Answer: Sorry, I cannot provide visual aids or diagrams. However, I can help with the mathematical calculations and solutions to the given problems.
(a) To construct a trapezium WXYZ, follow the steps below:
Draw a straight line segment WX of length 10.2 cm and draw a line segment YZ of length 5.8 cm parallel to WX, such that the distance between them is 8.3 cm.
Draw a line segment XY of length 5.6 cm perpendicular to both WX and YZ, joining their endpoints.
From the endpoint Z, draw a perpendicular line segment ZN to WX.
Angle LWXY is given as 60°, so mark a point L on WX, such that angle WLY is 60°.
Therefore, the trapezium WXYZ is constructed.
(b) From the diagram, we can see that ZN is perpendicular to WX, so triangles ZWX and ZYN are similar.
Using the similar triangles ZWX and ZYN, we can write:
WX/WY = ZN/XY
10.2/5.6 = ZN/5.8
ZN = (10.2/5.6) * 5.8
ZN ≈ 10.57 cm
(c) Using Pythagoras' theorem, we can find the length of WZ:
WZ² = WX² - XZ²
WZ² = 10.2² - 8.3²
WZ ≈ 4.3 cm
Therefore, |WZ| ≈ 4.3 cm and |ZN| ≈ 10.57 cm.
(a) Let the width of the frame be w and the length be l. Then, according to the problem,
cost ∝ w * √l
cost = k * w * √l, where k is the constant of proportionality.
Using the given information, we can find the value of k as follows:
N115 = k * 10 * √25
k = N115 / 50
k = N2.3
Therefore, the law of variation is cost = N2.3 * w * √l.
(b) For a frame of width 12 cm and length 49 cm,
cost = N2.3 * 12 * √49
cost = N2.3 * 12 * 7
cost = N193.2
(a) Since the range R = {2, 5, 10}, we know that f(x) can take only these three values. Therefore,
x² + 1 = 2 or x² + 1 = 5 or x² + 1 = 10
Solving each of these equations for x, we get:
x = ±√1 or x = ±√4 or x = ±√9
x = ±1 or x = ±2 or x = ±3
Therefore, the domain D = {-3, -2, -1, 1, 2, 3}.
To find f-¹(5), we need to find the values of x for which f(x) = 5. From the equation x² + 1 = 5, we get:
x² = 4
x = ±2
Therefore, f-¹(5) = {-2, 2}.
Explanation: