<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
