Answer 57737 by checkley75(3666) on 2007-05-02 19:49:15 (Show Source):
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Quadratic_Equations/80484: I hope you can help with this word problem. I don't know where to begin and I cannot find an example in the book to go by. Thank you
Problem
Time to swing
The speed T (time in seconds for one complete cycle) of a pendulum is related to the length L(in feet) of the pendulum by the formula 8T^2 = pi^2L. If a child is on a swing with a 10-foot chain, then how long does it take to complete one cycle of the swing.
Hope someone can help please.
1 solutions
Answer 57731 by checkley75(3666) on 2007-05-02 19:17:09 (Show Source):
You can put this solution on YOUR website!8T^2=pi^2L WHEN L=10 FEET THE THE TIME IS:
8T^2=3.14^2*10
8T^2=9.8596*10
8T^2=98.596
T^2=98.596/8
T^2=12.3245
T=SQRT12.3245
T=3.51 SECONDS TO COMPLETE ONE CYCLE (SWING)
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Surface-area/80401: To restore medieval castle in Eorope, the conical roof of one of its round towers had to be painted with a special protective silver paint. If the diameter of the conical roof base 5.84 m and its altitude is 9.76 m, what is the cost of gilding the roof if the rate of painting the roof is equivalent to $27.50/m squared?
1 solutions
Answer 57679 by checkley75(3666) on 2007-05-02 08:49:40 (Show Source):
You can put this solution on YOUR website!FIRST WE FIND THE SLOPE OF THE TOWER SURFACE USING THE TRIANGLE WITH SIDES OF 9.76 & 5.84/2=2.92 TO FIND THE SLOPE (HYPOTENUSE)
A^2+B^2=C^2
9.76^2+2.92^2=S^2
95.2576+8.5264=S^2
S^2=103.784
S=10.187 FOR THE SLOPE.
FORMULA FOR THE TOTAL SURFACE AREA OF A CONE IS
TSA=1/2piDS+piR^2 WHERE pi=3.14, D=DIAMETER, R=RADIUS
TSA=.5*3.14*5.84*10.187+3.14*2.92^2
TSA=93.4+26.77
TSA=120.17 IS THE TOTAL SURFACE AREA OF THE TOWER.
NOW WE MULTIPLY BY $27.50
120.17*27.50=$3,304.68 TO PAINT THE TOWER.
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Radicals/80346: Oh boy! tough one for me : (
One fourth of a herd of camels was seen in the forest, twice the square root of that herd had gone to the mountain slopes and 3 times 5 camels remained on the riverbank. What is the numerical measure of the herd of camels? Ugg! Please help! Thank you
1 solutions
Answer 57642 by checkley75(3666) on 2007-05-01 21:04:59 (Show Source):
You can put this solution on YOUR website!c/4+2sqrtc+3*5=c
c/4+sqrtc+15=c
c/4+15+2sqrtc=c
2sqrtc=c-c/4-15
2sqrtc=3c/4-15
2sqrtc=(3c-60)/4
sqrtc=(3c-60)/8
c=[(3c-60)/8]^2
c=(9c^2-360c+3600)/64
64c=9c^2-360c+3600
9c^2-360c-64c+3600=0
9c^2-424c+3600=0
using the quadratic equation we get:
c=(424+-sqrt[-424^2-4*9*3600])/2*9
c=(424+-sqrt[179,776-129,600])/18
c=(424+-sqrt50,176)/18
c=(424+-224)/18
c=(424+224)/18
c=648/18
c=36 size of the herd.
proof
36/4+2*sqrt36+15=36
9+2*6+15=36
9+12+15=36
36=36
this was not an easy one :) :)
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Graphs/80344: Write the equation of the line passing through (-2,5) and (1,3). Answer must be written in slope intercept form. HELP ME!!! ;0(
1 solutions
Answer 57637 by checkley75(3666) on 2007-05-01 20:26:03 (Show Source):
You can put this solution on YOUR website!FIRST WE NEED TO FIND THE SLOPE (m) THUS:
(Y2-Y1)/(X2-X1)=(3-5)/(1+2)=-2/3 WHICH IS THE SLOPE (m).
NOW WE REPLACE X & Y IN THE EQUATION Y=mX+b & SOLVE FOR THE Y INTERCEPT (b)
5=-2/3*-2+b
5=4/3+b
b=5-4/3
b=(15-4/3)
b=11/3 THUIS IS THE Y INTERCEPT.
THUS THE LINE EQUATION IS
Y=-2/3X+11/3
 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, y = -2x/3 +11/3).
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Rational-functions/80314: Two cars leave at noon from the same point, one traveling east at 50 mph, the other traveling due north at 60 mph.
(a) How far apart are they at 1 PM? at 1:30 PM?
(b) If t is the number of hours after noon, find an equation expressing the distance between the cars as a function of t.
1 solutions
Answer 57635 by checkley75(3666) on 2007-05-01 20:06:05 (Show Source):
You can put this solution on YOUR website!(50T)^2+(60T)^2=DISTANCE ^2
@ 1:00 THEY ARE
(50*1)^2+(60*1)^2=D^2
5062=60^2=D62
2500+3600=D^2
D^2=5100
D=SQRT5100
D=71.414 MILES APART @ 1:00.
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@ 1:30 THEY WILL BE:
(50*1.5)^2+(60*1.5)^2=D^2
75^2+90^2=D^2
D^2=5625+8100
D^2=13725
D=117.154 MILES APART @ 1:30.
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FORMULA IN TERMS OF T IS:
(S1T)^2+(S2T)^2=D^2
T^2(S1^2+S2^2)=D^2
T^2=D^2/(S1^2+S2^2)
T=(D/SQRT(S1^2+S2^2)
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Rate-of-work-word-problems/80330: Mike can paint a wall in three hours. Angelo can paint the same wall in two hours. How long will it take if they work together?
1 solutions
Answer 57629 by checkley75(3666) on 2007-05-01 19:45:44 (Show Source):
You can put this solution on YOUR website!THE ANSWER TO ALL THESE TYPE OF PROBLEMS ARE PRODUCT OVER SUM OR X*Y/(X+Y)
WHETHER IT IS PEOPLE WORKING, TWO WATER PIPES FILLING, RESISTERS IN PARALLEL, ETC.
YOUR CASE IS THE PRODUCT OF THE TWO TIMES 3*2=6 DIVIDED BY THE SUM (3+2)=5
3*2/(3+2)=6/5=1.2 hours when they work together.
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Inequalities/80307: My question is off a worksheet that if called Solving problems involving inequalities. It is "Find the largest pair of consectutive integers whos sum is less than 85."
My work is:
x+x+2<85
2x<83
1 solutions
Answer 57611 by checkley75(3666) on 2007-05-01 17:43:27 (Show Source):
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Geometry_Word_Problems/80304: The area of a circle is 64Pi. The area of a square is 256. Which is larger? the diameter of the circle or the side of the square?
1 solutions
Answer 57610 by checkley75(3666) on 2007-05-01 17:38:42 (Show Source):
You can put this solution on YOUR website!AREA=piR^2 OR
AREA=64pi OR
AREA=8pi WHERE THRE RADIUS ID 8 THUS THE DIAMETER IS 2*8=16
AREA OF A SQUARE IS X^2
X^2=256
X=16 WHICH THE LENGTH OF THE SIDE.
THEREFORE THE SIDE OF THE SQUARE (16) IS EQUAL TO THE DIAMETER (16) OF THE CIRCLE.
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Graphs/80286: Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 mi horizontally away from the of the mountain. Find the slope of his descent to the nearest hundreth.
And is it possible to explain to me how to solve this, for future refrence.
1 solutions
Answer 57605 by checkley75(3666) on 2007-05-01 17:28:01 (Show Source):
You can put this solution on YOUR website!THE BEST WAY TO SOLVE THIS IS TO SET UP A GRAPH. ASSIGN THE POINT (0,1800)FOT YHR TOP OF THE MOUNTAIN.
NOW SET A SECOND POINT (5280*3.25,0) FOR THE END OF THE DESCENT DOWN THE MOUNTAIN.
THESE 2 POINTS ARE (0,1800) & (17,160,0).
TO FIND THE SLOPE BETWEEN THESE TWO POINTS WE USE (Y2-Y1)/X2-X1) OR
(0-1800)/(17,160-0)
-1800/17,160=.104895 OR -.1 IS THE SLOPE OF THIS DESCENT.
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Linear-systems/80287: This question is from textbook Algebra I
Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions.
2x-y=-4
-3x+y=-9
1 solutions
Answer 57604 by checkley75(3666) on 2007-05-01 17:13:36 (Show Source):
You can put this solution on YOUR website!2X-Y=-4
-Y=-2X-4
Y=2X+4 NOW SUBSTITUTE (2X+4) FOR Y & SOLVE FOR X IN THE OTHER EQUATION.
-3X+(2X+4)=-9
-3X+2X+4=-9
-X=-9-4
-X=-13
X=13 ANSWER.
Y=2*13+4
Y=26+4
Y=30 ANSWER.
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