微積分
極限、導関数、最適化、関数挙動。
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question 6 of 10 the risk of being underinsured increases the most when…
D. a high deductible.
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8. which has a quotient of 0.6? a 0.204 ÷ 0.034 b 0.204 ÷ 0.34 c 2.04 ÷…
B. \(0.204\div0.34\) ### Question 9 #### Part A
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in exercises 14–22, simplify the expression. 14. \\(\\frac{3}{\\sqrt{3}…
\(\sqrt{3}\)
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1. evaluate |2t - 3| + 9, if t = -2. a. 2 b. 9 c. 16 d. 4 2. evaluate 3…
C. 16 ### Problem 2:
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use newton’s method to find an approximate solution of ln(x) = 9 - x. s…
\( 7.039941 \)
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f(x) = \\begin{cases} (x - 4)^2 - 9 & \\text{for } x \ eq 2 \\\\ 2 & \\…
\( 2 \)
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10. describe and correct the error in simplifying the expression. × (sq…
The error is that \( 4^3 = 64 eq16 \), so \( \sqrt[3]{16} eq4 \). The correct simplification is \( \sqrt[3]{16}=2\sqrt[3]{2} \).
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f(x) = \\begin{cases} -(x + 8)^2 + 1 & \\text{for } x \\leq -5 \\\\ 2x …
\( 0 \)
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use the situation to answer the questions. a function is used to calcul…
(for Question 2): The points \( (0.25, 0.5) \), \( (1, 1) \), \( (2.25, 1.5) \), \( (4, 2) \) do not form a straight line. The graph of \( y=\sqrt{x} \) is a curve.
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input output -2 -4 2 4
For \(x = 2\), the output is \(-4\); for \(x = 4\), the output is \(-6\)
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use the graph of a function to complete the table. input output -2 -4 2…
-4
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what is the y-value of this function when x = -4?
0
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use the situation to answer the questions. a function is used to calcul…
1) The completed table is as above. 2) The points do not form a straight line.
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a small island is 4 miles from the nearest point p on the straight shor…
\(\frac{12\sqrt{7}}{7}\)
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match each polar equation (a - d) with its associated polar graph. a. (…
A. $r = 1 + 2\cos\theta$ (assuming the graph matches this equation, e.g., opening right horizontally)
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use the graph of the function to complete the table. input | output -4 …
For x = - 4, output is 8; for x=-1, output is 0. So the completed table (partial) is: | Input (x) | Output (y) | |----|----| | - 4 | 8 | | - 3 | 5 | | - 1 | 0 |
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the time of flight for an object thrown from the rooftop of a tall buil…
A. \( x = v\cos(\theta)3.1 \)
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match each polynomial function to its graph. $f(x) = -x^3 - 18x^2 - 108…
\( f(x) = -x^3 - 18x^2 - 108x - 216 \) matches the Right Graph. \( g(x) = -x^3 + 21x^2 - 147x + 343 \) matches the Left Graph.
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find f(-3) if f(x) = 6x² - x. f(-3) = \\square (type an integer or a si…
57
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convert the polar equation $r = 4cos\theta$ into a rectangular equation…
\( x^{2}+y^{2}=4x \) (or the standard circle form \( (x - 2)^{2}+y^{2}=4 \))
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64. during a recent rain shower, zachary found that the relationship be…
2 ### Question 65
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log_{27}(5x - 1)^3 - log_{3}(3x - 5) = 2
\( x = 2 \)
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find the quotient, and write it in rectangular form. \\(\\frac{8(\\cos …
\( -4 + 0i \) (or simply \( -4 \) since the imaginary part is 0)
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match each function to its graph. 7. $y = \\sqrt3{x - 1}$ 8. $y = x^3 -…
To solve the problem of matching each function to its graph, we analyze the transformations of the parent function \( y = \sqrt[3]{x} \) or \( y = x^3 \): ### Function 7: \( y = \…
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example 4 solve a linear-quadratic system by graphing production a soft…
## Paso 1: La primera ecuación es \( R = -0.1x^2 + 4x \). La línea es \( R = 42 \). Sistema: \( R = -0.1x^2 + 4x \) (1) y \( R = 42 \) (2). ## Paso 3: El sistema tiene \(\boldsymb…
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use the situation to answer the questions. a function is used to calcul…
The completed table is as follows: | Area (\( \text{m}^2 \)) \( x \) | Process \( \sqrt{x} \) | Side Length (\( \text{m} \)) \( y \) | | --- | --- | --- | | 0.25 | \( \sqrt{0.25} …
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the general rule that all major groups of transactions should be suppor…
A. adequate records.
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webwork / hs hanna precal / test 6.3 double half angle pow previous pro…
C. \(\tan(x)\)
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webwork / hs hanna precal / test 6.3 double half angle power reduce pre…
# Explanation: ## Step1: Recall Trig Identities[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On …
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44. the expression $23(5)^{x + 7}$ is equivalent to which of the follow…
C. $23(5)^x(5)^7$ ### Question 45
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8. ( x^3 + 6x^2 = 6x + 6 )
The roots of the equation \(x^{3}+6x^{2}-6x - 6 = 0\) are approximately \(x\approx1.396\) and two complex roots (found by quadratic formula on the depressed cubic after factoring …
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webwork / hs hanna precal / test 6.3 double half angle power reduce / 6…
\(\frac{\sin^{3}(-x)}{\sin^{3}(x)-\sin(x)}=\boxed{\tan^{2}(x)}\) \(1 - \frac{1}{\cos^{2}(x)}=\boxed{-\tan^{2}(x)}\) \(\frac{\cos(x)\sin^{2}(x)+\cos^{3}(x)}{\sec(x)}=\boxed{\cos^{2…
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how do you write an equation for exponential decay? y = a(1 - r)^{\\fra…
The correct equation for exponential decay among the given options is \( y = a(1 - r)^{\frac{t}{t}} \) (the first option in the list, assuming the exponent's variable is a typo an…
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what is the slope in a linear function? the slope (m) is the y-intercep…
The slope (\(m\)) indicates the rate of change of the function, showing how much \(y\) changes for a unit change in \(x\).
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what is the y - intercept in a linear function? the slope of the line i…
The point where the line crosses the y - axis, represented by the value of \( b \) in the equation \( f(x)=mx + b \).
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find the exact value of s in the given interval that has the given circ…
\(\frac{5\pi}{6}\)
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which statement best describes the function? a) the function is onto. b…
C) The function is onto and one - to - one.
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question 36 · 1 point given the following functions, compute the compos…
\(56x - 55\) ### Question 37
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what is a common base for exponential functions? 3 2 e (approximately 2…
e (approximately 2.718)
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question 35 · 1 point determine the interval(s) for which the function …
\( (3, \infty) \)
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question 5 solve ( 2cos^{2} u - 7cos u + 5 = 0 ) for all solutions. exa…
\( u = 2k\pi \) (where \( k \) is an integer)
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solve the following logarithmic equation, using a calculator if necessa…
$\boxed{-0.23}$ (Wait, but let's check again. Wait, maybe I made a mistake in the sign. Wait, no, $e^2$ is about 7.389, so 7.389 - 9 is negative, so x is negative, but still great…
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what is a linear function? a function that creates a straight line when…
A function that creates a straight line when graphed, with the form \( f(x)=mx + b \)
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solve the following logarithmic equation, using a calculator if necessa…
\(23.1\)
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how can you identify exponential growth on a graph? a curve that oscill…
A curve that rises steeply as \( x \) increases, indicating rapid growth.
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question 13 of 15, step 1 of 1 solve the following logarithmic equation…
$x = 12$
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what is the growth factor in an exponential function? (1 + r) where r i…
The correct option is the first one: \((1 + r)\) where \( r \) is the growth rate expressed as a decimal.
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use the elementary properties of logarithms to solve the following equa…
$8$
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use synthetic division to rewrite the following fraction in the form $q…
\(3x^{4}+5x^{3}-5x^{2}+\frac{2}{x + 5}\)
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evaluate the following logarithmic expression without the use of a calc…
$\frac{2}{5}$
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60. which of these is not a cabinet-level position listed in the docume…
c) Speaker of the House ### Question 61
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indicate which of the following four graphs is the correct graph of thi…
The bottom - left graph (the third graph in the given set of four graphs)
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given $f(x) = -2x - 3$, find $f(2)$. answer attempt 1 out of 2
\( -7 \)
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the function $y = \\log(x)$ is translated 1 unit right and 2 units down…
The graph shown (the one with the curve starting near \( x = 1 \), passing through \( (2, - 2) \) and increasing as \( x \) increases) is the graph of \( y=\log(x - 1)-2 \). (If w…
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indicate which of the following four graphs is the correct graph of thi…
The fourth graph (the bottom - right graph)
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what are the domain and range of $f(x) = \\log(x + 6) - 4$?\ \ \\bigcir…
B. domain: \( x > -6 \); range: all real numbers
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what is the range of ( y = log_{e} x )? - all real numbers less than 0 …
all real numbers (the option: all real numbers)
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which of the following is the inverse of $y = 6^x$? $\\bigcirc\\ y = \\…
\( y = \log_{6}x \) (the first option)
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indicate which of the following four graphs is the correct graph of thi…
The bottom - right graph (the fourth graph in the given set of four graphs)
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which of the following is a logarithmic function? ○ $y = 0.25x$ ○ $y = …
\( y=\log_{0.25}x \) (the third option)
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9. ana entered this expression into a calculator at the jacket store: \…
An example question: A jacket at a store costs $64. The store is having a 20% off sale. What is the amount of the discount on the jacket? (The expression $\frac{20}{100}\cdot64$ c…
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if \\(\\sin x = \\frac{4}{5}\\), where \\(x\\) is in quadrant i, then f…
s: A. \(\sin 2x=\frac{24}{25}\) B. \(\cos 2x = -\frac{7}{25}\) C. \(\tan 2x=-\frac{24}{7}\)
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4. graph the function $y = 3 - 6(\\sin x)^2$ on the interval $0, 2\\pi$…
The function \(y = 3 - 6\sin^{2}x\) simplifies to \(y = 3\cos(2x)\) with period \(\pi\). The key points on \([0,2\pi]\) are \((0,3)\), \((\frac{\pi}{4},0)\), \((\frac{\pi}{2}, - 3…
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the tires of a bicycle have radius 12.0 in. and are turning at the rate…
16.1
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indicate which of the following four graphs is the correct graph of thi…
The bottom right graph (the fourth graph, located at the bottom right among the four graphs)
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a. $4 - |x + 3|$ b. $4 - |x - 3|$ c. $-|x + 3| - 4$ d. $-|x - 3| - 4$ g…
C. \(-|x + 3|-4\)
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question given $f(x) = -4x - 5$, find $f(-4)$. answer attempt 1 out of …
11
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like an eagle k. reiter 1. his palms were sweaty, and his heart was bea…
A. Overcome your fears, C. You can do anything that you put your mind to
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problem 2: part b here is your graph from the previous screen. write an…
\(y =-\frac{1}{3}x + 5\) (or \(x + 3y=15\))
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problem 2: part b here is your graph from the previous screen. write an…
\(y =-\frac{1}{5}x + 5\)
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problem 2: part b here is your graph from the previous screen. write an…
\(y = - x+5\) (assuming the slope is - 1 and y - intercept is 5)
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solve the following logarithmic equation, using a calculator if necessa…
\( x\approx1.16 \) (or if we use the exact fraction form \( x = \frac{e^{3}-12}{7}\), but the problem asks to round to two decimal places or write as a fraction. If we calculate t…
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solve the following logarithmic equation, using a calculator if necessa…
\(x = 7.1\)
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solve the following logarithmic equation, using a calculator if necessa…
14
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find the slope of the line through each pair of points. 66) (6, 4), (-1…
The slope is \(-\frac{3}{8}\) ### Problem 67:
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2. what is the equation in slope-intercept form of the line that passes…
\( y = -\frac{2}{3}x + 14 \)
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identify whether the graph of the function f(x) shown below is even, od…
The function's graph is neither even nor odd (it is not symmetrical over the \( y \)-axis or about the origin).
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identify whether the graph of the function $f(x)$ shown below is even, …
The graph is neither because it does not exhibit symmetry about the \( y \)-axis (even function) or about the origin (odd function).
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evaluate the following logarithmic expression without the use of a calc…
1
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evaluate the following logarithmic expression without the use of a calc…
$\frac{2}{3}$
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the table below shows select values of the function f, which is even an…
\( 6 \)
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the table below shows select values of the function f, which is odd and…
\(-16\)
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question 21 · 1 point graph the function $f(x) = 8^x$ by moving the key…
To graph \( f(x)=8^x \), the key integer points are \( (0, 1) \) (since \( 8^0 = 1 \)) and \( (1, 8) \) (since \( 8^1 = 8 \)). We move the incorrect point (2,1) (from the initial …
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the table below shows select values of the function f, which is odd and…
\( 5 \)
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indicate which of the following four graphs is the correct graph of thi…
The Top - Right Graph
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question 22 · 1 point let $f(x) = 5(4)^{x - 1}$. evaluate $f(3)$ withou…
\( f(3)=\boxed{80} \) ### Question 23
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use synthetic division to rewrite the following fraction in the form $q…
\(2x^{4}-6x^{3}+7x^{2}+7x+\frac{0}{x - 5}\) (or \(2x^{4}-6x^{3}+7x^{2}+7x\) as \(\frac{0}{x - 5}=0\))
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indicate which of the following four graphs is the correct graph of thi…
The fourth graph (the bottom - right graph)
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9. (5 points) if $y(x) = \\sin(x)$, find $y^{(4)}(x)$. 10. (15 points) …
The points on the curve where the tangent line is horizontal are \((-2,29)\) and \((1,2)\)
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identify whether the graph of the function $f(x)$ shown below is even, …
The graph is even because it is symmetric about the \( y \)-axis (satisfies \( f(-x) = f(x) \)).
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identify whether the graph of the function $f(x)$ shown below is even, …
odd, it is symmetric about the origin (satisfies \( f(-x) = -f(x) \))
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indicate which of the following four graphs is the correct graph of thi…
The top - left graph (the first graph in the top - left corner)
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question identify whether the graph of the function $f(x)$ shown below …
The graph is even because it is symmetric about the \( y \)-axis (satisfies \( f(-x) = f(x) \)).
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question 2 of 15, step 1 of 1 correct write the following logarithmic e…
$20^2 = F$
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use synthetic division to determine if the given value for k is a zero …
Yes
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write the equation of this line in slope-intercept form. write your ans…
\( y = -4x - 4 \)
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does the graph shown below represent y as a linear function of x? choos…
A. Yes
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write the equation of this line in slope-intercept form. write your ans…
\( y = 5x - 2 \)
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43. reasoning the end behavior of a polynomial function f is described …
As \( x ightarrow-\infty \), \( g(x) ightarrow-\infty \) and as \( x ightarrow+\infty \), \( g(x) ightarrow+\infty \). This is because \( g(x)=-f(x) \) reflects \( f(x) \) over th…
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determine the rule for $g \\circ f(x)$ given the functions below. $f(x)…
\( g\circ f(x)=\frac{1}{x^{4}} \)