PLEASE LAST FEW SETS OF QUESTIONS FOR SEMESTER PLEASE HELP 2

Problem 1

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Explanation:

a1 = 1.7 = amount of concrete for the first step

a4 = x = amount of concrete for the fourth step

Sn = sum of the first n terms of an arithmetic sequence

Sn = (n/2)*(a1 + an)

S4 = (4/2)*(a1 + a4)

S4 = 2(1.7+x)

S4 = 2x+3.4

S4 = 17

2x+3.4 = 17

2x = 17-3.4

2x = 13.6

x = (13.6)/2

x = 6.8

We need 6.8 cubic feet of concrete for the fourth step. We'll use this value to help us find the common difference d

an = nth term of an arithmetic sequence

an = a1 + d(n-1)

a4 = a1 + d(4-1)

a4 = a1 + 3d

6.8 = 1.7 + 3d

6.8-1.7 = 3d

5.1 = 3d

(5.1)/3 = d

1.7 = d

d = 1.7

Coincidentally, the common difference is the same as the first term. This won't always happen.

Now we can compute the 12th term

an = a1 + d(n-1)

a12 = 1.7 + 1.7(12-1)

a12 = 20.4

which is then used to find the sum of the first 12 terms

Sn = (n/2)*(a1 + an)

S12 = (12/2)*(a1 + a12)

S12 = 6(1.7 + 20.4)

S12 = 132.6

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Problem 2

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Explanation:

The center is (h,k) = (0,10) which is where the nozzle is located.

The distance from (0,10) to (0,25) is 15 units, so r = 15.

Also, the distance from (0,10) to (0,-5) is also 15 units.

Plug those values into the equation below.

That equation represents the boundary of the circle, which is where the water can reach.

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Problem 3

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Explanation:

Or note that,

a3 = 0.81*(a2) = 0.81*(0.81a1) = a1*(0.81)^2 = 6.7*(0.81)^2 =  4.39587

which must mean,

This is based off the idea that

So,

a6 = a1*(0.81)^5

a6 = 6.7*(0.81)^5

a6 = 2.33614554867

a6 = 2.336

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.

step-by-step explanation: