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question:Find all real solutions to the equation frac{log (x-22)}{log (8)}+frac{log (5-14 x)}{log (8)}=frac{log (13 x+2)}{log (8)}.
answer:Given equation: frac{log (x-22)}{log (8)}+frac{log (5-14 x)}{log (8)}=frac{log (13 x+2)}{log (8)} Simplify the equation by dividing both sides by log (8): frac{log (x-22)}{log (8)}+frac{log (5-14 x)}{log (8)}=frac{log (13 x+2)}{log (8)} Rightarrow log (x-22)+log (5-14 x)=log (13 x+2) Rightarrow log [(x-22)(5-14 x)]=log (13 x+2) Rightarrow (x-22)(5-14 x)=13 x+2 Rightarrow 5x-14x^2-110+28x=13x+2 Rightarrow -14x^2+33x-112=0 Rightarrow 14x^2-33x+112=0 Rightarrow (7x-16)(2x-7)=0 Rightarrow x=frac{16}{7}, x=frac{7}{2} However, x=frac{7}{2} does not satisfy the original equation, so we discard it. Therefore, the only real solution is x=frac{16}{7}. The answer is left{xto frac{1}{7} left(75-sqrt{5233}right)right},left{xto frac{1}{7} left(75+sqrt{5233}right)right}.
question:What is the term used to describe the surface where two blocks of the earth suddenly slip past one another during an earthquake?
answer:The correct term is A) fault.
question:As the number of carbon atoms in an alkane increases, its number of isomers increases dramatically. Which statement correctly explains this fact?
answer:Alkanes are hydrocarbons that consist of carbon and hydrogen atoms, with all carbon atoms bonded to each other by single bonds. As the number of carbon atoms in an alkane increases, the number of possible isomers also increases. This is because the carbon atoms can form different arrangements, or branches, off of the main carbon chain. For example, butane (C4H10) has two isomers: n-butane and isobutane. N-butane has a straight chain of four carbon atoms, while isobutane has a branched chain with three carbon atoms in a row and one carbon atom branching off. As the number of carbon atoms increases, the number of possible branches also increases, leading to a dramatic increase in the number of isomers. C) The bonding between carbon atoms allows for branches in carbon chains.
question:Calculate the mass of hydrogen chloride required to produce 5.00 L of chlorine gas at 25 degrees C and 1.05 atm, assuming the reaction proceeds according to the given equation: {eq}H_{2}+Cl_{2}to 2HCl {/eq}
answer:We can use the ideal gas law to find the number of moles of chlorine gas: {eq}n_{Cl_2} = frac{PV}{RT} = frac{(1.05 atm)(5.00 L)}{(0.0821 L atm/mol K)(298 K)} = 0.214 mol {/eq} From the balanced chemical equation, we know that 2 moles of HCl are required to produce 1 mole of Cl<sub>2</sub>. Therefore, we need: {eq}n_{HCl} = 2n_{Cl_2} = 2(0.214 mol) = 0.428 mol {/eq} Finally, we can convert moles of HCl to grams using its molar mass: {eq}m_{HCl} = n_{HCl} cdot MW_{HCl} = (0.428 mol)(36.46 g/mol) = boxed{15.6 g} {/eq}