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- University of Wisconsin - Madison
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- Mathematics 114
- Camacho
- Terms, Concepts and Things to Remember

Melanie S.

when you're given the slope of a line and one point, what formula do you use?

Point-Slope Form: y-y1=m(x-x1)

When you're given only two points , find the equation of the line by:

1.) first, finding m: y2-y1/x2-x1

2.) then, plug m in to the point-slope form equation and use either set of points.

2.) then, plug m in to the point-slope form equation and use either set of points.

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if two lines are perpendicular, their slopes will be:

Reciprocal and opposite (if one is +, the other will be -)

to find a common intersection between three lines, you must:

1.) set two of them equal to each other and solve for x

2.) plug x and either m value into the equation to get y

3.) plug x and y back into the equation with no numerical values and solve for m

2.) plug x and either m value into the equation to get y

3.) plug x and y back into the equation with no numerical values and solve for m

given g(x) = f(x+b) +c. where in this function can you find the shifts?

f= stretched or shrunk by this value

(x+b) = shifted to the left or right by this value

c= shifted up or down by this value

- or + (f) = denotes the direction the parabola will open

(x+b) = shifted to the left or right by this value

c= shifted up or down by this value

- or + (f) = denotes the direction the parabola will open

how do you find the vertex from an equation in the form (x+t)^{2} + c

t(f(t)) is the vertex.

or, (t,c)

or, (t,c)

X^{m}X^{n}=?

X^{m+n}

(X^{m})^{n}

X^{mn}

(xy)^{m}

x^{m}y^{m}

x^{0}x^{n}

x^{n}

x^{-n}

1/x^{n}

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x^{m}x^{-m}

1

how do you find the degree of a polynomial?

find the highest power in the polynomial; this is the degree

for |x| very large, the numerator and denominator (largest terms excluded):

are approximately 1

what is a rational function?

a function of the form r(x) = p(x) / q(x) where p and q are polynomials, and q can't equal 0.

How do you divide polynomials?

use standard long division

i^{2} = ?

1

define a sum and difference of two complex numbers

(a+bi) + (c+di) = (a+c) +(b+d)i

(a+bi)-(c+di) = (a-c) + (b-d) i

What is the complex conjugate?

if the expression is (a + bi), its complex conjugate is (a-bi)

Define multiplication of complex numbers

(a+bi)(c+di) = (ac-bd) + (ad-bc)i

Define division of complex numbers

(a+bi) / (c+di) = (ac + bd/c^{2}+d^{2}) + (bc-ad/c^{2}+d^{2}) i

What are the three ways to solve systems of linear equations?

substitution, standard elimination, and gaussian elimination with matrices

log_{b}y= x is the inverse of?

b^{x}=y

x^{logxy}=

y

log_{x}x^{t}=

t

log_{b}1 =

0

Log_{b}b=

1

log_{b}y=

logy/logb

log_{b}(xy)=

log_{b}x+log_{b}y

log_{b }(x/y) =

log_{b}x-log_{b}y

log_{b}y^{t} =

tlog_{b}y

Describe the expression B(t) = Pe^{rt}

B(t) = final amount

P= initial amount

r = growth/decay rate

t =time

what is the equation for the distance between two points?

√( (x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2})

What is the equation for the midpoint of a line?

(x_{1}+x_{2}/2 ), (y_{1}+y_{2}/2)

What is the equation of a circle?

(x-h)^{2 }+(y-k)^{2} = r^{2}

Area of a trapezoid

1/2 (b1+b2)h

Area of an ellipse/ equation in ellipse form

area = πab when the equation is in x^{2}/a^{2}+y^{2}/b^{2}=1 form

Area Stretch Theorem

The area of R' = cd times the original area (R)

what is the definition of *e*?

e is the number such that area(1/x,1,e) =1

lnx is a shorthand way of writing what?

log_{e}x

e^{0}=?

=1

lne^{x}=?

x

e^{lny}=?

y

What is the equation for the doubling time of a system?

70/R, where r = growth rate

What is the equation for the doubling rate of a system?

70/t, where t=time in years

how do you find the center, r, and area of a circle given in x^{2}+hx+y^{2}+ky=c form?

you complete the square, yielding the form (x-h)^{2}+(y-k)^{2}=r^{2}. from here you can find the center (h,k) and radius (r). area = πr^{2}

Cos(any ø)^{2} +sin(any ø)^{2} always equals...

1

any point in the region from π/2-->π is...

negative

what is the equation to find arc length?

L=øπ/180

what is the equation to find the area of a slice?

s=1/2ør^{2}

How do you convert from degrees to radians?

øπ/180

how do you convert from radians to degrees?

180/π

how do you find the 4 smallest + numbers ø such that sin or cosø = 0,-1 or 1?

go around the unit circle counterclockwise, stopping each time sin or cos= given integer x. do this 4 times. find the 1st one, add 2π to it to get the next one, etc...

how do you find the 4 smallest + numbers ø such that sin or cosø = 1/2 or √3/2?

find the first ø. (ex 30º). find the next ø in line on the unit circle (ex 150º). these are your 1st two numbers. Then, add your original ø to 360º, which yields the 3rd number. finally, add your second ø to 360 to get the 4th number.

secantø=

1/cosø

cosecantø=

1/sinø

cotangentø=

cosø/sinø

what is another way to write cotangent?

1/tanø

Cos^{2}ø+Sin^{2}ø =?

1

write tanø in terms of cosø

tanø= √(1-cos^{2}ø)/cosø

write secant in terms of tanø

1+tan^{2}ø=sec^{2}ø

what are the 3 trig identities with (π/2-ø)?

cos(π/2-ø) = sinø

sin(π/2-ø) = cosø

tan(π/2-ø) = 1/tanø

What are the 3 trig identities with (90-ø)?

cos(90-ø)= sinø

sin(90-ø)= cosø

tan(90-ø)= 1/tanø

What are the 3 trig identities with (ø+π)?

cos(ø+π) = -cosø

sin(ø+π) = -sinø

tan(ø+π) = tan ø

what are the 3 trig identities with (ø+2π)?

cos(ø+2π) = cosø

sin(ø+2π) = sinø

tan(ø+2π) = tanø

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