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question:Why did Freud eventually abandon hypnosis as a therapeutic technique?
answer:Freud initially embraced hypnosis as a therapeutic tool, inspired by the work of Jean-Martin Charcot. However, his enthusiasm waned due to several factors. Firstly, he encountered difficulties inducing altered states of consciousness in his patients. Secondly, he recognized that hypnosis could inadvertently introduce unwanted suggestions into the patient's mind. Thirdly, Freud believed that putting patients in a trance-like state would hinder their ability to gain awareness of their problematic symptoms, which was crucial for psychoanalysis as a depth/insight therapy. Additionally, he realized that patients could access their unconscious memories while fully conscious, eliminating the need for hypnosis. This led to the development of psychoanalytic techniques such as free association.
question:How do you solve the equation 9d^2 - 81 = 0?
answer:To solve the equation 9d^2 - 81 = 0, you can follow these steps: 1. Factor out 9 from both terms: 9(d^2 - 9) = 0 2. Factor the remaining quadratic expression: 9(d + 3)(d - 3) = 0 3. Set each factor equal to zero and solve for d: d + 3 = 0 or d - 3 = 0 d = -3 or d = 3 Therefore, the solutions to the equation 9d^2 - 81 = 0 are d = -3 and d = 3.
question:For a 2x2 matrix, what does it mean if the determinant is equal to zero?
answer:It means that the matrix does not have an inverse.
question:Calculate the mass of carbon dioxide produced when 20.0 mL of heptane burns completely, given the density of heptane as 0.6838 g/mL.
answer:We can use the same balanced chemical equation as before: {eq}displaystyle C_7H_{16} + 11O_2 to 7CO_2 + 8H_2O {/eq} From the equation, 1 mole of {eq}displaystyle C_7H_{16} {/eq} produces 7 moles of {eq}displaystyle CO_2 {/eq}. The number of moles of carbon dioxide is: {eq}displaystyle n_{CO_2} = 7n_{C_7H_{16}} {/eq} The number of moles of heptane can be calculated as before: {eq}displaystyle n_{C_7H_{16}} = frac{Vd}{MW} {/eq} where V = 20.0 mL, d = 0.6838 g/mL, and {eq}displaystyle MW_{C_7H_{16}} = 100.21 g/mol {/eq}. The mass of carbon dioxide, {eq}displaystyle m_{CO_2} {/eq}, is: {eq}displaystyle m_{CO_2} = n_{CO_2}MW_{CO_2} {/eq} where {eq}displaystyle MW_{CO_2} = 44.01 g/mol {/eq}. Substituting the expressions, we get: {eq}begin{align} displaystyle m_{CO_2} &= 7n_{C_7H_{16}}MW_{CO_2} &= 7 frac{Vd}{MW_{C_7H_{16}}}MW_{CO_2} &= 7 frac{(20.0 mL)(0.6838 g/mL)}{100.21 g/mol}times 44.01 g/mol &approx boxed{rm 26.2 g CO_2} end{align} {/eq}