Answer:
0.9675sq.cm
Step-by-step explanation:
Find a related diagram attached
Area of the shaded region = Area of rectangle - area of semicircle
Area of rectangle = 3cm * 1.5cm
Area of rectangle = 4.5sq.cm
Given
diameter of the semicircle = 3cm
area = πd²/8
Area of the semicircle = 3.14(3)²/8
Area of the semicircle = 3.5325sq.cm
Area of the shaded region = 4.5 - 3.5325
Area of the shaded region = 0.9675sq.cm
The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.
<h3>What is the Surface Area of a Box?</h3>The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.
<h3>What is the Surface Area of a Box?</h3>SA = 2(lw + lh + hw), where:
The image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:
The surface area to be covered = surface area of the box - area of the bottom rectangular face
The surface area to be covered = 2(lw + lh + hw) - (l)(w)
l = 26
w = 15
h = 8
Substitute
The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =
The surface area to be covered = 1436 - 390 = 1,046 cm
Area of one tile = 1 cm square
Number of tiles needed = 1,046/1
Number of tiles needed = 1,046 tiles.
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The asymptotes of the reciprocal function are x = 3 and y = 4. Also, the domain is x < 3 or x > 3 and the range is y < 4 or y > 4
<h3>How to determine the values of a, c, d and k?</h3>The function is given as:
f(x) = -2[1/0.5(x -3)] + 4
A reciprocal function is generally represented as:
f(x) = a[1/(x -c)] + k
So, we have:
a = -2
c = -3 * 0.5
c = -1.5
k = 4
d = 0
Hence, the values of a, c, d and k are -2, -1.5, 0 and 4
<h3>The asymptotes</h3>We have:
f(x) = -2[1/0.5(x -3)] + 4
Set the radical to 0
y = 0 + 4
Evaluate
y = 4
Set the denominator to 0
x - 3 = 0
Evaluate
x = 3
Hence, the asymptotes are x = 3 and y = 4
<h3>The graph of the function</h3>See attachment for the graph of the function f(x) = -2[1/0.5(x -3)] + 4
The table of values is
x y
-4 4.6
-2 4.8
2 8
4 0
From the graph of the function, the domain is x < 3 or x > 3 and the range is y < 4 or y > 4
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