Provide an appropriate response.The series of sketches below starts with an equilateral triangle having sides of length 1 (one). In the following steps, equilateral triangles are constructed by joining the midpoints of the sides of the preceding triangle. Develop a formula for the area of the nth new triangle. Use math induction to prove your answer.
What will be an ideal response?
n Proofs will vary.
Mathematics
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Solve the problem. Round your answer to the nearest tenth.A person is pulling a freight cart with a force of 49 pounds. How much work is done in moving the cart 30 feet if the cart's handle makes an angle of 34° with the ground?
A. 1218.7 ft-lb B. 82.2 ft-lb C. 822.0 ft-lb D. 1285.7 ft-lb
Mathematics
Graph the damped vibration curve for 0 ? t ? 2?.d(t) = e-t/? cos (2t)
A. 
B. 
Mathematics
Graph the hyperbola.y2 - x2 = -18
A. 
B. 
C. 
D. 
Mathematics
The radioactive substance neptunium-139 decays to 73.64% of its original amount after 24 hours. How long (to the nearest hour) would it take for 39% of the original neptunium to be present? ?
A. 83 hr B. 77 hr C. 39 hr D. 74 hr E. 68 hr
Mathematics