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Length-and-distance/695474: Write the equation of a line that passes through the points (4,4) and (-2,1).
Your answer should be in slope intercept form (y = mx + b)
im so confused i have no clue how to do any of this..
1 solutions
Answer 428502 by lwsshak3(6460)   on 2012-12-18 01:45:19 (Show Source):
You can put this solution on YOUR website!Write the equation of a line that passes through the points (4,4) and (-2,1).
Your answer should be in slope intercept form (y = mx + b)
**
equation of a line: y=mx+b, m=slope, b=y-intercept
slope=∆y/∆x=(4-1)/(4-(-2))=3/6=1/2
equation y=(1/2)x+b
solve for b using coordinates of one of the given points(4,4) (either point can be used)
4=(1/2)4+b
b=2
equation of given line: y=x/2+2
|
Travel_Word_Problems/695475: A plane leaves the airport and flies East at 200 mph. 2 hours later,
another plane leaves and flies West at 150 mph. Write and solve a
system of linear equations that can be used to determine when the
planes are 750 miles apart.
1 solutions
Answer 428500 by lwsshak3(6460) on 2012-12-18 01:26:08 (Show Source):
You can put this solution on YOUR website!A plane leaves the airport and flies East at 200 mph. 2 hours later,
another plane leaves and flies West at 150 mph. Write and solve a
system of linear equations that can be used to determine when the
planes are 750 miles apart.
**
let x-2=travel time of plane flying East
x=travel time of plane flying West(when planes are 750 miles apart)
distance=*travel time*speed
equation:
150(x-2)+200x=750
150x-300+200x=750
350x=1050
x=3
planes are 750 miles apart after 3 hrs
|
Travel_Word_Problems/695477: The speed of a stream is 3 km/h. A boat travels 4 km upstream in the
same time it takes to travel 10 km downstream. What is the speed of
the boat.
1 solutions
Answer 428499 by lwsshak3(6460) on 2012-12-18 00:59:03 (Show Source):
You can put this solution on YOUR website!The speed of a stream is 3 km/h. A boat travels 4 km upstream in the
same time it takes to travel 10 km downstream. What is the speed of
the boat.
**
let x=speed of the boat in still water
x-3=speed upstream
x+3=speed downstream
travel time=distance/speed (same for upstream and downstream)
4/(x-3)=10/(x+3)
10x-30=4x+12
6x=42
x=6
speed of the boat in still water=6 km/hr
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Age_Word_Problems/695458: The ratio of the ages of Rajesh to that of Ramesh is 5 : 8. After 10 years the new ratio of their ages will be 7 : 10. What is the age of Ramesh at present?
1 solutions
Answer 428498 by lwsshak3(6460) on 2012-12-18 00:48:32 (Show Source):
You can put this solution on YOUR website!The ratio of the ages of Rajesh to that of Ramesh is 5 : 8. After 10 years the new ratio of their ages will be 7 : 10. What is the age of Ramesh at present?
**
let y=Rajesh's present age
let x=Ramesh's present age
y/x=5/8
y=5x/8
..
After 10 years:
y+10=Rajesh's age
x+10=Ramesh's age
(y+10)/(x+10)=7/10
7x+70=10y+100
7x+70=10(5x/8)+100
7x+50x/8=30
56x+50x=240
6x=240
x=40
Ramesh's present age=40
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Travel_Word_Problems/695463: A bus leave Sacramento traveling South at 40 mph. A half hour hour
later, a car leaves from the same location on the same route at 60 mph.
How far from Sacramento will the car overtake the bus?
1 solutions
Answer 428496 by lwsshak3(6460) on 2012-12-18 00:14:31 (Show Source):
You can put this solution on YOUR website!A bus leave Sacramento traveling South at 40 mph. A half hour hour
later, a car leaves from the same location on the same route at 60 mph.
How far from Sacramento will the car overtake the bus?
**
let x=travel time of car
(x+.5)=travel time of bus
distance=speed*travel time(the same for car and bus)
..
60x=40(x+.5)
60x=40x+20
20x=20
x=1
distance car overtakes bus=60x=60 miles
|
Trigonometry-basics/694532: I don't know how to find the exact value of cos 23pi/12 using the properties of special triangles
1 solutions
Answer 428052 by lwsshak3(6460) on 2012-12-15 17:27:47 (Show Source):
You can put this solution on YOUR website!find the exact value of cos 23pi/12 using the properties of special triangles
Use cos half-angle identity
cos(x/2)=±√[(1+cos(x)/2]
cos(23π/12)=cos(23π/6)/2)=√[(1+cos(23π/6)/2]
For cos(23π/6) use reference angle π/6 in quadrant IV where cos>0
cos(23π/6)=cos(π/6)=√3/2
cos(23π/12)
=cos(23π/6)/2)
=√[(1+cos(23π/6)/2]
=√[(1+√3/2/2]
calculator check:
cos(23π/12)≈0.9659..
√[(1+√3/2/2]≈0.9659..
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absolute-value/693974: |4x-2 divided by 5| = |6x+3 divided by 2|
1 solutions
Answer 427963 by lwsshak3(6460) on 2012-12-15 03:30:57 (Show Source):
You can put this solution on YOUR website!|4x-2 divided by 5| = |6x+3 divided by 2|
|(4x-2)/5|=|(6x+3)/2|
solve for 2 equations
(4x-2)/5=(6x+3)/2
5(6x+3)=2(4x-2)
30x+15=8x-4
22x=-19
x=-19/22
check:
|(4x-2)/5|=|(6x+3)/2|
|(4(-19/22)-2)/5|=|(6(-19/22)+3)/2|
|-1.0909|=|-1.0909|
1.0909=1.0909
check ok
..
(4x-2)/5=-(6x+3)/2
-5(6x+3)=2(4x-2)
-30x-15=8x-4
-38x=11
x=-11/38
check:
|(4x-2)/5|=|(6x+3)/2|
|(4(-11/38)-2)/5|=|(6(-11/38)+3)/2|
|-.6316|=|.6316|
.6316=.6316
check ok
solution: x=-19/22, -11/38
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absolute-value/694488: |10x+65|=7x+25
1 solutions
Answer 427960 by lwsshak3(6460) on 2012-12-15 03:08:41 (Show Source):
You can put this solution on YOUR website!|10x+65|=7x+25
solve for 2 possibilities
..
10x+65=7x+25
3x=-40
x=-40/3
check:
(10x+65)=7x+25
|10*-40/3+65|=7*-40/3+25
|10*-40/3+65|=7*-40/3+25
|-68.33|=-68.33
68.33≠-68.33
does not check, no solution
..
-(10x+65)=7x+25
-10x-65=7x+25
-17x=90
x=-90/17
check:
|10x+65|=7x+25
|10*-90/17+65|=7*-90/17+25
|12.06|=-12.06
12.06≠-12.06
does not check, no solution
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Quadratic-relations-and-conic-sections/694194: what is the vertex, axis of symmetry, and direction of opening for y=x^2-18x+79?
1 solutions
Answer 427927 by lwsshak3(6460) on 2012-12-14 20:30:35 (Show Source):
You can put this solution on YOUR website!what is the vertex, axis of symmetry, and direction of opening for
y=x^2-18x+79?
complete the square
y=(x^2-18x+81)+79-81
y=(x-9)^2-3
This is an equation of a parabola that opens upwards. (lead coefficient positive)
Its standard form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex.
For given equation: y=(x-9)^2-3
vertex:(9,-3)
Axis of symmetry: x=9
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Quadratic-relations-and-conic-sections/694199: Identify the center and foci of the ellipse. (x-2)^2/16 + (y-7)^2/169 =1
1 solutions
Answer 427925 by lwsshak3(6460) on 2012-12-14 20:15:24 (Show Source):
You can put this solution on YOUR website!Identify the center and foci of the ellipse. 
This is an equation of an ellipse with vertical major axis.(y-denominator > x-denominator
Its standard form:  , a>b, (h,k)=(x,y) coordinates of center
For given equation:
center: (2,7)
a^2=169
b^2=16
c^2=a^2-b^2=169/16=153
c=√153≈12.4
foci: (2,7±c)≈(2,7±12.4)≈(2,-5.4 and (2,19.4)
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Quadratic-relations-and-conic-sections/694202: Use the information provided to write the standard form equation of each hyperbola. Vertices: (-2, 8), (-2,-2) Endpoints of Conjugate Axis:(8,3) (-12,3)
1 solutions
Answer 427914 by lwsshak3(6460) on 2012-12-14 19:02:48 (Show Source):
You can put this solution on YOUR website!Use the information provided to write the standard form equation of each hyperbola. Vertices: (-2, 8), (-2,-2) Endpoints of Conjugate Axis:(8,3) (-12,3)
**
This is a hyperbola with vertical transverse axis (y-coordinates of vertices change but x-coordinates do not)
Its standard form of equation:  , (h,k)=(x,y) coordinates of center
For given hyperbola:
center: (-2,3) (midpoints of changing x and y-coordinates)
length of vertical transverse axis=10(-2 to 8)=2a
a=5
a^2=25
length of conjugate axis=20 (-12 to 8)=2b
b=10
b^2=100
Equation of given hyperbola: 
|
Quadratic-relations-and-conic-sections/694423: Graph the quadratic function f(x)=5-x^2 and identify the Vertex. Give the Domain and Range.
1 solutions
Answer 427908 by lwsshak3(6460) on 2012-12-14 18:38:50 (Show Source):
You can put this solution on YOUR website!Graph the quadratic function f(x)=5-x^2 and identify the Vertex. Give the Domain and Range
This is an equation of a parabola that opens downwards. (negative lead coefficient)
Its standard form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex.
For given equation: y=-x^2+5 (rewritten)
vertex(0,5)
domain: (-∞,∞)
range: (-∞,5]
see graph below:
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Trigonometry-basics/694182: A belt connects two pulleys with a radio 3in(point B) and 5in (point C). The velocity of point A on the pelt is 10ft/sec. What is the linear velocity (ft/sec) and the angular velocity (rad/sec) for point B?What is the linear velocity (ft/sec) and the angular velocity (rad/sec) for point C?
Hint: every point on the belt is moving at the same speed.
1 solutions
Answer 427798 by lwsshak3(6460) on 2012-12-14 02:23:56 (Show Source):
You can put this solution on YOUR website!A belt connects two pulleys with a radius 3in(point B) and 5in (point C). The velocity of point A on the belt is 10ft/sec. What is the linear velocity (ft/sec) and the angular velocity (rad/sec) for point B?What is the linear velocity (ft/sec) and the angular velocity (rad/sec) for point C?
**
At point B (3in pulley)
Convert linear velocity to angular velocity
circumference=π*diameter=π*6 in=π/2 ft
10 ft/sec*rev/π/2 ft*2π rad/rev
10*2*2 rad/sec=40 rad/sec
...
At point B (3in pulley)
Convert linear velocity to angular velocity
circumference=π*diameter=π*10 in=π*5/6 ft=5π/6 ft
10 ft/sec*rev/5π/6 ft*2π rad/rev
(10*6*2)/5 rad/sec=24 rad/sec
..
linear velocity is constant at all points on the belt at 10 ft/sec
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Age_Word_Problems/693739: How old is Anna if she's 3yrs older than chuck, and in 5yrs, her age and chucks age would equal 54?
1 solutions
Answer 427681 by lwsshak3(6460) on 2012-12-13 16:35:58 (Show Source):
You can put this solution on YOUR website!How old is Anna if she's 3yrs older than chuck, and in 5yrs, her age and chucks age would equal 54?
**
let x=anna's present age
x-3=chuck's present age
..
in 5 yrs
x+5=anna's age
x-3+5=x+2=chuck's age
..
(x+5)+(x+2)=54
2x+7=54
2x=47
x=23.5
anna's present age=23.5
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Age_Word_Problems/693994: Eighteen years ago Alan was twice as old as Tony. Alan is eight years older than Tony. Find Tony's age now.
1 solutions
Answer 427680 by lwsshak3(6460) on 2012-12-13 16:21:13 (Show Source):
You can put this solution on YOUR website!Eighteen years ago Alan was twice as old as Tony. Alan is eight years older than Tony. Find Tony's age now.
**
let x=tony's age now
x+8=alan's age now
..
18 years ago
x-18=tony's age
x+8-18=x-10
..
x-10=2(x-18)
x-10=2x-36
x=26
tony's age now=26
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Rational-functions/693581: Determine wheather the following relation represents a function. If the relation is a function, then state its domain and range (2,8),(-2,8),(8,10),(2,17)
1 solutions
Answer 427666 by lwsshak3(6460) on 2012-12-13 15:12:58 (Show Source):
You can put this solution on YOUR website!Determine wheather the following relation represents a function. If the relation is a function, then state its domain and range (2,8),(-2,8),(8,10),(2,17)
This relation is not a function because (2,8)and (2,17) show that you have 2 different y=values for the same x-value.
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Rational-functions/693642: X =(y+2)^2
Solve and state the domain and range, and write in interval notation. Is this equation a function?
1 solutions
Answer 427665 by lwsshak3(6460) on 2012-12-13 15:00:33 (Show Source):
You can put this solution on YOUR website!X =(y+2)^2
Solve and state the domain and range, and write in interval notation. Is this equation a function?
This is a parabola that opens rightwards with the vertex at (0,0)
Its standard form of equation: (y-k)^2=4p(x-h)X
(y+2)^2=x
This is a sqrt function where the radican x≥0
domain: [0,∞)
range: (-∞,∞)
equation is not a function.
To be a function, for each x-value, there can be only one y-value, and given equation has 2 different y-values for each x.
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Quadratic-relations-and-conic-sections/693238: Write in standard form.It is a Hyperbola. The vertices are (0,+-1) and the foci are (0, +-5).
1 solutions
Answer 427554 by lwsshak3(6460) on 2012-12-13 03:05:29 (Show Source):
You can put this solution on YOUR website!Write in standard form.It is a Hyperbola. The vertices are (0,+-1) and the foci are (0, +-5).
**
This is a hyperbola with horizontal transverse axis.
Its standard form of equation: , (h,k)=(x,y) coordinates of center
For given hyperbola:
center:(0,0)
a=1 (distance from center to vertices on transverse axis)
a^2=1
c=5 (distance from center to foci on transverse axis)
c^2=25
c^2=a^2+b^2
b^2=c^2-a^2=25-1=24
Equation of given hyperbola: 
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Quadratic-relations-and-conic-sections/693239: Write in standard form. It is a ellipse. The center is (0,0) and the foci is (+-3,0) and the major axis is 12.
1 solutions
Answer 427553 by lwsshak3(6460) on 2012-12-13 02:53:26 (Show Source):
You can put this solution on YOUR website!Write in standard form. It is a ellipse. The center is (0,0) and the foci is (+-3,0) and the major axis is 12.
**
This is an ellipse with horizontal major axis.
Its standard form of equation:  , a>b, (h,k)=(x,y) coordinates of center.
For given ellipse:
Given center: (0,0)
length of horizontal major axis=12=2a
a=6
a^2=36
c=3 (distance from center to foci)
c^2=9
c^2=a^2-b^2
b^2=a^2-c^2=36-9=25
b=5
Equation of given ellipse: 
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Quadratic-relations-and-conic-sections/693240: Write in standard form. It is a parabola. The vertex is (0,0) and the focus is (-6,0).
1 solutions
Answer 427552 by lwsshak3(6460) on 2012-12-13 02:42:48 (Show Source):
You can put this solution on YOUR website!Write in standard form. It is a parabola. The vertex is (0,0) and the focus is (-6,0).
This is a parabola that open leftwards.
Its standard form of equation: (y-k)^2=-4p(x-h), (h,k)=(x,y) coordinates of the vertex
For given parabola:
given vertex: (0,0)
Axis of symmetry: y=0 or x-axis
From focus:
p=6 (distance from focus to vertex on the axis of symmetry)
4p=24
Equation: y^2=-24x
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Quadratic-relations-and-conic-sections/693660: Find an equation of the ellipse that has center (1,3) , a major axis of length 12 , and endpoint of minor axis (0,3) .
1 solutions
Answer 427551 by lwsshak3(6460) on 2012-12-13 02:31:43 (Show Source):
You can put this solution on YOUR website!Find an equation of the ellipse that has center (1,3) , a major axis of length 12 , and endpoint of minor axis (0,3) .
**
Standard form of equation for an ellipse with vertical major axis: , a>b, (h,k)=(x,y) coordinates of center.
given center: (1,3)
given length of vertical major axis:=12=2a
a=6
a^2=36
length of minor axis=6=2b
b=3
b^2=9
equation of given ellipse: 
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Trigonometry-basics/693314: A square of side x is inscribed in a circle. Express the area A of the circle as a function of x.
1 solutions
Answer 427550 by lwsshak3(6460) on 2012-12-13 02:12:11 (Show Source):
You can put this solution on YOUR website!A square of side x is inscribed in a circle. Express the area A of the circle as a function of x.
**
Use sector area formula to solve:
area of one of 4 sectors=(1/2)r^2A
diameter of circle=(√2/2)x
r=√2/4)x
r^2=(2/16)x^2=(x^2)/8
A=π/2(central angle)
Area of circle=4*(1/2)(x^2/8)*π/2=πx^2/8
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Trigonometry-basics/693416: Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
4 cos θ + 1 = 0
1 solutions
Answer 427549 by lwsshak3(6460) on 2012-12-13 02:02:55 (Show Source):
You can put this solution on YOUR website!Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
4 cos θ + 1 = 0
cos θ=-1/4
reference angle≈1.32 in quadrants II and III where cos<0
θ≈1.82+2πk, 4.46+2πk, k=any integer
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Trigonometry-basics/693461: the question asks,"cos^-1 0.5=?"
and also
"The sine is positive in __?"
A q2 and q3
B q1 and q2
C q1 and q3
1 solutions
Answer 427548 by lwsshak3(6460) on 2012-12-13 01:53:05 (Show Source):
You can put this solution on YOUR website!he question asks,"cos^-1 0.5=?"
and also
"The sine is positive in __?"
A q2 and q3
B q1 and q2
C q1 and q3
..
cos^-1 0.5= 30º or π/6
The sine is positive in q1 and q2 (top half of the unit circle)
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Trigonometry-basics/693620: if sin theta=12/13 and tan <0, find the exact values of the remaining trigonometric functions of theta.
1 solutions
Answer 427547 by lwsshak3(6460) on 2012-12-13 01:48:34 (Show Source):
You can put this solution on YOUR website!if sin theta=12/13 and tan <0, find the exact values of the remaining trigonometric functions of theta.
**
use x for theta
O for opposite side
A for adjacent side
H for hypotenuse
if sin theta=12/13 and tan <0, reference angle must be in quadrant II
..
sin x=12/13=O/H
O=12, H=13
A=√(H^2-O^2)=√(13^2-12^2)=√(169-144)=√25=5
cos x=A/H=-5/13
tan x=O/A=-12/5
csc x=13/12
sec x=-13/5
cot x=-5/12
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