Solve the problem. Be sure to make a diagram of the situation with all the given information labeled.
?
If a 73.0-foot flagpole casts a shadow 49.0 feet long, what is the angle of elevation of the sun (to the nearest tenth of a degree)?
?

A. 61.1°
B. 61.6°
C. 58.1°
D. 52.5°
E. 56.1°

Answer: E

Mathematics

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Use an associative property to complete the statement. Do not simplify.(8y + 3) + (-3) =  

A. (-3) + (8y + 3) B. (8y)(3 + (-3)) C. (-3)(8y + 3) D. 8y + (3 + (-3))

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Mathematics

Change the order of integration and evaluate the integral.

A. ?
B. ?
C. ?
D. ?

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Mathematics

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

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Mathematics

Solve the problem.A particular substance decays in such a way that it loses half its weight each day. How much of the substance is left after 8 days if it starts out at 64 grams?

A.  g
B. 2 g
C. 4 g
D.  g

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Mathematics