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sorry i posted the question wrong its when does the sin theta$ graph equal negative root three all over two. i know that the first time the sin graph equals negative root 3 all over 2 is at 4pi/3 but how do you know that it also occurs at 5pi/3. i understand myself that it will equal it again by looking at the sin graph but how do you know it exactly occurs at 5pi/3
when does sin(x)=sin(-Π/3) where x is greater than 0 but less than 4Π. x stands for theta. i could work out the first place where they cross it is 4Π/3 and i would of said the next place where they cross is 3Π. but the back of the book says it is 5Π/3. im a bit confused. if you put in 3Π in to both of them they both equal 0. yet this is not one of the answers?
a particle is projected from ground level with initial speed 8i+28j m/s. find the two times when its speed will be 10 m/s. i tried working this out by this.
√(8²+(21-gt)²)=100 (by the way the square root goes over it all even though it doesnt look like it) but when i solved for t i did not get the right answer. the right answer is 110/49 and 170/49.
A particle travels srating with a initial speed u, with uniform acceleration a. Show that the distance travelled during the nth second is u+an-.5a.
I tried working this out by putting this information into the formula
S=ut+.5at^2 but it did not work
sorry i do not know to work it out from here i tried factorising but didnt get anywhere
prove by induction that 2^n is greater than or equal to 1+n when n are natural numbers. i tried subbing in k+1 in for n but i get stuck
prove by induction for all positive integers n: 1+5+9+13+........+(4n-3)= n/2(4n-2)
i tried this by trying to prove n/2(4n-2)+ (4(k+1)-3) = k+1/2(4(k+1)-2) but it did not work out for me.
A particle is projected vertically upwards with velocity u m/s . It's height is h after t1 and t2 seconds. Prove that. t1× t2 = 2h/g
ok thanks for the graph and which uvast equation are you using thickhead.
A car, starting from rest and travelling from p to q on a straight level road,
where | pq | = 10 000 m, reaches its maximum speed 25 m/s by constant
acceleration in the first 500 m and continues at this maximum speed for the
rest of the journey.
A second car, starting from rest and travelling from q to p, reaches the same
maximum speed by constant acceleration in the first 250 m and continues at
this maximum speed for the rest of the journey.
(i) If the two cars start at the same time, after how many seconds do the
two cars meet ?
Find, also, the distance travelled by each car in that time.
i am trying to use uvast equations to solve this but i cant. can someone help me
they use the formula 1/root n on my course where n stands for the size of the sample i all ready worked out the first bit but i cant work out the second part of the question
A survey is being conducted of voters’ opinions on several different issues.
(i) What is the overall margin of error of the survey, at 95% confidence, if it is based on a
simple random sample of 1111 voters.
(B) A political party had claimed that it has the support of 23% of the electorate. Of the
voters in the sample above, 234 stated that they support the party. Is this sufficient
evidence to reject the party’s claim, at the 5% level of significance?
Find the moment of inertia of a disc of mass m and radius r with a point mass of m on its circumference. i cant work this out can someone help me. i can work out that the moment of inertia of the disc is 1/2mr^2 but i dont know what to do with the point mass. i think it could have to do with some thing with the parallel axes theorem. the answer at the back of the book is 11/2 ml^2
John has 32 red balloons, 24 white balloons and 16 blue balloons. she wants to make a number of identical balloon arrangements for a party. what is the greatest number of arrangements she can make if all the balloons are used . how many balloons of each colour are in these arrangements.
A spherical snowball is melting at a rate proportional to its surface area. That is, the rate at
which its volume is decreasing at any instant is proportional to its surface area at that instant.
If the snowball loses half of its volume in an hour, how long more will it take for it to
melt completely?
Give your answer correct to the nearest minute.
a uniform annulus consists of disc of radius 3 meters with a disc of radius 1 meters removed from its center. the mass of the annulus is m. Prove that the moment of inertia of the annulus about an axis through its center is 5m.
ok thanks i get it now
thanks for your help but i dont even understand the question. why does the amount he needs each year go down for example the first year he needs 20000 and then the next year he only needs 20000/1.03 and so on why is the amount of money he needs going down
john is 25 years old and is planing for his pension . he intends to retire in 40 years time, when he is 65. first he calculates how much he wants to have in his pension fund when he retires. then he calculates how much he needs to invest to achieve this. he assumes that in the long run money can be invested at an inflation adjusted annual rate of 3%. your answers should be based on a 3% annual growth rate
(I) john wants to have a fund from the date of his retirement, give him a payment of £20000 at the start of each year for 25 years.show how to use the sum of geometric series to calculate the value on the date of retirement the fund required.
i cant work this out. the answer is 358710.84 by the way
A particle of mass 5 kg is suspended from a fixed point by a light elastic stringwhich hangs vertically. The elastic constant of the string is 500 N/m.The mass is pulled down a vertical distance of 20 cm from the equilibriumposition and is then released from rest.(i) Show that the particle moves with simple harmonic motion.
what i tryed to do was find the force down and the force up find the resultant force and let it equal to F=5a and then that would prove it but to do this when i am finding the force in the string i need the natural length of the string but it is not given in the question. to find the force up i use F=k(length-natural length)
two functions are f:x -> |x-3| and g:x-> 2. at what co-ordinates does f:x cut the x and y axsis. at what 2 co-ordinates do the 2 functions cut each other
prove that the differentiation of a constant is always zero from first principals.
i am trying to divide x^3+(1-k^2)x+k by (x+k) but i cant do this can you show me how to.
f:x x³+(1-k²)x+k is a cubic function where k is a constant.1. show that -k is a root of f.2.find in terms of k the other two roots of f
they are the right answers but how did you work it out?