A 14-gauge copper wire that is 40 centimeters long is being used to form a rectangle with a width that is 3 times the length. How long are the sides of the rectangle?
First identify the equations you'll need and fill in the information where you can. Perimeter formula: 40= 2L + 2W Width to length ratio: W= 3L Now that you have 2 equations we can substitute in a value for 2 into the perimeter formula. 40= 2L + 2(3L) With only one variable in the equation you can solve. 40= 2L + 6L 40= 8L 5=L Plug the length back into the perimeter formula to get width. 40= 2(5) + 2W 40= 10+ 2W 30= 2W 15=W So: Length= 5cm Width= 15cm
Both Evans Pritchard and Melenovsky wrote ethnographies on “primitive” cultures to prove they are just as rational as Western culture. However, they each went about it differently, and in doing so each made a different point about other cultures. How did they differ and what were the resulting messages?
Melenovsky was saying that they are rational if you take the practices and ideas of the peoples and apply a Western lens or explanation to them. Melenovsky’s approach was still very ethnocentric by assuming the popular line of thought that rational thought is ideal. Western schools of thought are the most objective and rational. Therefore to make sense of something or prove it’s worth it must be applicable or make sense in Western/European schools of thought. Evans Pritchard followed that sentiment with the then radical idea that any people is perfectly rational by the rules of their own culture. The point of his ethnography was to say that there is no need for a Western lens to justify the worth of a people. If they don’t seem rational it is up to us to understand them from their own perspective. It is not our job to justify their lifestyle or, rank it as inferior as many before these men had done, through the logic of our own culture.
Solve the quadratic below using one of the four methods. Give your answer in simplest form. Then briefly explain why you chose that method. x² + 1 = -6x
Quadratic Formula: Move the terms to one side: x² + 6x + 1 = 0 Identify a, b, c. a=1; b=6; c=1 Plug into formula. -(6)± √((6)²-4(1)(1)) ___________ 2(1) Reduce and solve. -6±√(36-4) ___________ 2 -6±√32 ___________ 2 Because √32 isn't a whole number we must simplify this using a factor tree. 32 / \ 4 8 /\ /\ 2* 2* 4 2 /\ 2* 2* Where the branching stops pull out the pairs* and multiply, leave unpaired numbers under the √ and simplify. -6±(2)(2)√2 ___________ 2 -6±4√2 ___________ 2 Answer: x= -3±2√2 Explanation: The terms could not be factored or grouped. The quadratic formula or factor by grouping would work. I chose the quadratic formula because it works for all quadratics. Factor by grouping: Move the terms to one side: x² + 6x + 1 = 0 Move term c to the other side of the equation leaving a space for the new square on BOTH sides. x² + 6x + __ = -1 + ___ To figure out the new square divide term b by 2 then square that number. b=6 6/2=3 3²=9 The new equation is: x² + 6x + 9 = -1 + 9 x² + 6x + 9 = 8 Factor with the new square: (x+3)(x+3)=8 (x+3)²=8 Solve for x. √(x+3)²=±√8 *REMEMBER* When taking the square of a number it can be positive OR negative. x+3=±√8 x= -3±√8 Answer must be in simplest form so we must use a factor tree to simplify √8. √8 / \ 2 4 / \ 2* 2* Where the branching stops pull out the pairs*, leave unpaired numbers under the √ and simplify. Answer: x= -3± 2√2 Explanation: The terms could not be factored or grouped. The quadratic formula or factor by grouping would work. I chose factor by grouping because the leading coefficient was 1, and this method is often shorter than the quadratic formula.