Prove that f(x) = (x – 1)² + (x + 1)² is an even function.
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- A higher-order differential equation given as y" + p(x)y' g (x)y = O is a homogenous equation, even if p(x) = 0. A higher-order differential equation given as y" + p(x)y' + q(x)y = 0 is also a homogenous equation, even if g(x) = 0. O Only first statement is true. O Only second statement is true. O Both first and second statements are true. O Both first and second statements are false.In Figure , the radial distribution function P(r) for the 2s state of hydrogen has two maxima. Find the values of r (in terms of a0) where these maxima occur.For irreversible adiabatic expansion or compression of an ideal gas, work is equal to the internal energy change. Select one: True False
- For the statements in them, put T if they are true and F if they are false. b) ( ) An ideal diatomic gas loses energy in the form of heat Q. Since cp > cv, we can state that the gas loses less internal energy if the process is at constant volume thanin a process under constant pressure.c) ( ) Two gases A and B, of equal mass, are at the same temperature. the molar mass of gas A is greater than the molar mass of gas B. In this case, it is correct to state that the energy internal gas B is greater than that of gas A.d) ( ) For a diatomic gas with molecular rotation cv = (5/2)R and cp = (7/2)R. for highs At temperatures the atoms of the gas molecules begin to vibrate. In this case, it is correct to state that for high temperatures we can have cv = 3R and cp = 4R for gas.e) ( ) In the diagram below, the ideal gas performs 5 J of work along the isotherm ab and 4 J along the adiabatic line bc. In this case, we can say that the variation of energy internal gas along the straight path ac is…Which of the following is a scalar quantity A) electric current B) electric field C) Acceleration D) linear momentumThe marketing research department of a large manufacturing company has determined that the demand equations for two major items it produces are given by p = 2,000 - 5x + 8y and q = 4,000+ 9x - 7y where p is the price of item A. is the price of item B , x is the monthly demand for item A , and y is the monthly demand for item B. Find the total monthly revenue from items A and B when x = 15 and y = 5 .
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