Question Solved1 Answer The function 𝑠(𝑡)=9−15𝑡+8𝑡2 describes the distance 𝑠 from the origin at time 𝑡 of an object in rectilinear motion. Find the velocity 𝑣 of the object at any time 𝑡. The function s(t) = 9 – 15t + 8t² describes the distance s from the origin at time t of an object in rectilinear motion. Find the velocity v of the object at any time t. (Use symbolic notation and fractions where needed.) v(t) = When is the object at rest? (Use symbolic notation and fractions where needed.) t =

Use the graph of f' to identify the critical numbers of f, identify the open interval (s) on which fis increasing or decreasing, and determine whether fhas a relative maximum, a relative minimum, or neither at each critical number. (If an answer does not exist, enter DNE.) (a) (i) Identify the critical numbers of f. (Enter your answers as a comma-separated list.) 2 X (i Identify the open interval(s) on which fis increasing or decreasing. (Enter your answer using interval notation.) (2, oo) increasing (-oo, 2) decreasing X (ii Determine whether fhass a relative maximum, a relative minimum, or neither at each critical number. (Enter your answers as a comma-separated list.) relative minimum X relative maximum 2 X (Ь () Identify the critical numbers of f. (Enter your answers as a comma-separated list.) x = X (ii) Identify the open interval(s) on which fis increasing or decreasing. (Enter your answer using interval notation.) increasing X decreasing X (iii Determine whether fhas a relative maximum, a relative minimum, or neither at each critical number. (Enter your answers as a comma-separated list.) relative minimum х 3 relative maximum х 3 X (c) (i) Identify the critical numbers of f. (Enter your answers as a comma-separated list.) X = X (ii) Identify the open interval(s) on which fis increasing or decreasing. (Enter your answer using interval notation.) increasing X decreasing X (iii) Determine whether fhas a relative maximum, a relative minimum, or neither at each critical number. (Enter your answers as a comma-separated list.) relative minimum х 3 X relative maximum X

Find the elevation h (km) where the weight of an object one-tenth its weight on the surface of the earth.

5. Justify your answers to the following with calculations. [8] a) You were driving at a speed of 75 miles per hour and you were pulled over by the police for going over the speed limit of 100 km/h. How many km/h over the speed limit were you driving? b) A T-bone steak sells for $4.99/1b at store A and for $10/kg at store B. Which price is the better buy? c) 5. Justify your answers to the following with calculations. [8] a) You were driving at a speed of 75 miles per hour and you were pulled over by the police for going over the speed limit of 100 km/h. How many km/h over the speed limit were you driving? b) A T-bone steak sells for $4.99/1b at store A and for $10/kg at store B. Which price is the better buy? c) A can of paint states that it will cover 40 m². Is one can enough to paint walls with a total area of 500 ftº? d) An advertisement states that a car's fuel consumption is 35 mpg. What is this fuel consumption in litres per 100 km?

please answer the following, thank you **Show ALL of your work. 1. Solve the following inequalities using an algebraic method. ✓✓ & ✓✓✓ a) x(x + 2)(x-2)(x + 3) ≥ 0 b) x²-2x-15 x²-16 20 for a function with a vertical asymptote at x = -2 and a kx-c 2. Determine an equation in the form f(x)=; y-intercept of✔✔ 3. Prove that sin (x+) = cos x is an identity. ✔✔

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.

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)