Answer:
108 th term is zero
Step-by-step explanation:
The nth term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₉ = 99 and a₉₉ = 9 then
a₁ + 8d = 99 → (1)
a₁ + 98d = 9 → (2)
Subtract (1) from (2) term by term to eliminate a₁
0 + 90d = - 90
90d = - 90 ( divide both sides by 90 )
d = - 1
Substitute d = - 1 into (1) for value of a₁
a₁ + 8(- 1) = 99
a₁ - 8 = 99 ( add 8 to both sides )
a₁ = 107
Then
107 - (n - 1) = 0
107 - n + 1 = 0
- n + 108 = 0 ( subtract 108 from both sides )
- n = - 108 ( multiply both sides by - 1 )
n = 108
The 108th term is zero
Answer:
Volume of the frustum = 225.0952
Surface area = 274
Step-by-step explanation:
The volume can be calculated as the difference of the complete pyramid and the tip of the pyramid.
To find the height of the frustum, we can use pythagoras theorem in the following triangle:
first side: 9 - 5 = 4
second side h (height)
hypotenusa: slang = 6
6^2 = h^2 + 4^2
h^2 = 36 - 16 = 20
h = 4.4721
To find the height of the complete pyramid (H), we can use the following rule of three:
H / 9 = (H - 4.4721) / 5
5H = 9H - 40.2489
4H = 40.2489
H = 10.0622
Volume of complete pyramid:
V_complete = (1/3)*9^2*10.0622 = 271.6794
Volume of the tip:
V_tip = (1/3)*5^2*(10.0622 - 4.4721) = 46.5842
Volume of the frustum:
V_frustum = V_complete - V_tip = 225.0952
The surface area is the bigger base area + smaller base area + four side areas.
Bigger base area = 9^2 = 81
Smaller base area = 5^2 = 25
Side area = (9+5)*6/2 = 42
Total surface area: 81 + 25 + 4*42 = 274
Answer:
x=-9/4
Step-by-step explanation:
4(4x+15)=24 - divide both sides
4x+15=6 - move constant to the right
4x=6-15 -solve for the difference
4x=-9 - divide both sides
Answer: can u check out the image cuz the answer is in the photo and hope this helps can u give me brainliest
Step-by-step explanation:
24=3(n-5)
Distribute.
24=3(n) + 3(-5)
24 = 3n -15
Add 15 to both sides.
39 = 3n
Divide both sides by 3.
n = 13.
I hope this helps!.
