#$&* course Phy121 Question: `q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4). Then evaluate each expression for x = 2.
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Given Solution: `aThe order of operations dictates that grouped expressions must be evaluated first, that exponentiation must be done before multiplication or division, which must be done before addition or subtraction. It makes a big difference whether you subtract the 2 from the x or divide the -2 by 4 first. If there are no parentheses you have to divide before you subtract. Substituting 2 for x we get 2 - 2 / 2 + 4 = 2 - 1 + 4 (do multiplications and divisions before additions and subtractions) = 5 (add and subtract in indicated order) If there are parentheses you evaluate the grouped expressions first: (x - 2) / (x + 4) = (2 - 2) / ( 2 + 4 ) = 0 / 6 = 0. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:4 ********************************************* Question: `q002. Explain the difference between 2 ^ x + 4 and 2 ^ (x + 4). Then evaluate each expression for x = 2. Note that a ^ b means to raise a to the b power. This process is called exponentiation, and the ^ symbol is used on most calculators, and in most computer algebra systems, to represent exponentiation. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: the first expression is to be worked from left to right, the second expression is to be worked from inside the parentheses then from left to right, causing the outcome of the problem in the parentheses to be the power of what 2 will be raised. 2^x+4 2^2+4 4+4=8 2^(x+4) 2^(2+4) 2^6=64 confidence rating #$&*: ok ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a2 ^ x + 4 indicates that you are to raise 2 to the x power before adding the 4. 2 ^ (x + 4) indicates that you are to first evaluate x + 4, then raise 2 to this power. If x = 2, then 2 ^ x + 4 = 2 ^ 2 + 4 = 2 * 2 + 4 = 4 + 4 = 8. and 2 ^ (x + 4) = 2 ^ (2 + 4) = 2 ^ 6 = 2*2*2*2*2*2 = 64. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating:4 ********************************************* Question: `q003. What is the numerator of the fraction in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x? What is the denominator? What do you get when you evaluate the expression for x = 2? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: numerator=3 denominator=7 x-3/ [(2x-5)^2*3x+1] -2+7x 2-3/ [(2*2-5)^2*3*2+1]-2+7*2 2-3/[(4-5)^2*6+1]-2+14 2-3/[(-1)^2*6+1]-2+14 2-3/[1*6+1]-2+14 2-3/7-2+14=13.57 " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q003. What is the numerator of the fraction in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x? What is the denominator? What do you get when you evaluate the expression for x = 2? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: numerator=3 denominator=7 x-3/ [(2x-5)^2*3x+1] -2+7x 2-3/ [(2*2-5)^2*3*2+1]-2+7*2 2-3/[(4-5)^2*6+1]-2+14 2-3/[(-1)^2*6+1]-2+14 2-3/[1*6+1]-2+14 2-3/7-2+14=13.57 " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&! ********************************************* Question: `q003. What is the numerator of the fraction in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x? What is the denominator? What do you get when you evaluate the expression for x = 2? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: numerator=3 denominator=7 x-3/ [(2x-5)^2*3x+1] -2+7x 2-3/ [(2*2-5)^2*3*2+1]-2+7*2 2-3/[(4-5)^2*6+1]-2+14 2-3/[(-1)^2*6+1]-2+14 2-3/[1*6+1]-2+14 2-3/7-2+14=13.57 " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!