Question Solved1 Answer Knowledge/Understanding (15 marks) 1. If ū= [1.-3,-2) and 1 = [4.–5,3] find: a) 2 - 3 121 b) u + 1-5/1 c) Find Q, where P (-7,5,-1) and PQ = 2 [31 d) Find w which is orthogonal to both ü & v [3]

A reservoir has the shape of a sphere with radius 5 m. It is filled up to 8 m with water. (i) Let x be the height in meters measured from the base of the reservoir. The weight in Newtons of a thin layer of water between X and X + Ax is approximately P (2) Ax . What is P (C) ? P (C) = Express the answer using a formula. Recall that the density of water is p= 1000 Kg/m” and the acceleration due to gravity on the earth's surface is q = 9.8 (ii) The work in Joules required to pump the thin water layer to 2 meters above the reservoir is approximately w (2) Ax . What is w (x)? w (x) = Express the answer as a formula. (iii) Using previous results, find, in Joules, the amount of work required to pump all of the water to 2 m above the reservoir. Give the numerical value with 3 significant digits. Answer: Ż Joules

The smooth surface of the vertical cam is defined in part by the curve \( r=(0.2 \cos \theta+0.3) \mathrm{m} \) (Figure 1) If the forked rod is rotating with a constant angular velocity of \( \dot{\theta}=4 \mathrm{rad} / \mathrm{s} \), determine the force the cam and the rod exert on the 1.5-kg roller when \( \theta=30^{\circ} \). The attached spring has a The smooth surface of the vertical cam is defined in part by the curve \( r=(0.2 \cos \theta+0.3) \mathrm{m} \) (Figure 1) If the forked rod is rotating with a constant angular velocity of \( \dot{\theta}=4 \mathrm{rad} / \mathrm{s} \), determine the force the cam and the rod exert on the 1.5-kg roller when \( \theta=30^{\circ} \). The attached spring has a stiffnesss \( k=30 \mathrm{~N} / \mathrm{m} \) and an unstretched length of \( 0.1 \mathrm{~m} \). Express your answers in newtons using three significant figures separated by a comma.

Flower Arrangements has just completed operations for the year ended December 31, 2024. This is the third year of operations for the company. The following data have been assembled for the business: E (Click the icon to view the assembled data.) Prepare the income statement of Flower Arrangements for the year ended December 31, 2024. (If a box is not used in the table leave the box empty; do not select a label or enter a zero.) Data Table Insurance Expense $ 4,000 Salaries Expense $ 40,000 Service Revenue 75,000 Accounts Payable 6,200 Utilities Expense 600 Office Supplies 2,000 Rent Expense 13,000 Ruth, Withdrawals 1,800 Ruth, Capital, Jan. 1, 2024 12,500 Accounts Receivable 6,000 Cash 3,800 Equipment 28,200 Owner contribution during the year 5,700 Net Income Print Done

4. In humans, the antibiotic Ceftriaxone has the mean values for the apparent volume of distribution 300 L and total clearance CL=14L/h and t1/2= 8 h. . Salmonella infection is susuceptible to Ceftriaxone at concntration above 5 ug/mL and patient gets overdosed at the levels above 80ug/L. Calculate an IV dose ad infusion rate that provides steady-state level of 30ug/mL in human. b)The doctor decides to give a dose of 12 mg and started a constatnt infusion at the same Ro calculated . Ceftriaxone is eliminated as unchanges in the urine and the drug concentrations were recorded as; Time (h.) Con. Ug/L 0 4 12 6 24 6.8 36 7.5 360 10 a) Compute the Vd for patient (10pts) b) Compute the CL (10pts)

4. In humans , the antibiotic Ceftriaxone has the mean values for the apparent volume of distribution 300 L and total clearance CL=14L/h and t1/2= 8 h. . Salmonella infection is susuceptible to Ceftriaxone at concntration above 5 ug/mL and patient gets overdosed at the levels above 80ug/L. Calculate an IV dose ad infusion rate that provides steady-state level of 30 ug/mL in human. b)The doctor decides to give a dose of 12 mg and started a constatnt infusion at the same R, calculated . Ceftriaxone is eliminated as unchanges in the urine and the drug concentrations were recorded as ; Time (h.) Con. Ug/L 0 4 12 6 24 6.8 36 7.5 360 10 a) Compute the Vd for patient (10pts) b) Compute the CL (10pts)

  please calculate both part of question thanks 4. In humans, the antibiotic Ceftriaxone has the mean values for the apparent volume of distribution \( 300 \mathrm{~L} \) and total clearance \( \mathrm{CL}=14 \mathrm{~L} / \mathrm{h} \) and \( \mathrm{t} 1 / 2=8 \mathrm{~h} \). Salmonella infection is susuceptible to Ceftriaxone at concntration above \( 5 \mathrm{ug} / \mathrm{mL} \) and patient gets overdosed at the levels above 80ug/L. Calculate an IV dose ad infusion rate that provides steady-state level of \( 30 \mathrm{ug} / \mathrm{mL} \) in human. b)The doctor decides to give a dose of \( 12 \mathrm{mg} \) and started a constatnt infusion at the same \( \mathrm{R}_{0} \) calculated. Ceftriaxone is eliminated as unchanges in the urine and the drug concentrations were recorded as ; a) Compute the Vd for patient (10pts) b) Compute the CL (10pts)