Tutor profile: Katy W.
What conic section is described by the equation 9x^2 + 3x + 16y^2 + 4y = 8 ?
There are four conic sections: parabolas, circles, ellipses, and hyperbolas. To tell the difference by looking at the equations, we first investigate the degree of x and y. Both of our variables are squared, so we can rule out a parabola. In a circle, the coefficients of the squared terms must be the same number. Ours are different, so this is not a circle. In a hyperbola, the signs of the squared terms must be different. Ours are not different, so this is not a hyperbola. Therefore, this equation is an ellipse.
A researcher evaluates 40 samples, which end up with a mean of 13 and a standard deviation of 1. Later, she discovers that her measurement tool was misaligned and all of her measurements were consistently too large by 2. How will this affect the sample mean and standard deviation?
While some students would like to try and calculate a new mean and standard deviation, that is unnecessary! If every data point was too large by 2, and we subtract 2 from each one, the mean will be 13 - 2 = 11. The standard deviation is a measure of spread, the variation in the data would not change if they are all consistently off by 2, so the standard deviation remains the same. In more mathematical sense, the mean is calculated by the sum of the observations divided by the number of observations. In this case, we know the sum of all the observations was originally 40*13. If we subtract 2 for all 40 observations and divide by the number of observations, we have (40*13 - 2*40) / 40, or 11.
Where does the graph of y = x^2 + 3x - 10 cross the x-axis?
Graphs cross the x-axis where y=0, so we can say 0 = x^2 + 3x - 10 At this point, we can solve via the quadratic equation if we wanted to, but this one can also be solved by factoring. We need to find two numbers that multiply to make -10, but add to make 3. We know one has to be negative, and one positive in order to multiply to -10, and there are two possible integer pairs: 1 and 10 2 and 5 If we use +5 and -2, this will multiply to -10 and also add to 3, so we can factor it this way: 0 = (x+5)(x-2) We can now break this into x + 5 = 0 or x -2 = 0 x = -5 or x = 2 The graph of the equation will cross the x-axis at x=-5 and again at x=2.
needs and Katy will reply soon.