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Which of the following are solutions to the inequality below? Select all that apply.\newline-6 > w\newlineMulti-select Choices:\newline(A) w=−4w = -4\newline(B) w=−3w = -3\newline(C) w=−6w = -6\newline(D) w=−7w = -7

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Q. Which of the following are solutions to the inequality below? Select all that apply.\newline−6>w-6 > w\newlineMulti-select Choices:\newline(A) w=−4w = -4\newline(B) w=−3w = -3\newline(C) w=−6w = -6\newline(D) w=−7w = -7
  1. Understand the inequality: Understand the inequality.\newlineThe inequality –6 > w means that we are looking for values of ww that are less than −6-6.
  2. Test choice (A): Test choice (A) w=−4w = -4.\newlinePlug in w=−4w = -4 into the inequality -6 > w.\newline-6 > -4\newlineThis is not true because −4-4 is greater than −6-6.
  3. Test choice (B): Test choice (B) w=−3w = -3.\newlinePlug in w=−3w = -3 into the inequality -6 > w.\newline-6 > -3\newlineThis is not true because −3-3 is greater than −6-6.
  4. Test choice (C): Test choice (C) w=−6w = -6. Plug in w=−6w = -6 into the inequality -6 > w. -6 > -6 This is not true because −6-6 is not greater than −6-6; they are equal.
  5. Test choice (D): Test choice (D) w=−7w = -7. Plug in w=−7w = -7 into the inequality -6 > w. -6 > -7 This is true because −7-7 is less than −6-6.

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Posted 10 months ago

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Posted 9 months ago

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Let f(x)=cos⁡(π⋅x)3 f(x)=\sqrt[3]{\cos (\pi \cdot x)} .\newlineBelow is Issac's attempt to write a formal justification for the fact that the equation f(x)=0.1 f(x)=0.1 has a solution where 1.5≤x≤2 1.5 \leq x \leq 2 .\newlineIs Issac's justification complete? If not, why?\newlineIssac's justification:\newlinef(1.5)=0 and f(2)=1, so f(1.5)<0.1<f(2). \begin{array}{l} f(1.5)=0 \text { and } \\ f(2)=1 \text {, so } \\ f(1.5)<0.1<f(2) . \end{array} \newlineSo, according to the intermediate value theorem, f(x)=0.1 f(x)=0.1 must have a solution when x x is between x=1.5 x=1.5 and x=2 x=2 .\newlineChoose 11 answer:\newline(A) Yes, Issac's justification is complete.\newline(B) No, Issac didn't establish that 00.11 is between f(1.5) f(1.5) and f(2) f(2) .\newline(C) No, Issac didn't establish that f f is continuous.
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Posted 9 months ago

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Posted 9 months ago

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Posted 9 months ago

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Posted 9 months ago

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Posted 9 months ago

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Let f(x)=x+x3 f(x)=\sqrt{x+\sqrt{x^{3}}} .\newlineBelow is Lena's attempt to write a formal justification for the fact that the equation f′(x)=23 f^{\prime}(x)=\frac{2}{3} has a solution where 0<x<9 0<x<9 .\newlineIs Lena's justification complete? If not, why?\newlineLena's justification:\newlinef(0)=0 f(0)=0 and f(9)=6 f(9)=6 , so the average rate of change of f f over the interval 0≤x≤9 0 \leq x \leq 9 is 23 \frac{2}{3} .\newlineSo, according to the mean value theorem, f′(x)=23 f^{\prime}(x)=\frac{2}{3} must have a solution somewhere in the interval 0<x<9 0<x<9 .\newlineChoose 11 answer:\newline(A) Yes, Lena's justification is complete.\newline(B) No, Lena didn't establish that the average rate of change of f f over[0,9] [0,9] is equal to 23 \frac{2}{3} .\newline(C) No, Lena didn't establish that f f is differentiable.
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