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  1. M

    Central Limiting Theorem?

    Homework Statement The amounts of time that a cashier spends processing individual customers' orders are independent random variables with mean 2.5 minutes and standard deviation 2 minutes. a) What is the approximate probability that it will take more than 4 hours to process orders of 100...
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    Poisson, Binomial Distributions

    Homework Statement The number of claims that an insurance company receives per week is a random variable with the Poisson distribution with parameter λ. The probability that a claim will be accepted as genuine is p, and is independent of other claims. a) What is the probability that no claim...
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    Linear Algebra: Spans and Dimensions

    Homework Statement Given v1, v2 ... vk and v, let U = span {v1, v2 ... vk} and W = span {v1, v2 ... vk, v}. Show that either dim W = dim U or dim W = 1 + dim U. The Attempt at a Solution I'm not really sure where to start. If I knew that {v1, v2 ... vk} was linearly independent, then it would...
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    Linear Algebra: Linear indepency of a set of Polynomials

    Homework Statement Let {p, q} be linearly independent polynomials. Show that {p, q, pq} is linearly independent if and only if deg p ≥ 1 and deg q ≥ 1. Homework Equations λ1p + λ2q = 0 ⇔ λ1 = λ2 = 0 The Attempt at a Solution λ1p + λ2q + λ3pq = 0 I know if λ3 = 0, then the coefficients of...
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    Linear Algebra: Prove that the set of invertible matrices is a Subspace

    Homework Statement Is U = {A| A \in nℝn, A is invertible} a subspace of nℝn, the space of all nxn matrices? The Attempt at a Solution This is easy to prove if you assume the regular operations of vector addition and scalar multiplication. Then the Identity matrix is in the set but 0*I and...
  6. M

    Differentiating This Function

    Somebody want to help with this derivative: y = (7.75x3 + 2250) / 750x I differentiate it with the quotient rule and get: dy/dx = 31x / 1500 - 3 / x2 But that's wrong. It's got a zero around 5 - 6 and the original function has its minimum at (4.03, 1.12). Not sure what I did wrong.
  7. M

    Help with This Derivative

    Does somebody want to help me with differentiating this function: (0.003 + 0.004\sqrt{2})∏r2 + 0.004∏r [(2250 - ∏r3) / 3∏r2)] Originally I tried simplifying it by distributing the 0.004∏r into the fraction, but whenever I did that the two expressions were never equivalent when I checked them...
  8. M

    Determining Tangent Slope w/Point Not On Curve

    How do you determine the equation of all possible tangents to a curve (say, a parabola) that pass through a given point that is not on said curve? This is more of a conceptual question, and it's not homework, so I thought it fit in this forum. I think there might be a question like this on the...
  9. M

    Stargazing Looking to buy my first telescope

    Right so I'm looking to buy my first telescope and rather than start a thread I thought I'd post here. How does this look for a beginner telescope? Keeping in mind its my first and I really only want to look at the moon, some of the closer planets, and maybe some nearby galaxies or nebulae. I am...
  10. M

    Young's Double Slit Experiment science fair

    I plan on trying to recreate a version of Young's double slit experiment for a science fair. All the methods I've found for it recommend using a helium-neon laser. Would a laser pointer or some other cheaper laser work? For the slits my idea is to get a glass microscope slide, paint over it then...
  11. M

    Electrons Colliding - Totally Confused

    Homework Statement Two electrons separated by a large distance are fired directly at each other. The closest approach in this head-on collision is 4.0 * 10-14 m. One electron starts with twice the speed of the other. Assuming there is no deflection from the original path, determine the initial...
  12. M

    Elastic Collision - two carts

    Homework Statement Two carts equipped with spring bumpers on an air track have an elastic collision. The 253-g cart has an initial velocity of 1.80 m/s [N]. The 232-g cart is initially stationary. What is the velocity of each cart after the collision? Homework Equations I know because cart 2...
  13. M

    Recommended Software Language to Learn?

    I am just finishing up grade 11 and thought it would be worthwhile to learn a programming language over the summer. However, I'm unsure which language I would do best to learn. I can already code in Turing, HTML, and Java. I am most likely going to pursue an education in science or engineering...
  14. M

    Admissions Canadian wondering about applying to School in US for Engineering

    Well, I'm in grade 11, I think the major for me is Aerospace engineering. Unfortunately, there are only two schools in Canada that offer a dedicated aerospace engineering program, and neither of them are extremely well-regarded in terms of academics (as I understand). Which leads me to my...
  15. M

    Calculating Constant speed of an Elevator Rising

    Homework Statement The motor for an elevator can produce 14kW of power. The elevator has a mass of 1100 kg, including its contents. At what constant speed will the elevator rise? Homework Equations I'm not really sure. Probably Gravitational potential = mgh. Kinetic energy = 1/2mv^2...
  16. M

    Question about necessary concentration of urea for radish growth

    I have a project in my grade 11 biology class to design a controlled experiment showing how some factor affects plant growth, specifically radishes. I have decided to add urea as a nitrogen fertilizer to one group and do nothing to the other leaving all other factors the same between the two...
  17. M

    Question on Lottery Probabilities

    I have a question on the chances of winning a lottery: If you buy 10 tickets in a lottery where the odds of you winning are 30,000,000 to 1, is your probability of winning 1 in 3,000,000?
  18. M

    EngiSci Option in Aerospace at UofT?

    I have a question regarding The Aerospace Option at UofT EngSci: Will getting this degree limit me in any way in terms of job opportunities after I graduate? Would I be better off going to Carleton or Ryerson for a full Aero program? My dilemma is that UofT is much more well-respected nationally...
  19. M

    Aerospace Engineering Programs in Canada?

    I'm in grade 10, wondering what Universities in Canada offer dedicated Aerospace engineering programs, and which one is in your opinion, the best. Any help is appreciated. I'm sorry if this is the wrong section, or a duplicate thread.
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