<span>If the two numbers are positive, then since each is greater than 1, the product will be greater than either factor.</span>

Answer:

15.924 feets

Step-by-step explanation:

The height I'd the flagpole can be obtained using trigonometry ;

Solution triangle has been attached below,

The height, h of flagpole

Tan θ = opposite / Adjacent = h / 12

Tan 53 = h / 12

h = 12 * tan 53

h = 15.924

**Step-by-step explanation:**

11887249635951.291207505

Is the correct answer

**Answer:**

Rounded to the nearest dollar, Robert will have $ 505 more than Cooper on his account.

**Step-by-step explanation:**

Given that Cooper invested $ 3,100 in an account paying an interest rate of 2% compounded quarterly, while Robert invested $ 3,100 in an account paying an interest rate of 3% compounded continuously, to determine, after 12 years, how much more money would Robert have in his account than Cooper to the nearest dollar, the following calculation must be made:

Compound interest formula: Initial x (1 + interest / composition) ^ composition x years

Continuous compound interest formula: Initial x exp ^ (interest x years)

Cooper:

3,100 x (1 + 0.02 / 4) ^ 12x4 = X

3,100 x (1 + 0.005) ^ 48 = X

3,100 x 1,005 ^ 48 = X

3,100 x 1,270 = X

3,938.51 = X

Robert:

3,100 x 2.71828182845904 ^ (3x12) = X

4,443.32 = X

4,443.32 - 3,938.51 = X

504.51 = X

Therefore, rounded to the nearest dollar, Robert will have $ 505 more than Cooper on his account.

**Answer:**

n=9 and n = 12

**Step-by-step explanation:**

an = a1 +d(n-1) is the formula for an arithmetic series

The first term is a1 and is 2.5

The 3rd term is

2 =a1 + d(3-1)

2 = 2.5 + 2d

Solve for d

Subtract 2.5 from each side

2-2.5 = 2.5 -2.5 +2d

-.5 = 2d

Divide by 2

-.5/2 = 2d/2

-.25 =d

an = 2.5 -.25(n-1)

The sum is found by using

Sn = n/2 (a1+an)

Sn = 13.5

Substituting the formula for an)

13.5 = n/2 (2.5 + 2.5 -.25(n-1))

Multiply each side by 2 to get rid of the fraction

2*13.5 = 2* n/2 (2.5 + 2.5 -.25(n-1))

27 = n*(2.5 + 2.5 -.25(n-1))

Combine like terms

27 = n*(5- .25(n-1))

Distribute inside the parentheses

27 = n(5-.25n +.25)

Combine like terms

27 = n(5.25-.25n)

Distribute

27 = 5.25n - .25n^2

Subtract 27 on each side

27-27 = 5.25 n - .25 n^2 -27

0 = 5.25 n - .25 n^2 -27

Multiply by -4 so that the coefficient on the x^2 term is 1

0 =-21n +n^2 +108

Rewrite in standard order

0= n^2 -21n +108

Factor

0=(n-9) (n-12)

Using the zero product property

n = 9 and n=12

It Sums to 13.5 twice

When n= 9 and when n=12

Check:

a1 =2.5 a2 =2.25, a3 = 2 a4 = 1.75 a5 = 1.5 a6 = 1.25 a7 = 1 a8=.75

a9 = .5 a10 =.25 a11 =0 a12 = -.25