University:
University of Central Arkansas
Course:
MATH 1496 | Calculus I
Academic year:

2024
Views:

83

Pages:

3
Author:

Travis Ballard

Question 1 "CVP analysis is both straightforward and oversimplified. If you want realistic analysis to underpin your decisions, look beyond CVP analysis." Do you agree? Explain. Answer The CVP analysis is limited by the assumptions mentioned in the question 2 of this chapter and that makes it simplistic. One of the assumptions is that: costs will either fall under variable or fixed costs, but in reality some costs will be mixed. It also says that variable and fixed costs are known and constant which also in reality will not always be the case. Question 2 The value of the expression log 100 + log ∛10. Answer Formula used: √a = a¹/2 and log 10ˣ = x Calculation: The expression is log 100 + log ∛10. We can rewrite the expression as, log 100 + log ∛10 = log(10)² + log(10)¹/³ = (10²)² and ∛a = a¹/³ As, we know that log 10ˣ = x. log (10)² + log (10)¹/³ = 2 + 1/3 = (2*3 + 1)/3 = 7/3 Hence, the value of log 100 + log ∛10 is 7/3. Conclusion: The value of log 100 + log ∛10 is 7/3 Question 3 Represent the following function using unit step functions and find its Laplace transform. {2x², 0 < x < 2 f(x) = {x + 3, x > 2 Answer Step 1: Introduction Piecewise functions are those whose function expression varies depending on where in their domain they occur. Unit step functions are functions with values of zero for negative input and one for positive input. Step 2: Computation Piecewise function f(x) = {f1(x), 0≤x< x₁ , can be written in unit step function as {f2(x), X1 ≤ x f(x) = f₁(x) + u(x-x₁) (f₂(x) -f₁(x)) So, the given function f(x) ={2x², 0 2 f(x) = 2x² + u(x-2)(x+3-2x²) Step 3:Computation Now, to find Laplace transform of given function f(x), solve the equation L(f) = L(2x²) + L[u(x-2)(x+3-2x²)]. Use the property L(u(t-a)f(t)) = e⁻ᵃˢ. L (g(t+a)) and L (tⁿ) = n!/sⁿ⁺¹ L(f) = L (2x²) + L[u(x-2)(x+3-2x²)] = 2L (x²) + L(u(x-2)(x+3-2x²)) = 2 (2!/s³) + e⁻²s L ( (x+2) + 3 - 2 (x+2)²) = 4/s³ + e⁻²s L (x+5 -2x² - 8 -8x ) = 4/s³ + e⁻²s L (-2x² - 3 - 7x) = 4/s³ + e⁻²s( -4/s³ - 3/s - 7/s²) Question 4 Fill in the missing value for the following percent frequency distribution. Annual Salaries Percent Frequency Under $30,000 10 $30,000 - 49, 999 35 $50,000 - 69,999 24 $70,000 - 89, 999 $90,000 and over 5 Answer Step 1 Percentage Frequency: A percentage frequency distribution is a display of data that specifies the percentage of observations that exist for each data point or grouping of data points. It is a particularly useful method of expressing the relative frequency of survey responses and other data. Many times, percentage frequency distributions are displayed as tables or as bar graphs or pie charts. The process of creating a percentage frequency distribution involves first identifying the total number of observations to be represented; then counting the total number of observations within each data point or grouping of data points; and then dividing the number of observations within each data point or grouping of data points by the total number of observations. The sum of all the percentages corresponding to each data is equal to 100. Step 2 Given data represents frequency distribution of annual salaries. It is stated that sum of percentage frequency is equal to 100. Let, x be the missing percent frequency. 10 + 35 + 24 + x + 5 = 100 74 + x = 100 x = 100 - 74 x = 26 Complete frequency table is shown below: Annual Salaries Percent Frequency Under $30,000 10 $30,000 - 49, 999 35 $50,000 - 69,999 24 $70,000 - 89, 999 26 $90,000 and over 5 Question 5 Calculate the value of the annuity due without a table (Do not round intermediate calculations. Round your answer to the nearest cent.) Amount of payment=3,100 Payment payable = Annually Years = 3 Interestrate=7 Valueofannuity=______ Answer Given: P=Periodic payment=3100 r=Interest rate=7%=0.07 n=Number of periods=3 The future value of an annuity is deremined using the formula: A = P [((1+r)ⁿ)-1)/r] with P the periodic payment, r the periodic interest rate and n the number of payments. A = P [((1+r)ⁿ)-1)/r] = 3100 [((1 + 0.07)³) - 1)/0.07] = 9966.19 Thus the value of the annuity is $9966.19

Various Math #60 - Q&A

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