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1 using specific examples describe how variations in dna sequence between individuals can lead to risk of disease describe how a range of techniques
1 prove that zorns lemma is equivalent to axiom of choice2 use zorns lemma to prove the existence of
the length of a simple pendulum is about 100cm known to have a accuracy of 1mmits period of oscillation is 2s determined by measuring the time for
the resistances of commercially-available discrete resistors are restricted to particular sets for example the available values of resistors with 10
select one membrane industrial separation application for i reverse osmosis ro ii ultrafiltration uf and iii microfiltration mf at least one of
by what percentage should the pressure of a given mass of gas be increasedso as to decrease its volume by 10 at a constant
1 a square in the 2d plane has the x and y co-ordinates of 0 0 1 0 0 1 and 1 1 apply a scaling of 05 units in the x direction followed by a
1 what is the time complexity of a convolution with an n by n sized kernel when using a direct convolution with a 2d mask and when using a separable
solve the subsequent lp problem graphically through enumerating the corner pointsmax 3x1
in the thin lens equation first prove that zz ff hint use this diagram along with the characteristics of similar triangles then use this
a 10l helium balloon at a pressure of 2 bar at 27c some o2 is now in balloon and final volume is made 30l the pressure also fell to 1 bar at same
which electronic level would allow the hydrogen atom to absorb a photon but not to emit a
1 a 3d rotation matrix has 9 3 by 3 entries and a 2d rotation matrix has 4 2 by 2 entries how many actual degrees of freedom are there in a 3d or 2d
a stone is dropped from the top of the tower and travel 245 m in last second of its journey the height of the tower is
the sides of a quad taken at random are x3y-70 x-2y-503x2y-70
three-person problem of points pascal fermat and their old friend the chevalier de mere each put 1000 into a pot and agree to play a game that has
1 for a function f z rarr z let r be the relation on z given by xry iff fx fya prove that r is an equivalence relation on zb if for every x z the
1 let s be the set of all nonzero real numbers that is s r - 0 consider the relation r on s given by xry iff xy gt 0a prove that r is an equivalence
1 let r and s be relations on a set a for each statement conclude whether it is true or false in each case provide a proof or a counterexample
the fourier series expansion for the periodic function ft sin t is defined in its fundamental interval taking pi 3142 calculate
1 let a 12 3 na how many relations on a are both symmetric and anti-symmetricb if r is a relation on a that is anti-symmetric what is the maximum
the unit circle will be parametrized by cosw sinw provide a point on it the region cut out by circle the x-axis and the line from the origin to this
suppose a regular polygon which is an n-sided with equal side lengths s and similar angles at each corner there is an inscribed circle to
theres a nice way to show why the expresion for the area of a circle of radius r ispi r2it has an comman relationship with the experation for the
if e were rational then e nm for some positive integers m n so then 1e mn but the series expansion for 1e is1e 1 - 11 12 - 13 call the first n