this is for math please answer ASAP ONLY ANSWER NO EXPLANTION. THANK YOU

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Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. |n(a) |n(b) = |n(a b) for all positive real numbers a and b. 0 True. Take a = 4 and b = 2. Then |n(a) |n(b) = |n(4) |n(2) = |n(g) = |n(2). And |n(a b) = |n(4 2} = |n(2). 0 True. This is one of the Laws of Logarithms. 0 False. |n(a b) = |n(a) |n(b} only for negative real numbers a and b. 0 False. |n(a b) = |n(a) |n(b} only for positive real numbers a > b. 0 False. Take a = 2 and b = 1. Then |n(a) |n(b) = |n(2} |n(1) = |n(2} 0 = |n(2). But |n(a b) = |n(2 1) = |n(1) = O. Revenue. Suppose the graph of the revenue R(X) and cost C(X) are shown below where R(x) = X22x+2 and C00 = x2 + 0.5 The profit, or the area enclosed between the two curves is Note: Round to 4 digits after the decimai point, if rounding is required 0 -2.6667 0 4.6667 0 2.6667 0 o 0 none of the other answers 0 4.5 O -4.5 0 -4.6667 Let f(t) = 2t3 + 27:2 84f + 120 The interval where f(t) is increasing is O (m,2) U (7, so) 0 (0, '30) 0 none of the other answers 0 (2. 7) Object Height. Suppose an object is thrown straight up from the ground. The height after 1' seconds is given by the formul h(t} = 5t3 + 90:2 + 192 (a) The time in seconds when the object reached the highest point was Note: Round to 4 digits after the decima.i point, if rounding is required 0 9 s O 27 s 0 None of the other answers Q 0 s O 192 s O 12 s (b) The height is maximized at the critical point X = 3 because the second derivative test found 0 f'(a) was negative to the left of X = a and positive to the right 0 f"(a) > 0 O f'(a) was positive to the left ofx = a and negative to the right 0 f'(a) = 0 O f"(a)