Answer:
see explanation
Step-by-step explanation:
The n th term ( explicit formula ) of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₁₂ = - 95 and a₃₇ = - 270 , then
a₁ + 11d = - 95 → (1)
a₁ + 36d = - 270 → (2)
Subtract (1) from (2) term by term to eliminate a₁
25d = - 175 ( divide both sides by 25 )
d = - 7
Substitute d = - 7 into (1) and solve for a₁
a₁ + 11(- 7) = - 95
a₁ - 77 = - 95 ( add 77 to both sides )
a₁ = - 18 , thus
= - 18 - 7(n - 1) = - 18 - 7n + 7 = - 7n - 11
= - 7n - 11 ← explicit formula
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The recursive formula allows a term in the sequence to be found by adding the common difference d to the previous term, thus
= 
- 7 with a₁ = - 18 ← recursive formula
Answer:
5/6
Step-by-step explanation:
cuz there's 6 sides and there are 5 more sides than the 1
Answer:
The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet
Step-by-step explanation:
At first, let us find the perimeter of the playground
∵ Perimeter of a triangle is P = S1 + S2 + S3
∵ The sides of the triangular playground are (2x) ft, (x - 1) ft, and x ft
∴ S1 = 2x, S2 = x - 1, S3 = x
→ Substitute them in the rule of the perimeter above
∵ P = 2x + x - 1 + x
→ Add the like terms
∴ P = (2x + x + x) - 1
∴ P = 4x - 1
∵ The perimeter of this playground is 27 feet
∴ P = 27
→ Equate the two values of P
∴ 4x - 1 = 27
→ Add 1 to both sides
∴ 4x - 1 + 1 = 27 + 1
∴ 4x = 28
→ Divide both sides by 4
∵ 
= 
∴ x = 7
→ Substitute the value of x in each side to find their lengths
∵ S1 = 2(7)
∴ S1 = 14 feet
∵ S2 = 7 - 1
∴ S2 = 6 feet
∵ S3 = 7 feet
∴ The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet
The answer is p=2s+7. Two plants can be grown from each seed packet, and Erin already has seven plants so you add that to the equation as well.
The cost of a utility pole with a diameter of 1.5 ft and a height of 40 ft is $782.1
<h3>How to calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 40 ft?</h3>
The given parameters are:
Cost per cubic foot = $11.07 per cubic foot
Height = 40 feet
Diameter = 1.5 feet
Shape = Cylinder
The volume of the cylinder is calculated as:
V = πr^2h
Where
r = Diameter/2
So, we have
r = 1.5/2
Evaluate
r = 0.75
The volume of the cylinder becomes
V = 3.14 * 0.75^2 * 40
Evaluate
V = 70.65
The cost per cubic foot is $11.07 per cubic foot.
So, the cost of a utility pole is
Cost = $11.07 * 70.65
Evaluate
Cost = $782.1
Hence, the cost of a utility pole with a diameter of 1.5 ft and a height of 40 ft is $782.1
Read more about volume at:
brainly.com/question/1972490
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