Angle E=130degrees because those two are congruent. Therefore if you 180-130 you'll get the other angle in the triangle with 70degrees and y. 180-130=50degrees. Then add 50 and 70. 50+70=120degrees. A triangle is supposed to have 180 degrees inside.
180-120=60degrees.
Therefore y=60degrees
Answer:
(a) $ 1.60
(b) $ 0.96
Step-by-step explanation:
(a) Cost of printing 2000 posters = Cost of first thousand + cost of second thousand = 1500 + 1200 = 2700
Total cost = 2700 + 500 = 3200
Average Total Cost = Total cost/Number of posters = 3200/2000 = $ 1.60
(b) Cost of printing 10000 posters = Cost of first thousand + cost of second thousand + (800 × Number of additional thousands)
Number of additional thousands = (10000 - 1000 - 1000)/1000 = 8000/1000 = 8
Cost of printing 2000 posters = 1500 + 1200 + (800 × 8) = 2700 + 6400 = 9100
Total cost = 9100 + 500 = 9600
Average Total Cost = Total cost/Number of posters = 9600/10000 = $ 0.96
1. Find the equation of tangent line at point (2,20).
![y'=(5x^2)'=5\cdot 2x=10x,\\ \\y'(2)=10\cdot 2=20.](https://tex.z-dn.net/?f=y%27%3D%285x%5E2%29%27%3D5%5Ccdot%202x%3D10x%2C%5C%5C%20%5C%5Cy%27%282%29%3D10%5Ccdot%202%3D20.)
The equation of the tangent line is
![y=20(x-2)+20,\\ \\y=20x-20.](https://tex.z-dn.net/?f=y%3D20%28x-2%29%2B20%2C%5C%5C%20%5C%5Cy%3D20x-20.)
2. Express x:
![y=20x-20\Rightarrow x=\dfrac{y}{20}+1;\\ \\y=5x^2\Rightarrow x=\sqrt{\dfrac{y}{5}}.](https://tex.z-dn.net/?f=y%3D20x-20%5CRightarrow%20x%3D%5Cdfrac%7By%7D%7B20%7D%2B1%3B%5C%5C%20%5C%5Cy%3D5x%5E2%5CRightarrow%20x%3D%5Csqrt%7B%5Cdfrac%7By%7D%7B5%7D%7D.)
3. Find the area of bounded region:
![A=\int\limits^{20}_0 {\left(\dfrac{y}{20}+1-\sqrt{\dfrac{y}{5}} } \right)\, dy=\left(\dfrac{y^2}{40}+y-\dfrac{2\sqrt{y^3} }{3\sqrt{5} } \right)\big|^{20}_0=](https://tex.z-dn.net/?f=A%3D%5Cint%5Climits%5E%7B20%7D_0%20%7B%5Cleft%28%5Cdfrac%7By%7D%7B20%7D%2B1-%5Csqrt%7B%5Cdfrac%7By%7D%7B5%7D%7D%20%7D%20%5Cright%29%5C%2C%20dy%3D%5Cleft%28%5Cdfrac%7By%5E2%7D%7B40%7D%2By-%5Cdfrac%7B2%5Csqrt%7By%5E3%7D%20%7D%7B3%5Csqrt%7B5%7D%20%7D%20%5Cright%29%5Cbig%7C%5E%7B20%7D_0%3D)
![=\dfrac{400}{40}+20-\dfrac{2\sqrt{20^3} }{3\sqrt{5} }=30-\dfrac{80}{3}=\dfrac{10}{3}\ sq. un.](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B400%7D%7B40%7D%2B20-%5Cdfrac%7B2%5Csqrt%7B20%5E3%7D%20%7D%7B3%5Csqrt%7B5%7D%20%7D%3D30-%5Cdfrac%7B80%7D%7B3%7D%3D%5Cdfrac%7B10%7D%7B3%7D%5C%20sq.%20un.)
Answer: ![\dfrac{10}{3}\ sq. un.](https://tex.z-dn.net/?f=%5Cdfrac%7B10%7D%7B3%7D%5C%20sq.%20un.)
Answer:110.9
Step-by-step explanation:
- 1031.60/9.30
- Divide
- Answer: 110.9