b. Find the length of the transverse and conjugate axes. c. Find the slopes of the asymptotes. d. Find the coordinates of the foci. e. Graph the hyperbola.
The point x-y is on the line, where x is the mean of the x values, and y is the mean of the y values. 4. Its form is y(hat) = a + bx. (Note that b is slope and a is the y-intercept.) 5. b = r(sy/sx).
The volume in cubic feet of a box can be expressed as V(x) = x 3 − 6x 2 + 8x, or as the product of three linear factors with integer coefficients. The width of the box is 2 – x. a. Factor the polynomial to find linear expressions for the height and the width. b. Graph the function. Find the x-intercepts.
Dim count As Integer = 27 8. Write a pseudocode statement that assigns the sum of 10 and 14 to the variable total. Total = 10 + 14 9. Write a pseudocode statement that subtracts the variable downpayment from the variable total and assigns the result to the variable due. due = downpayment – total 10.
Find the perimeter and area of the shaded sections of these shapes. (i) [7] (ii) [7] Total 60 marks Geometry and trigonometry Solutions to Topic assessment 1. The curve is a circle, centre O and radius 2. [2] 2. Substituting [pic] into [pic] gives [pic] Since the equation has a repeated root, the line meets the circle just once, and so the line is a tangent to the circle.
(b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9. (c) Assume X follows a continuous distribution which is symmetric about 0. If , then . (d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter. (e) In a right-tailed test, the value of the test statistic is 1.5.
Tin's actual atomic radius is 140 pm. Use the math equation below to determine the percent error of your estimated value. Percent error = fraction: | actual value minus experimental (estimated value | over actual value × 100 This equation means that you subtract to find the difference between the actual value (given in this problem) and the experimental value (estimated from the graph). The numerator is in an absolute value sign, so the difference should always be positive. Take that difference and divide by the actual value (given in this problem) of tin’s atomic radius.
 Precision: measure of how close a series of measurements are to one another.  Accepted Value: the correct value based on reliable references  Experimental Value: the value measured in the lab.  Error: o Error = experimental value – accepted value  Percent error: o Percent Error = |error| x 100% Accepted value  Significant Figures: all of the digits that are known, plus a last digit that is estimated. o
Calculate the impedance by the measured values of voltage and current from the oscilloscope. Also calculate the impedance from = − C. Answer: Impedance, Z = 5∠0 34.65 60.48°) = 173.25 - 60.48⁰ = 85.37 Ω - j150.76 Ω Again, XC = 1/ = 1/ (6280 x 10-6) = 159.24
8 5 7 8 (a) 7 7 8 6 6 11 7 5 5 7 9 9 6 7 6 7 Construct a frequency table from the above data and add a cumulative frequency column. For this data, find: (i) the median; (ii) the lower quartile; (iii) the upper quartile. 2 (b) 1 1 1 2 (c) Construct a boxplot for this data. [Turn over [ X100/201] Page three Marks 3. The diagram below represents a sphere.