I see 12 t<span>riangles!!!!</span>
1² + 3² + 4² + 4(n - 1)² = ¹/₃n(2n - 1)(2n + 1)
1² + 3² + 4² + (2n - 2)² = ¹/₃n(2n - 1)(2n + 1)
1 + 9 + 16 + (2n - 2)(2n - 2) = ¹/₃n(2n(2n + 1) - 1(2n + 1))
10 + 16 + (2n(2n - 2) - 2(2n - 2)) = ¹/₃n(2n(2n) + 2n(1) - 1(2n) - 1(1) 16 + (2n(2n) - 2n(2) - 2(2n) + 2(2)) = ¹/₃n(4n² + 2n - 2n - 1)
26 + (4n² - 4n - 4n + 4) = ¹/₃n(4n² - 1)
26 + (4n² - 8n + 4) = ¹/₃n(4n² - 1)
26 + 4n² - 8n + 4 = ¹/₃n(4n²) - ¹/₃n(1)
4n² - 8n + 4 + 26 = 1¹/₃n³ - ¹/₃n
4n² - 8n + 30 = 1¹/₃n³ - ¹/₃n
+ ¹/₃n + ¹/₃n
4n² - 7²/₃n + 30 = 1¹/₃n³
-1¹/₃n³ + 4n² - 7²/₃n + 30 = 0
-3(-1¹/₃n³ + 4n² - 7²/₃n + 30) = -3(0)
-3(-1¹/₃n³) - 3(4n²) - 3(-7²/₃n) - 3(30) = 0
4n³ - 12n² + 23n - 90 = 0
The answer needs the volume of the original pyramid minus the small pyramid cut off.
Volume of pyramid = (area of base x height)/3
(12 x 6 x 14)/3 - (4 x 10 x 6)/3 = 256 m^3
The diagram is completely wrong so this problem is actually impossible to solve!
If you slice horizontally across a rectangular pyramid the ratios of the edges will remain constant.
The two rectangles are not the same shape! 12:6 is not the same ratio as 10:4
If the original pyramid in this question was sliced in half the top rectangle of the frustum would be 6 x 3.
In this diagram the height was reduced from 14m to 8m so the top 6m was removed.
If the base was 12 x 6 the top rectangle should be 6/14 smaller = 5.14m by 2.57m (not 10 x 4)
If you are brave you could point this out to your teacher
Answer:
1
Step-by-step explanation:
2x^2 + x -1 = 2
2x^2 + x-1-2 = 0
2x^2 + x -3 = 0
2x^2 -2x + 3x-3 = 0
2x(x-1) + 3(x-1) = 0
(2x + 3)(x-1) = 0
2x + 3 = 0
or x-1 = 0
x = -3/2 or 1
Let x be the number of tickets sold
Cost of x tickets = 32.5.x
Cost of convenience = 3.3.x
Process charges (for ONE ORDER, whatever the number of tickets) = $5.90
Hence:
$32.5(x) + $3.3(x) + $5.90 = $220.70
$35.8(x) = $220.90-$5.90
$35.8(x) = $214.8
And x = 214.8/35.8 = 6 tickets