Extension Flashcards by Lilien R

What is column vector notation?

Representation of a vector in the form (a
b)

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When is maximum height reached?

When the projectile’s vertical velocity is 0

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What is component form?

Representation of a vector in the form xi + yj

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What proves if vectors are parallel?

u . v = +/- |u||v|

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What is the horizontal equation of acceleration?

ẍ = 0

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What is the horizontal equation of velocity?

ẋ = Vcosθ

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What is the horizontal equation of displacement?

x = Vtcosθ

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What is the vertical equation of acceleration?

ÿ = -g

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What is the vertical equation of velocity?

ẏ = -gt + Vsinθ

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What is the vertical equation of displacement?

y = -1/2gt^2 + Vtsinθ + h

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What can (x,y) for vectors also be written as?

(Vcosθ, Vsinθ)

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What is the equation for the acceleration vector?

a = -gj

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What is the equation for the velocity vector?

v = Vcosθi + (-gt + Vsinθ)j

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What is the equation for the displacement vector?

r = Vtcosθi + (-1/2gt^2 + Vtsinθ + h)j

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How do you find time of flight?

Let vertical component (j) of r(t) equal 0 then solve for t

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How do you find the range of flight?

Substitute time of flight into the horizontal component (i) of r(t)

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How do you find the maximum height of a projectile using time of flight?

Half the time of flight and substitute into the j component of r(t)

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How do you find the maximum height of a projectile using velocity?

Let the vertical component (j) of v(t) equal 0 then solve t and sub into r(t)

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What is the formula to find a unit vector?

1/|a| x a

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What is the projection of a onto b?

projba = a . b / |a|^2 X a

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How do you find the Cartesian equation of vector displacement?

Rearrange x to get t on its own and then sub in y
Make sure final equation only has tan

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How do you find the maximum range?

Change θ but not velocity

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What degree gives the maximum range?

How do you find speed?

|V(t)|

What is the angle of projection for horizontal or waterfall?

What is the relationship between f(x) and g(x) when they are inverse?

f(x) = 1/g'(x)

What is the shape of cos^-1 graph?

Starts at (-1,π) passes through π/2 and ends at (1,0)

What is the shape of sin^-1 graph?

Starts at (-1,-π/2) passes through the origin and ends at (1,π/2)

What is the shape of tan^-1 graph?

Sideway tan function which starts in the negative y, passes through the origin and finishes in the positive asymptotes at y=+/-π/2

How do you calculate the volume of a graph rotated around the y axis?

π ∫x^2 dy

How do you calculate the volume of a graph rotated around the x axis?

π ∫y^2 dx

When do you permutations?

When order matters

What do you do if there are repetitions in a permutation?

n!/r! n - number of items r - number of repetition

How do you calculate a circle arrangement?

(n-1)!

How do you calculate a bracelet or necklace arrangement?

(n-1)!/2

When do you use combinations?

When order doesn't matter

What is the pigeonhole principle statement?

By the pigeonhole principle...

What should be stated at the beginning of a pigeonhole principle question?

Let the ... be pigeons and the ... pigeonholes

What is the pigeonhole principle?

If there are n pigeons in k pigeonholes at least one of the holes contain n/k or more pigeons

How do you calculate the smallest number needed using the pigeonhole principle?

n=mk+1

Rules for square root function graphing?

- Does not exist in y < 0 - Has the same x intercepts - New graph under old when y > 1 - New graph intercepts at y = 1 - New graph above the old when y < 1

Rules for reciprocal functions graphing?

- x intercepts give vertical asymptotes - Intersect at y=+/- 1 - When y > 1 inverse is <1 - When y < 1 inverse is >1 - When original increases inverse decreases and vice versa

Rules for y =|f(x)| graphing?

- When f(x) > 0 graph is same as y=f(x) - When f(x) < 0 y-values are made positive

Rules for y = f(|x|) graphing?

- When x > 0 the graph is the same - When x < 0 graph on right hand side reflected across the y-axis

Rules for y^2 function graphing?

Same as square root but also reflected in the x-axis

Rules for y = f(|x|) graphing?

- When x > 0 the graph is the same - When x < 0 graph on right hand side reflected across the y-axis

What is E(p^)?

What is Var(p^)?

p(1-p)/n

a^2+b^2+g^2

(a+b+g)^2-(ab+ag+bg)

What is an even function?

f(x) = f(-x)

What is an odd function?

-f(x) = f(-x)

Rules for y^2 function graphing?

Same as square root but also reflected in the x-axis

Rules for square root function graphing?

- Does not exist in y < 0 - Has the same x intercepts - New graph under old when y > 1 - New graph intercepts at y = 1 - New graph above the old when y < 1

Rules for reciprocal functions graphing?

- x intercepts give vertical asymptotes - Intersect at y=+/- 1 - When y > 1 inverse is <1 - When y < 1 inverse is >1 - When original increases inverse decreases and vice versa

Rules for y =|f(x)| graphing?

- When f(x) > 0 graph is same as y=f(x) - When f(x) < 0 y-values are made positive

What is the formula for the dm/dt for water concentration?

Concentration pumped in x volume rate pump in - concentration pump out x volume rate pumped out kg/L x L/h - m/V x L/h