The graph of the equation y = 4x + 2 passes through the point (1, y).
2 answers:
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The sum of the lengths of three sides of the rectangle, gives the length
of the fencing, while one third of the rectangle area is for the pavement.
Responses:
Project A: The formula for the length of the fencing is, L = 4·x - 1
Project B: Length of the fancy wall = 2·x + 1
<h3>Which method can be used to find the length and area of paving from the given equations?</h3>
Project A: Let QP and SR represent the longest sides of the rectangle, we have;
PQ = SR = 2·x + 1
Given parameters are;
Length of the rectangular plot = 2·x + 1
Width of the rectangular plot = x - 1
Vertices of the rectangular plot are; QPSR
Project A: Let QP and SR represent the longest sides of the rectangle, we have;
PQ = SR = 2·x + 1
Which gives;
SP = QR = x - 1
The length of the fencing, L = SP + PQ + QR = x - 1 + 2·x + 1 + x - 1 = 4·x - 1
- The formula for the length of the fencing is, L =<u> 4·x - 1</u>
Project B: The front side is SR
Therefore;
- Length of the fancy wall = <u>2·x + 1</u>
Project C:
Area, A = Length × Width
Area of the plot, A = (2·x + 1) × (x - 1) = 2·x² - x - 1
Learn more about writing equations here:
<h3>Answer: Bottom right corner (ie southeast corner)</h3>
This 3D solid is a strange sideways bowl shape. Each cross section is a ring to show the empty space.
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Explanation:
Check out the diagram below. The graph was created with GeoGebra. We have y = x^2 in red and x = y^2 in blue.
The gray region is the region between the two curves. We spin this gray region around the horizontal green line y = 1 to generate the answer mentioned above.
Note how (1,1) is a fixed point that does not move as this is on the line y = 1. Every other point moves to sweep through 3D space to create the solid figure. One way you can think of it is to think of propeller blades. Or you can think of a revolving door (the door is "flat" so to speak, but it sweeps out a 3D solid cylinder).