Show that the projection into the xy-plane of the curve of intersection of the parabolic cylinder z=1−5y2 and the paraboloid z=x2+y2 is an ellipse. (a) Find a vector-parametric equation r⃗ 1(t)=⟨x(t),y(t),z(t)⟩ for the ellipse in the xy-plane.

Compare the cost of the bike trips from the two companies shown.for both the cost in a linear function of the number of days which statements is true

Problem 2. find the exact value of the remaining trigonometric functions. sketch theangle 8 for each problem. (3 points each)(a) tan 0 =o is in quadrant 2

According to a research study, parents with young children slept 6.4 hours each night last year, on average. a random sample of 18 parents with young children was surveyed and the mean amount of time per night each parent slept was 6.8. this data has a sample standard deviation of 0.9. (assume that the scores are normally distributed.) researchers conduct a one-mean hypothesis at the 5% significance level, to test if the mean amount of time parents with young children sleep per night is greater than the mean amount of time last year. the null and alternative hypotheses are h0: μ=6.4 and ha: μ> 6.4, which is a right-tailed test. the test statistic is determined to be t0=1.89 using the partial t-table below, determine the critical value(s). if there is only one critical value, leave the second answer box blank.