Math 1155 -- Written Assignment 1 (v2) 1. Solve the following formulas for the variables indicated. Show step by step work. (6 marks) a. Q= 3P - 7N(T + W), solve for W b. 7+R o+x - Solve for xMath 1155 -- Written Assignment 1 (v2) 2. Part I (4 marks) Plot the following data with minutes on the horizontal axis and psig on the vertical axis. Label your axes and indicate the scale. Part of this challenge is making sure you can scale your graph appropriately so if you use your own graph paper it must have the same dimensions as the graph shown below. Minutes 5 10 20 35 60 Tank 152 128 93 59 38 Pressure (psig) Part II (2 marks) What kind of relationship is shown by your graph (linearon-linear) and possibly what kind of equation (exponential, sinusoidal, polynomial, hyperbolic). Part III (3 marks) Use linear interpolation to determine the pressure in the tank was at 53 minutes.Math 1155 -- Written Assignment 1 [v2} 3. [6 marks] Plot the following two equations on the same graph. Be sure to include both positive and negative values of x. Label the graph appropriately and use a scale that shows the correct level of detail. Show your work on a table ofvalues. A y : D.5x + 1.4 B 3.: = 415st + 1.4 Math 1155 -- Written Assignment 1 (v2) 4. (6 marks ) 33* 23* F 116 51' 88" 39' 98 52' 98 47 121* 45' 40 = (Show work and solution using degrees and minutes) 20 = (Show work and solution using degrees and minutes)5. Part I ( 4 marks ) A circular duct runs inside a square enclosure that is 87.0 cm on a side (the circle is inscribed in the square here). The contractor would like to cut off a corner of the enclosure just so that the new edge can sit flush with (tangent to) the duct. What is the length of AM where the square should be cut? Explain and show work. Hints: See Discussion Board for Hints. Cut corner-> 87.0 cm 87.0 cm #6 Part II: [3 marks] Now that you have found the distance AM, the contractor has decided not to cut the square but to run a pipe inside the cavity instead. What size pipe (diameter d) can fit into the triangular space you calculated? A M6. Pattern for a cone-shaped vent cap. Part A: The formula for the arclength L of a circle is L = = x 2nr. Solve this formula for 0. Show your work (2 marks): Part B. (2 marks) You need to build a cone-shaped vent cap according to the following dimensions. Note there is no base to the cone because the bottom is open. Use the diagram of the cone shown on the 14.25 in left to find the circumference of the base and the slant height s. 11.75 in circumference of base = L Part C (2 marks) The pattern for the cone. Now find the angles used on the pattern to make CD the cone for part B. Note that the circumference of the cone base becomes L on the pattern and the slant height s is the radius r of pattern's circle. Use the formula you found in part A above to find 0 and then find o. ( is NOT 90 )7. Find the missing parts: (6 marks) W Side w = 5.36 m and p = 6.78 m For each answer below, round to 3 significant digits. Include units where appropriate. t= sin 0 = 0 = sin d = = tan d =