Pujan Gor

why do containers that store liquid oxygen not have a lid?

A particle P moves in a straight line such that at time T seconds its displacement, S meters from a fixed point O on the line is given by

S=T^3-7T^2+10T T>0

a) find the values of t (t>0) at which P passes through O.

b)find the speed of P each time it passes through O.

c) Find the greatest speed of P in the interval 0<T<5

the curve with equation y=k cos 3x where x is in radians and k is a constant. the curve cuts the x axis at point A.

a) write down the coordinates of point A

b) find as a multiple of k, the area of the region R bounded by the x axis , the y axis and the curve.

( there is a sketch of the curve given but is see no way to put it on the internet. however it has no numerical values. It starts of when X=0 and y is a positive value and slopes downwards ....the gradient keeps getting steeper until a point where y=0 and x is a positive value )

1) reffered to a fixed point origin O, the positional vector of points P and Q are (-2i+3j) and ( ki + lj ) respectively, where k and l are constants. The point M is the midpoint of PQ. given the position vector of M relative to O is (2i+4j)

a) find the values of k and l

the point R is such that PQ : QR = 1:2

b)find, in terms of i and j, the expression for OR

3) A can is made out of thin sheet metal and is in shape of a right circular cylinder closed at both ends. the radius of the circular cross section of the can is r cm. the height of the can is h cm and the total surface area is A cm^2 . given that the capacity of the can is 31.25*pie cm^3.

a) show that r^2 *h = 31.25

b)find an expression of A in terms of pie and r only

c) calculate , to one decimal place , the value of dA/dr when r=3

d) show that A has a stationary value when r=2.5

e) find, giving your answer as a multiple of pie , the stationary value of A establishing whether this is a maximum or minimum value.

Please help me by answering any questions you can from the following.....the more the better.

1) reffered to a fixed point origin O, the positional vector of points P and Q are (-2i+3j) and ( ki + lj ) respectively, where k and l are constants. The point M is the midpoint of PQ. given the position vector of M relative to O is (2i+4j)

a) find the values of k and l

the point R is such that PQ : QR = 1:2

b)find, in terms of i and j, the expression for OR

2) solve the equation sin2x = sin 120, giving all solutions for 0<x<360

3) A can is made out of thin sheet metal and is in shape of a right circular cylinder closed at both ends. the radius of the circular cross section of the can is r cm. the height of the can is h cm and the total surface area is A cm^2 . given that the capacity of the can is 31.25*pie cm^3.

a) show that r^2 *h = 31.25

b)find an expression of A in terms of pie and r only

c) calculate , to one decimal place , the value of dA/dr when r=3

d) show that A has a stationary value when r=2.5

e) find, giving your answer as a multiple of pie , the stationary value of A establishing whether this is a maximum or minimum value.

4) find the set of values for x which 2x(x-2)<(x+1)(x-2)

5) Sn= nSIGMA NOTATION (SUMMATION ) SYMBOL r=1 ( 50-4r)

a) write down the first three terms of the series

b)Calculate the value of S20

c) find n such that Sn=0

ii) the sum of the first four terms of a geometric series of positive terms is 78.336 and the sum to infinity of the series is 90. calculate

a) the common ratio of the series

b) the first term of the series

c) the difference, to 3 significant figures, between the sum to infinity of the series and the sum of the first thirty terms. Give your answer in standard form

Thanks in advance :-)

1. sand is poured onto horizontal ground. the sand forms a right circular cone. the volume of the cone increases in such a way that the height is always half the radius of the base. Find an estimate for the percentage change in in the volume of the cone when the radius increases by one percent.

2. A curve has equation y=3+ (1/x+3) where x is not equal to -3.

a) find an equation of the asymptote to the curve which is parallel to

i) the x axis

ii) the y axis

b) calculate the coordinates of the points where the curve crosses the coordinate axes

a) expand (1+x/2)^1/4 in ascending powers of x, up yo and including the term is x^2 simplifying your terms as far as possible.

b) by substituting x=1/8 into your expression , obtain an approximation to 4 decimal places of quad root of 17

c)expand (1-x/2)^-1/4 in ascending powers of x up to and including the terms in x^2, simplifying your terms as far as possible

d) using your answer to parts a) and c) , expand (2+x / 2-x) ^ 1/4 in ascending powers of x up to and including the terms in x^2 , simplifying your terms as far as possible

e)use your answers from part (d) to find an estimate to 4 decimal places of

0 $ integration symbol $ 0.2 (2+x / 2-x) ^ 1/4 dx

The third and fifth terms of a geometric series S are 45 and 405 respectively. Find

a) two possible values of the common ratio of S,

b) the first term of s

given that the sum of the third, fourth, and fifth terms is 315

c)find the first twelve terms of S

another series T is formed with all its terms positive. the first term of T is the same as the first term of S. The common ratio of T is the reciprocal of one of the answers to part (a).

d) find the sum to infinity of T

A chemical factory wishes to make a cylindrical container, of thin metal to hold 10 cm^3, using the least possible area of metal. If the outside surface is S cm^2, and the radius is R cm , show that S=2pieR^2 + 20/r and hence find the required radius and height for the container ( leave pie in the answer)

Find the equation of the tangents to the curve y=x^ 3 - 6x^ 2 + 12x + 2 which are parallel to the line y = 3x

i am looking for a swiss government website which has a record of all businesses . i looking to see if international camp suisse is genuine

For -pie/2<x<pie/2 give your answer in terms of pie

a) sin 2x = cos 2x

b) 5 sin x - 14= 2/sin x

(1-2x)^-1/2 - (1+2x)^1/2 = ax^2 + bx^3

where a and b are constants and x is sufficiently small that terms in x^4 and higher powers of x can be ignored, find the values of a and b.

a) solve for -90<x<90

tan x=3sin x

b) 4x^2+px+2p=0

where p is a positive constant. find the values of p for which this equation has equal roots.

Solve for value of x between 0 degrees and 360 degrees

a) 2sinx=cos(x+60)

b) cos(x+45)=cosx

c) sin(x-30)=1/2cosx

d) 3sin(x+10)=4cos(x-10)

compare and contrast the poem if and ance upon a time

1) intro What both poems are about

2)&3) similarities and differences Techniques to convey the subject at matter

4) poems effect on you

5)conclusion

Expand (1-3x)^1/2 ascending powers of x up to and including the term x^3 simplifying each term as far as possible

State the range of values of x for which the expansion is valid

Show that root 10 = 5 root (2/5)

Hence by using your expansion with a suitable value of x obtain an approximation to 5 significant figures for root 10

Calculate to 3 significant figures the percentage error in the approximation obtained in part (d)

*sorry for using the word root instead of the symbol as there is no symbol on my keyboard