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lwsshak3 answered: 6511 problems
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Please use synthetic division.
1 solutions
Answer 451098 by lwsshak3(6513)   on 2013-04-18 20:16:37 (Show Source):
You can put this solution on YOUR website!Given (x^2+4x+8)divided by (x+k), find the values of k so that the remainder is 20.
Please use synthetic division.
***
...-k..|....1........4.............8......
......................-k.......(-4k+k^2)
..............1....(4-k)....(8-4k+k^2)
8-4k+k^2=20
k^2-4k-12=0
(k-6)(k+2)=0
k=6
or
k=-2
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Systems-of-equations/739378: Can someone show me how this is done please .Thanks
Write f(x)=-9x^2+18x in standard form.
1 solutions
Answer 451096 by lwsshak3(6513) on 2013-04-18 19:57:07 (Show Source):
You can put this solution on YOUR website!Write f(x)=-9x^2+18x in standard form.
complete the square:
This is an equation of a parabola that opens downward.
Its standard form:  , (h,k)=(x,y) coordinates of the vertex, A is a coefficient that affects the slope or steepness of the curve.
For given equation:
vertex:(1,9)
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Quadratic-relations-and-conic-sections/739168: Write the equation of the conic section satisfying the given conditions
vertices (3,5) and (3,-5) and minor axis of length 4
1 solutions
Answer 451062 by lwsshak3(6513) on 2013-04-18 15:35:17 (Show Source):
You can put this solution on YOUR website!Write the equation of the conic section satisfying the given conditions
vertices (3,5) and (3,-5) and minor axis of length 4
***
This is an ellipse with vertical major axis. (y-coordinates of vertices change but x-coordinates do not)
Its standard form of equation:  , (a>b), (h,k)=(x,y) coordinates of center.
For given ellipse:
center: (3,0)
a=5 (distance from center to vertex on vertical major axis)
a^6=25
b=2 (distance from center to end point of minor axis)
b^2=4
Equation: 
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logarithm/738910: Given that log_8(t) = 2.68, log_8(r) = -0.22, and log_8(z) = -0.45, find the following:
log_8((root(9)(r^11))/(t^10z^4))
1 solutions
Answer 451005 by lwsshak3(6513) on 2013-04-18 03:56:16 (Show Source):
You can put this solution on YOUR website!Given that log_8(t) = 2.68, log_8(r) = -0.22, and log_8(z) = -0.45, find the following:
log_8((root(9)(r^11))/(t^10z^4))
**
=0.53-2.42-26.8+1.80
=-26.89
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logarithm/739055: log(3)(x-4)=2-log(3)(x+4)
please help me solve this equation.
the two on the other side is throwing me off. i just dont get it.
1 solutions
Answer 451001 by lwsshak3(6513) on 2013-04-18 02:42:58 (Show Source):
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logarithm/739058: This is a story problem. It reads, "you deposit 2500 dollars in an account that pays 3.5% annual interest compounded continuously. What is the balance after eight years?
1 solutions
Answer 451000 by lwsshak3(6513) on 2013-04-18 02:19:54 (Show Source):
You can put this solution on YOUR website!This is a story problem. It reads, "you deposit 2500 dollars in an account that pays 3.5% annual interest compounded continuously. What is the balance after eight years?
**
Formula for continuous compounding:
A=Pe^rt, P=initial deposit, r=interest rate, t=years, A=amt after t years
For given problem:
P=2500
r=.035
t=8
A=2500*e^(.035*8)≈3308
Balance after eight years=$3308
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Trigonometry-basics/739045: Please help me solve this equation: Direction: Find all solution in the interval [0,2pi) by algebraically: 2sin(^2)*2x+5sin2x-3=0
1 solutions
Answer 450999 by lwsshak3(6513) on 2013-04-18 02:07:29 (Show Source):
You can put this solution on YOUR website!Find all solution in the interval [0,2pi) by algebraically: 2sin(^2)*2x+5sin2x-3=0
***
..
(2sin(2x)-1)=0
sin(2x)=1/2
2x=π/6, 5π/6 (in Q1 and Q2 where sin>0)
x=π/12, 5π/12
..
or
(sin(2x)+3)=0
sin(2x)=-3(reject, (-1 ≤ sin(2x) ≤ 1)
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Trigonometry-basics/738988: Use an Addition or Subtraction Formula to find the exact value of the expression
Sin(165)
1 solutions
Answer 450975 by lwsshak3(6513) on 2013-04-17 21:24:34 (Show Source):
You can put this solution on YOUR website!Use an Addition or Subtraction Formula to find the exact value of the expression
Sin(165)
***
sin(165)=sin(135+30)
=(sin(135)cos(30))+(cos(135)sin(30))
=(√2/2*√3/2)+(-√2/2*1/2)
=√6/4-√2/4
=(√6-√2)/4
calculator check:
sin(165)≈0.2588..
(√6-√2)/4≈0.2588..
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Trigonometry-basics/738963: Find the first three x-intercepts of the graph of the given function on the positive x-axis.
f(x) = 2 − 4 cos(x +π/3)
a.
b.2pi
c.
1 solutions
Answer 450967 by lwsshak3(6513) on 2013-04-17 20:53:16 (Show Source):
You can put this solution on YOUR website!Find the first three x-intercepts of the graph of the given function on the positive x-axis.
f(x) = 2 − 4 cos(x +π/3)
set f(x)=0
2 − 4 cos(x +π/3)=0
4 cos(x+π/3)=2
cos(x+π/3)=2/4=1/2
x+π/3=π/3, 5π/3, 7π/3
x=0, 4π/3, 2π
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Trigonometry-basics/738727: Find cot^-1(- square root of 3/ 3 ) in both radians and degrees. Can you please go step by step so i can learn how to do it on my own? thank you!
1 solutions
Answer 450959 by lwsshak3(6513) on 2013-04-17 20:06:20 (Show Source):
You can put this solution on YOUR website!Find cot^-1(- square root of 3/ 3 ) in both radians and degrees.
cot^-1(- square root of 3/ 3 )
can also be read:
cot(x)=-√3/3
x=120º or 2π/3 radians (in quadrant II where cot<0)
To convert degrees to radians, multiply degrees by (π/180)
To convert radians to degrees, multiply radians by (180/π)
π*degree=radian*180
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Trigonometry-basics/738273: State the phase shift of y=cos(theta-pi/3). Then graph the function. The graph that it asks me to use has pi and 2pi as the x coordinates, I'm not sure how to graph on it.
1 solutions
Answer 450874 by lwsshak3(6513) on 2013-04-17 03:43:39 (Show Source):
You can put this solution on YOUR website!State the phase shift of y=cos(theta-pi/3). Then graph the function. The graph that it asks me to use has pi and 2pi as the x coordinates, I'm not sure how to graph on it.
***
Form of equation for cos: y=Acos(Bx-C), A=amplitude, period=2π/B, phase shift=(C/B)
For given equation: y=cos(x-π/3)
amplitude=1
B=1
period=2π/B=2π
(1/4) period=π/2
phase shift: C/B=π/3/1=π/3 (shift to the right)
Graphing:
start with coordinates of basic cos curve for one period: (x-axis scale in radians)
(0,1), ((π/2),0), (π,-1), (3π/2,(-1)), (2π,0)
shift curve (π/3) to the right
(0,.5), ((π/3),1), ((5π/6),0), (4π3,-1), (11π/6,(-1)), (7π/3,0)
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Trigonometry-basics/738501: If angle A is acute and tanA is 2/3, them...
how do you get the answer of cot(90° − A) =2/3?
1 solutions
Answer 450869 by lwsshak3(6513) on 2013-04-17 03:09:37 (Show Source):
You can put this solution on YOUR website!If angle A is acute and tanA is 2/3, them...
how do you get the answer of cot(90° − A) =2/3
Say, you are working a 30-60 right triangle, for example:
let A=30º
tan(30º)=1/√3
cot (90-30)=cot(60º)=1/√3
I used 30º for this example, but it will work for any acute angle.
This identity also works for sin and cos functions.
sin 30º=1/2
cos (90-30)=cos(60º)=1/2
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Trigonometry-basics/738265: What is the exact value of sine of 13pie/12 ?
1 solutions
Answer 450807 by lwsshak3(6513) on 2013-04-16 17:40:29 (Show Source):
You can put this solution on YOUR website!What is the exact value of sine of 13pie/12 ?
**
 (in Q3 where sin <0)
Use sin half-angle formula to solve: 
sin(π/12)=sin((π/6)/2)
=±√(1-cos(π/6)/2)
=-√(1-(√3/2)/2)
=-√(2-√3/4)
=-√(2-√3)/2
Check with calculator:
sin(13π/12)≈-0.2588..
-√(2-√3)/2≈-0.2588..
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Quadratic-relations-and-conic-sections/737563: Parabolas:
Write each question in standard form. Identify the vertex, axis of symmetry and direction of opening of the parabola.
y=x^2+2x+2
1 solutions
Answer 450722 by lwsshak3(6513) on 2013-04-16 03:34:04 (Show Source):
You can put this solution on YOUR website!Write each question in standard form. Identify the vertex, axis of symmetry and direction of opening of the parabola.
y=x^2+2x+2
complete the square:
y=(x^2+2x+1)-1+2
This is an equation of a parabola that opens upward.
Its standard form of equation:  , (h,k)=(x,y) coordinates of the vertex, A is a coefficient that affects the slope or steepness of the curve.
..
For given parabola:
vertex: (-1,1)
axis of symmetry: x=-1
parabola opens upward.
see graph below as a visual check:
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Quadratic-relations-and-conic-sections/737564: Hyperbolas:
Graph each hyperbola. Identify the verices, foci, and asymptotes
X^2/4 - y^2/16 = 1
1 solutions
Answer 450721 by lwsshak3(6513) on 2013-04-16 03:21:41 (Show Source):
You can put this solution on YOUR website!Graph each hyperbola. Identify the verices, foci, and asymptotes
This is a hyperbola that has a horizontal transverse axis (x-term listed first ahead of y-term)
Its standard form of equation: 
For given hyperbola:
center: (0,0)
a^2=4
a=2
vertices: (0±a,0)=(0±2,0)=(-2,0) and (2,0)
..
b^2=16
b=4
..
c^2=a^2+b^2=4+16=20
c=√20≈4.47
foci: (0±c,0)=(0±4.47,0)=(-4.47,0) and (4.47,0)
..
Asymptotes: (equations of lines that go thru center, y=mx+b, m=slope, b= y-intercept)
Slopes of asymptotes of hyperbolas with horizontal transverse axis=±b/a=±4/2=±2
..
Equation of asymptote with negative slope=-2
y=-2x+b
b=0
y=-2x
..
Equation of asymptote with positive slope=2
y=2x+b
b=0
y=2x
...
y=±(4x^2-16)^.5
See graph below as a visual check:
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Quadratic-relations-and-conic-sections/737799: How do you find an equation of the parabola with vertex (-3,-4) and focus (-3,-3)?
1 solutions
Answer 450719 by lwsshak3(6513) on 2013-04-16 02:48:14 (Show Source):
You can put this solution on YOUR website!How do you find an equation of the parabola with vertex (-3,-4) and focus (-3,-3)?
This is a parabola that opens upward:
Its basic equation:  , (h,k)=(x,y) coordinates of the vertex
For given parabola:
vertex: (-3,-4)
axis of symmetry: x=-3
p=1 (distance from vertex to focus on the axis of symmetry)
4p=4
Equation: 
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Quadratic-relations-and-conic-sections/738106: write the standard form of the equation of the parabola with the directrix x=(-1/2) and vertex at (0,0)
1 solutions
Answer 450717 by lwsshak3(6513) on 2013-04-16 02:35:30 (Show Source):
You can put this solution on YOUR website!write the standard form of the equation of the parabola with the directrix x=(-1/2) and vertex at (0,0)
***
Given parabola opens rightward.
Its basic equation: y^2=4px
axis of symmetry: y=0
p=1/2 (distance from vertex to directrix on the axis of symmetry)
4p=2
equation: y^2=2x
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Age_Word_Problems/738177: when andy was born, sarah, his mother was 25 years old. three years ago his mother was six times as old as andy was then. how old is andy now. show method you used to solve the problem.
1 solutions
Answer 450716 by lwsshak3(6513) on 2013-04-16 02:04:13 (Show Source):
You can put this solution on YOUR website!when andy was born, sarah, his mother was 25 years old. three years ago his mother was six times as old as andy was then. how old is andy now. show method you used to solve the problem.
***
let x=Andy's age now
x+25=mother's age now (mother will always be 25 yrs older than Andy)
3 years ago:
x-3=Andy's age
x+25-3=x+22=mother's age
At this time, his mother was six times as old as andy
x+22=6(x-3)
x+22=6x-18
5x=40
x=8
x+25=33
Andy's age now=8
mother's age now=33
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Linear_Algebra/737927: graph of the function -2(x - 1)^2 = y + 5?
1 solutions
Answer 450608 by lwsshak3(6513) on 2013-04-15 16:25:49 (Show Source):
You can put this solution on YOUR website!graph of the function -2(x - 1)^2 = y + 5
This is an equation of a parabola that opens downward:
Its standard (vertex) form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. A is a coefficient that affects the slope or steepness of the curve.
..
For given equation: -2(x - 1)^2 = y + 5
rearrange terms to standard form:
A=-2
vertex: (1,5)
axis of symmetry: x=1
y-intercept
set x=0
y=-2+5=3
see graph below:
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Trigonometry-basics/737549: Use the given information to find cos 2x, sin 2x, and tan 2x. (Enter your answers in exact form.)
cos x = sqrt(2)/7 ,3π/2 < x < 2π
a)cos 2x
b)sin 2x
c)tan 2x
I know that for cos 2x, the answer will be #/49 but that is really as far as I got
1 solutions
Answer 450521 by lwsshak3(6513) on 2013-04-15 04:09:48 (Show Source):
You can put this solution on YOUR website!Use the given information to find cos 2x, sin 2x, and tan 2x. (Enter your answers in exact form.)
cos x = sqrt(2)/7 ,3π/2 < x < 2π
a)cos 2x
b)sin 2x
c)tan 2x
***
let O=opposite side
let A=adjacent side
let H=hypotenuse
..
...
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