Math Answers

Find the nullity and the range of the space spanned by 𝑢 = (1,0,2), 𝑣 = (−3,1,1), 𝑤 = (0,1,4) and 𝑥 = (−1, −3,5)

Find the dimension and a basis for 𝑊 = {(𝑥, 𝑦, 𝑧, 𝑤,𝑡): 𝑥 + 𝑦 + 𝑧 + 𝑤 + 𝑡 = 0, 𝑥 − 𝑦 + 𝑧 − 𝑤 + 𝑡 = 0}

Find the solution:

2(dS)/(dt) - S/t = 5t^3 S^3

What is the limits of (1/n)

IX is uniformly distributed over the interval [0,10], compute P{2<X<9} , P{1<X<4} and P{X<5}.

Write down 𝑇3(𝑥), 𝑇4(𝑥), 𝑎𝑛𝑑 𝑇5(𝑥) for the Taylor series of 𝑓(𝑥) = ln (3 + 4𝑥) about 𝑥 = 0

Find the particular solution of:

1.) x^2 y' -2xy=x^4 +3; where y = 2 and x = 1

A penny is dropped into a tank of water at the water’s surface. If falls to the bottom according to the relation below , where d is the depth of the water measured in metres and t is the time after the penny was dropped, measured in seconds. How deep is the water?

Suppose that the standard deviation of the tube life of a particular brand of TV picture

tube is known to be 500, the population of tube life cannot be assumed to be normally

distributed. However, the sample mean of x = 8900 is based on a sample of n = 35.

Construct the 95% confidence interval for estimating the population mean.

last year the employees of the city health department donated an average of $ 8 to the rescue squad. test the hypothesis at the 0.01 level of significance that the average contribution this year is still $ 8 if a random sample of 35 employees showed an average donation of $ 8.90 with a standard deviation of $ 1.75.