Determine the order of integration and then evaluate the integral.
A. (1 - cos 64)
B.
C. (1 - cos 64)
D.
Answer: C
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Perform the indicated operation.-5 - 8
A. -13
B. -13
C. 3
D. 40
Provide an appropriate response.(i) List the sequence of pentagonal numbers that corresponds to the sequence of dot patterns above and find two in addition to these. (ii) Complete the following list of equations suggested by the sequence of dot patterns and the pentagonal numbers you find in part (i). 1 = 1 1 + 4 = 5 1 + 4 + 7 = 12 1 + 4 + 7 + 10 = 22 _________________ = ___ _________________ = ___Observe that each pentagonal number is the sum of an arithmetic progression.(iii) Compute the eleventh term in the arithmetic progression 1, 4, 7, 10, ... .(iv) Compute the eleventh pentagonal number.(v) Determine a
formula for nth term in the arithmetic progression 1, 4, 7, 10, ... .(vi) Determine a formula for the nth pentagonal number pn. A. 1, 5, 7, 9, 11, 13, ... (ii) 1 + 3 + 5 + 7 + 9 = 25 1 + 3 + 5 + 7 + 9 + 11 = 36 (iii) Eleventh term: 1 + 3(11) = 34 (iv) Eleventh pentagonal number: 182 (v) nth term: 1 + 3(n) or 3n + 1 (vi) pn = 3n(n)/2 B. 1, 6, 18, 40, 76, 128, ... (ii) 1 + 4 + 7 + 10 + 13 = 35 1 + 4 + 7 + 10 + 13 + 16 = 51 (iii) Eleventh term: 3(10)- 1= 29 (iv) Eleventh pentagonal number: 220 (v) nth term: 1 + 3(n - 2) or 3n - 1 (vi) pn = 2n(n - 1) C. (i) 1, 5, 12, 22, 35, 51, ... (ii) 1 + 4 + 7 + 10 + 13 = 35 1 + 4 + 7 + 10 + 13 + 16 = 51 (iii) Eleventh term: 1 + 3(10) = 31 (iv) Eleventh pentagonal number: 176 (v) nth term: 1 + 3(n - 1) or 3n - 2 (vi) pn = n(3n - 1)/2 D. 1, 5, 13, 23, 36, 52, ... (ii) 1 + 4 + 7 + 10 + 13 = 35 1 + 4 + 7 + 10 + 13 + 16 = 51 (iii) Eleventh term: 1 + 3(12) = 37 (iv) Eleventh pentagonal number: 187 (v) nth term: 1 + 3(n + 1) or 3n + 4 (vi) pn = n(3n + 1)/2
Solve the problem.Use the equation to complete the table. Then use the table to list some ordered pairs that satisfy the equation.y + 4x = -9
A.
B.
C.
D.
Find the following product and express your answer in simplest radical form.
A.
B.
C.
D.
E.