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1. The demand for a product, in dollars, is = 2000 - 0.2- 0.01x2

Find the consumer surplus when the sales level is 250.

2.1. Find the area of the region that lies inside the circle r = 3sin(x)and

outside the cardioid r = 1+ sin(x).

2.2 Find the length of the cardioid r = 1+ sin(x)


1.Find the Maclaurin series for thefunction f(x)= (x^2+ 2-x)5/2and its radiusofconvergence


Consider a population consisting of 1 2 3 4 and 5, suppose sample size of 2 are drawn from the population what is the mean, variance and standard deviation of the sampling distribution?


Earth orbits the sun once every 365.25 days.




Find the average angular speed of Earth




about the sun.




Answer in units of rad/s.

The damage threshold for the retina is 100 W/m2. This means that a damage to the retina can occur at an average intensity greater than this. The light coming from a 5.0 mW green laser has a diameter of 1.2 mm. (a) Will this laser exceed the damage threshold for the retina? (b) What are the maximum values of the electric and magnetic fields of the beam coming from this laser?


1.What is the stimulus in the feedback loop below?

2.What is the control center in the feedback loop below?

3.Mention 2 effector organs that process so that the body could return to a set point?

When body temperature drops, the hypothalamus initiates several physiological responses to increase heat production and conserve heat: Narrowing of surface blood vessels (vasoconstriction) decreases the flow of heat to the skin; shivering commences, increasing production of heat by the muscles; Adrenal glands secrete stimulatory hormones such as norepinephrine and epinephrine to increase metabolic rates and hence heat production. These effects cause body temperature to increase. When it returns to normal, the hypothalamus is no longer stimulated, and these effects cease.

(feedback mechanism)

Find the measurement of the angle of refraction

68.1 g of a titanium complex P were dissolved in water and its ligand field splitting energy was measured as 59.05 KJ. Calculate the molar mass of P if the complex absorbs a wavelength of 733nm


1.How is Gibbs free energy change determined when ΔH and ΔS are available?




2. How is free energy change in non-standard states (ΔG) related to the standard free energy change (ΔG°)?

HG is a hypothetical weak acid. given that the pH at the equivalence point for the titration between 0.073 M potassium hydroxide and 20.0ml of 0.046 M HG is 10.44 calculate the base dissociation constant of G


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