(-1)(*+1) + 1 -sin L NAX sinh (nxy/L) 0(x, y) = Σ n sinh (naW/L) n=1 Using this expression, calculate the temperature at the point (x,y) = (0.75, 0.5) by considering the first five nonzero terms of the infinite series that must be evaluated. Assume that L = 1.5 m. iM:

A 10-cm copper wire with one end in an ice bath is heated at the other end, so that the temperature at each point x along the wire (in degrees Celsius) is given by T (x) = 50 cos πx 20 . Find the average temperature over the wire.

A cylindrical tank has a radius of 8 ft and a height of 10ft. Both dimensions are measured with a maximum possible error of +0.05 ft. a. Use the total differential to estimate the maximum possible error in calculated volume. (Hint: The formula for the volume of the cylindrical tank is V = Tr?h , where the total differential requires the product rule, resulting in dv = "(r*dh + 2rhdr) .) dV = ft3 2. Compute the actual maximum possible error in the calculated volume. AV = |ft3

Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 µm (mg/m³): 90 177 180 354 365 442 964 y 0.38 0.60 0.47 0.66 0.62 0.69 0.91 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? shows a reasonable linear relationship. O No, a scatter plot does not show a reasonable linear relationship. (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.) (c) The investigators were particularly interested in…

Calc 3: The dimensions of a closed rectangular box are measured as 89 cm, 52 cm, and 31 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.

Find the temperature distribution u(x, t) in a laterally insulated bar Of 80 cm long if the initial temperature is 100 Sin 80 C and the ends are kept at 0°C. How long will it take for the maximum temperature in the bar to drop 50°C given that p = 8.92 gm cm-3, 0.95 cal cm-1 sec° C. S = 0.092 calgm-1°C and thermal conductivity k =

formi RON a+bT+cT'+dT' +eT* (2) Where RON is the clear research octane number and T (Tb-273.15)/100 in which Tb is the boiling point in kelvin. Based on the data taken from the API-TDB, the coefficients a- e were determined and are given in Table below: Coefficients of eq. 2 for estimation of RON Hydrocarbon family n-Paraffins isoparaffins 2-Methyl-pentanes 3-Methyl-pentanes 2,2-Dimethyl-pentanes 2,3-Dimethyl-pentanes Naphthenes Aromatics 92.809 -70.97 -53 20 10 -600 200 95.927 92.069 109.38 97.652 -77.536 145.668 -157.53 57.63 -38.83 -20.8 471.59 -54.336 561 -65 -26 58 -418 16.276 0. 100 -200 100 0. Example: A naphtha sample from an Australian crude oil has the following characteristics: boiling point range 15.5 70 C specific gravity 0.6501, n-paraffins 49.33%, isoparaffins 41.45%, naphthenes IP 9.14%, aromatics 0.08%, clear RON 69.6, and MON 66.2. a) Estimate RON from the pseudo component method using experimental composition Apply how to get (RON) for each co mpound and explain the…

Q1/ Use the chain rule to find and du when z = tan- X = u cos V, dv y = u sin v at point (u, v)=(1.3, n/6). Q2/ Consider a closed rectangular box with a square base as shown in the accompanying figure. If x is measured with error at most 2% and y is measured with error at most 3%, use a differential to estimate the corresponding percentage error in computing the box's (volume) y Q3/ Find the area of the region common to the interiors of the cardioids r = 1 + cos0 and r = 1 - cose. Q4/ Evaluate SS, xy dx dy where R is the region bounded by the x-axis, ordinate at x 2a and x2 = 4ay a²+y2 Q5/ Evaluate AN y/x? + y2 dxdy by changing into polar form Q6/ Find all the local maxima, local minima, and saddle points of the function f(x, y) = ex²+y²-4x %3D

Calculate the average rate of change of f(x) = 4x²-3x+5 on the interval [1, 4]. O a.) 21 b.) 31.5 c.) 1 O 17 O d.) 17 SUBMIT MY ANSWER 70°F Mostly sunny OL V

Do just part f urgent solution required