answer:* Cevian: y = frac{sin left(frac{4 pi }{45}right)}{cos left(frac{4 pi }{45}right)} x * Symmedian: y = -frac{cos left(frac{11 pi }{45}right)}{sin left(frac{11 pi }{45}right)} x + frac{4 sin left(frac{11 pi }{45}right)}{sin left(frac{11 pi }{45}right) - 2 cos left(frac{7 pi }{45}right)} * Median: y = frac{sin left(frac{4 pi }{45}right)}{cos left(frac{4 pi }{45}right)} x * Altitude: y = frac{sin left(frac{8 pi }{45}right)}{cos left(frac{4 pi }{45}right)} x + frac{4 sin left(frac{4 pi }{45}right)}{cos left(frac{4 pi }{45}right)}

answer:To find the sum of these two polynomials, we will expand each polynomial and then combine like terms. 1. Expand p(x): begin{align*} p(x) &= -frac{8}{3sqrt{3}} left(27x^3 - 108x^2 + 144x - 64right) &= -24sqrt{3}x^3 + 96sqrt{3}x^2 - 128sqrt{3}x + frac{64}{3sqrt{3}} end{align*} 2. Expand q(x): begin{align*} q(x) &= frac{16}{9} left(16x^4 + 64x^3 + 112x^2 + 392x + 2401right) &= frac{256x^4}{9} + frac{1024x^3}{9} + frac{1792x^2}{9} + frac{6272x}{9} + frac{38416}{9} end{align*} 3. Add p(x) and q(x): begin{align*} p(x) + q(x) &= left(-24sqrt{3}x^3 + frac{256x^4}{9}right) + left(96sqrt{3}x^2 + frac{1024x^3}{9}right) &quad + left(-128sqrt{3}x + frac{1792x^2}{9}right) + left(frac{64}{3sqrt{3}} + frac{6272x}{9}right) + left(frac{64}{3sqrt{3}} + frac{38416}{9}right) &= frac{256x^4}{9} - 24sqrt{3}x^3 + frac{1024x^3}{9} + 96sqrt{3}x^2 + frac{1792x^2}{9} - 128sqrt{3}x &quad + frac{64}{3sqrt{3}} + frac{64}{3sqrt{3}} + frac{6272x}{9} + frac{38416}{9} &= frac{256x^4}{9} - frac{144x^3}{9} + frac{2784x^2}{9} + frac{6272x}{9} + frac{128}{3sqrt{3}} + frac{38416}{9} &= frac{256x^4}{9} - frac{16x^3}{3} + frac{928x^2}{3} + frac{6272x}{9} + frac{128}{3sqrt{3}} + frac{38416}{9} end{align*} So, the sum of the two polynomials is: p(x) + q(x) = frac{256x^4}{9} - frac{16x^3}{3} + frac{928x^2}{3} + frac{6272x}{9} + frac{128}{3sqrt{3}} + frac{38416}{9}

answer:1. First, we need to find the largest and smallest numbers in the set. 2. The largest number is 0, and the smallest number is -10. 3. The range is then calculated as the difference between the largest and smallest numbers: 0 - (-10) = 10. 4. Therefore, the range of the given set of numbers is 10. The range of the given set of numbers is 10.

answer:Pope Urban II spread the message of the Clermont speech through a combination of strategies: 1. **Synod Gathering:** Before delivering the speech, Pope Urban II summoned a mixed synod of ecclesiastics and laypeople to Clermont. This gathering provided a platform for him to address a diverse audience and disseminate his message. 2. **Scheduled Meeting:** The meeting was scheduled for the eleventh month of 1095 and lasted for ten days, from the 17th day of the month. This extended duration allowed for thorough discussions and ensured that the message reached a wider audience. 3. **Call to Arms:** During the Clermont speech, Pope Urban II issued a call to arms, urging Christians to join the First Crusade. This call for military action was a central part of the speech and resonated with many listeners. 4. **Response to Byzantine Emperor:** Pope Urban II also addressed the request for military assistance from the Byzantine emperor. By acknowledging and responding to this request, he demonstrated his commitment to supporting fellow Christians in need. 5. **Cluniac Reforms:** Additionally, Pope Urban II mentioned the Cluniac reforms of the Church, highlighting the importance of spiritual renewal and moral conduct. This aspect of the speech emphasized the broader context of the Crusades as a religious movement. Through these strategies, Pope Urban II effectively spread the message of the Clermont speech, inspiring many to join the First Crusade and shaping the course of European history.