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- i) Compute the value of X in Table 2. ii) Estimate mass that dissolved in the water if the temperature is set at 100 Celcius.If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at what rate does the cube’s a. surface area change? b. volume change?About how accurately must the interior diameter of a 10-m-high cylindrical storage tank be measured to calculate the tank’s volume to within 1% of its true value?
- A mass of 1 kgkg is attached to the end of a spring whose restoring force is 180 NmNm. The mass is in a medium that exerts a viscous resistance of 156 NN when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object. Suppose the spring is stretched 0.07 mm beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 7sin(3t)7sin(3t) NN at time tt seconds. Find an function to express the steady-state component of the object's displacement from the spring's natural position, in mm after tt seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.)a. About how accurately must the interior diameter of a 10-m-high cylindrical storage tank be measured to calculate the tank’s volume to within 1% of its true value? b. About how accurately must the tank’s exterior diameter be measured to calculate the amount of paint it will take to paint the side of the tank to within 5% of the true amount?The edges of a cube are found to be 10cm with an error ± 0.03cm The volume of the cube is then estimated to be 1000 cubic cm. Use differentials to estimate the maxiumum error on this estimate of the volume.
- A patient with hypokalemia has orders for potassium 60 mEq in 250 ml of d5w. The institution’s policy states to infuse over 3 hours. How many milliliters per hour should the IV pump be programmed forA substance evaporates at a rate proportional to the exposed surface. If a sphericalmothball of radius 1/2 cm has radius 0.4 cm after 6 months, how long will it take:(a) For the radius to be 1/4 cm?(b) For the volume of the mothball to be half of what it was originally?A toxic radioactive substance with a density of 9 milligrams per square cm is detected in the ventilating ducts of a nuclear processing plant that was used 55 years ago. If the half life is 20 years, what was the density of the substance when it was depoited 55 years ago?
- 5. A company wants to manufacture cylindrical aluminum cans with a volume of 1000 cm^3. Determine the radius and height of the can that will minimize the amount of aluminum used. Decimals to one decimal place are permitted.If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what rate does the cube’s surface area change?A mass of 1.75 kg is attached to the end of a spring whose restoring force is 100 N/m. The mass is in a medium that exerts a viscous resistance of 15 N when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object.Suppose the spring is stretched 0.03 mm beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 3sin(2t) NN at time tt seconds.Find an function to express the steady-state component of the object's displacement from the spring's natural position, in mm after tt seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.) Enter exact value for the constants, or 8 decimal places. u(t) =