Answer:
The nth term of the given sequence
Step-by-step explanation:
<u><em>Explanation:-</em></u>
Given sequence -5,-4,-1,4,11,20,31
a₀ = -5
a₁ = a₀ +1 = -5 +1 = -4
a₂ = a₁ + 3 = -4+3 = -1
a₃ = a₂ + 5 = -1 +5 = 4
a₄ = a₃ + 7 = 4 + 7 =11
a₅ = a₄ + 9 = 11+9 = 20
a₆ = a₅ + 11 = 20+11 = 31
a₇ = a₆ + 13 = 31 +13 =44
and so on
The nth term of the given sequence
Answer:
Step-by-step explanation:
The formula of a volume of a square pyramid:
a - base edge
h - height of a pyramid
We have H = 8in.
Substitute and solve for a:
Refer to the diagram shown below.
When x = 30 ft, the cable is at 15 ft, therefore y(30) = 15.
That is,
a(30 - h)² + k = 15 (1)
Also, because the distance between the supports is 90 ft, therefore
y(0) = 6 ft, and y(90) = 6 ft
That is,
a(-h)² + k = 6 (2)
a(90 - h)² + k = 6 (3)
From (2) and (3), obtain
a(90 - h)² = ah²
90² - 180h + h² = h²
180h = 90²
h = 45 ft.
From (1) and (2), obtain
225a + k = 15
2025a + k = 6
Therefore
1800a = -9
a = - 0.005
k = 15 - 225(-0.005) = 16.125 ft
Answer:
The equation for the cable is
y = - 0.005(x - 45)² + 16.125
A graph of the solution verifies that the solution is correct.
Answer: -5 and 2
Because it equals 3 when added.
And -10 when multiplied.
