course Phy 201 I have not yet received the lab materials. I ordered them Wed and am hoping to receive today to do the labs over the weekend, but should it not come today how should I proceed? Thanks.
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12:30:59 `q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4).
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RESPONSE --> x - 2 / x + 4 would be read as: A quantity, x, minus two over x, plus 4.Since there are no parenthesis x is the first quantity, 2/x is the second quantity, and 4 is the last quantity. (x - 2) / (x + 4) would be read as: The quantity, x - 2 is divided by the quantity x + 4.
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12:34:30 The 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 2 or divide the -2 by 4 first. If there are no parentheses you have to divide before you subtract: 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) / ( 4 - 2) = 0 / 2 = 0.
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RESPONSE --> The order of operations would determine that for the equation, x - 2 / x + 4, the quantity 2/x would be the first operation. For (x-2) / (x+4), the quantities in parentheses would be determined before division is carried out. The absence or presence of parentheses make a considerable difference in the answer.
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12:38:49 `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.
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RESPONSE --> Once again, parentheses make a difference in the order of operations. 2^x + 4 would be solved in this way if x = 2: 2^2 + 4 = 4 + 4 = 8 Since there is no parenthesis, we would carry out the exponential function before the addition. 2^(x+4) would be solved this way if x = 2: 2^(2+4) = 2^6 = 64 Since parentheses are present, we would do the addition within them before the exponential function.
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12:39:07 2 ^ 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.
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RESPONSE --> I answered this problem correctly.
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12:45:09 `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?
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RESPONSE --> The numerator is 3. The denominator is [(2x-5)^2 * 3x + 1]. If x = 2: 2 - 3/[(2*2-5)^2 * 3(2) +1] - 2 +7(2) = 2 - 3/7 - 2+14 = 13.57
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12:45:55 The numerator is 3. x isn't part of the fraction. / indicates division, which must always precede subtraction. Only the 3 is divided by [ (2x-5)^2 * 3x + 1 ] and only [ (2x-5)^2 * 3x + 1 ] divides 3. If we mean (x - 3) / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x we have to write it that way. The preceding comments show that the denominator is [ (2x-5)^2 * 3x + 1 ] Evaluating the expression for x = 2: - 3 / [ (2 * 2 - 5)^2 * 3(2) + 1 ] - 2 + 7*2 = 2 - 3 / [ (4 - 5)^2 * 6 + 1 ] - 2 + 14 = evaluate in parenthese; do multiplications outside parentheses 2 - 3 / [ (-1)^2 * 6 + 1 ] -2 + 14 = add inside parentheses 2 - 3 / [ 1 * 6 + 1 ] - 2 + 14 = exponentiate in bracketed term; 2 - 3 / 7 - 2 + 14 = evaluate in brackets 13 4/7 or 95/7 or about 13.57 add and subtract in order. The details of the calculation 2 - 3 / 7 - 2 + 14: Since multiplication precedes addition or subtraction the 3/7 must be done first, making 3/7 a fraction. Changing the order of the terms we have 2 - 2 + 14 - 3 / 7 = 14 - 3/7 = 98/7 - 3/7 = 95/7.
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RESPONSE --> I answered this problem correctly
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12:59:21 `q004. Explain, step by step, how you evaluate the expression (x - 5) ^ 2x-1 + 3 / x-2 for x = 4.
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RESPONSE --> When x = 4 we solve the equation (x-5)^2x -1+3/x-2 this way: First values within parenthesis must be done: (x - 5)^2x -1+3/x-2 = (4 - 5)^2x-1+3/x-2=(1)^2x-1+3/x-2 Then exponential functions must be completed: 1^2x -1+3/x-2 = 1^(2) x -1+3/x-2 = 1^ 2 x-1+3/x-2 = 1 x-1+ 3/x-2 Next, division or multiplication functions must be done: 1* x-1+ 3/x - 2 = x-1 + 3/4 - 2 = x-1 + 0.75 - 2 Then addition and subtraction can be completed from left to right: 4 -1 + 0.75 - 2 = 3.75 - 2 = 1.75
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13:04:17 We get (4-5)^2 * 4 - 1 + 3 / 1 - 4 = (-1)^2 * 4 - 1 + 3 / 4 - 2 evaluating the term in parentheses = 1 * 4 - 1 + 3 / 4 - 2 exponentiating (2 is the exponent, which is applied to -1 rather than multiplying the 2 by 4 = 4 - 1 + 3/4 - 2 noting that 3/4 is a fraction and adding and subtracting in order we get = 1 3/4 = 7 /4 (Note that we could group the expression as 4 - 1 - 2 + 3/4 = 1 + 3/4 = 1 3/4 = 7/4). COMMON ERROR: (4 - 5) ^ 2*4 - 1 + 3 / 4 - 2 = -1 ^ 2*4 - 1 + 3 / 4-2 = -1 ^ 8 -1 + 3 / 4 - 2. INSTRUCTOR COMMENTS: There are two errors here. In the second step you can't multiply 2 * 4 because you have (-1)^2, which must be done first. Exponentiation precedes multiplication. Also it isn't quite correct to write -1^2*4 at the beginning of the second step. If you were supposed to multiply 2 * 4 the expression would be (-1)^(2 * 4). Note also that the -1 needs to be grouped because the entire expression (-1) is taken to the power. -1^8 would be -1 because you would raise 1 to the power 8 before applying the - sign, which is effectively a multiplication by -1.
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RESPONSE --> I answered this problem correctly.
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