微積分
極限、導數、最優化與函數性質。
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1) $f(x) = \\frac{3(x + 2)}{(x - 2)(x + 2)}$ x - intercept: v.a. hole: …
for Function 1: x-intercept: None y-intercept: $(0, -1.5)$ V.A.: $x=2$ H.A.: $y=0$ Hole: $(-2, -0.75)$ Domain: $x eq -2, 2$ Range: $y eq 0, -0.75$ --- # For Function 2: $f(x)=\f…
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which statements are true about the graph of the function $f\\left(x\ i…
- There is a zero at $x = -4$. - There is a hole at $x = 9$. - There is an asymptote at $x = -9$.
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neil, a real estate agent, earned a big commission for selling a house.…
6 years and 11 months
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use the function $f\\left( x \ ight) = \\frac{ -6 }{ 7(x - 2) }$ to eva…
1. As $x \to +\infty, f(x) \to -\frac{6}{7}$: $\boldsymbol{\text{False}}$ 2. There is an asymptote at $x=2$: $\boldsymbol{\text{True}}$ 3. There is an asymptote at $y=0$: $\boldsy…
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cindy found a collection of baseball cards in her attic worth $8,000. i…
### Exponential growth function: $f(x) = 8000(1.015)^x$ ### Value after 7 years: $\$8878.76$
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cole wanted to buy a new motorcycle and put $7,000.00 into an account w…
7.3%
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for which values of ( x ) is the function ( fleft(x ight)=\frac{x^{2}+2…
$(-8, -4)$ and $(1, 2)$
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algebra 2 362403 - 6 fy - 1 6 - 1: mathxl for school: practice & proble…
$a=1$
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30. a group of researchers investigated the effects of two vocabulary l…
30. D. independent; dependent 31. B. reliability 32. C. Institutional Review Board 33. C. naturalistic observation 34. C. the inability to generalize the findings from this approa…
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choose a possible sketch of the graph of ( y = \frac{4}{x} ) and ( y = …
A. <The graph with two distinct intersection points between the two curves>
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the volume of a cube with side length ( x ) is ( v(x)=x^{3} ). the volu…
When x = 1, the volume of the **cylinder** is greater.
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cities are often defined by their skylines—the distinctive outlines cre…
They evolved over time and gradually became more popular, allowing for much taller buildings.
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algebra 2 362403-6 fy - i benchmark test 2 over what interval is the gr…
A. $(-\infty, 0.27)$ and $(3.73, \infty)$
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simplify the following expression. -45.93 + 112 + (-61.24) a. 5.83 b. 4…
B. 4.83
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algebra 2 362403 - 6 fy - 1 benchmark test 2 the graph of function f is…
B. $f(x) = x^3 + x^2 - 12x$
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a ball is thrown from the top row of seats in a stadium. the function $…
8
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directions: use this information to answer parts a and b. $f(x)=x - 7$ …
$f^{-1}(x) = x + 7$
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question #9: which sentence contributes most to developing the central …
Question #9: D. All of the above Question #10: C. Schools are debating screen time. Question #11: (Note: Incomplete options provided; Option A is incorrect as supporters of screen…
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f(x) = -2^x + 1 x-intercept: y-intercept: asymptote: domain (interval):…
s: x - intercept: \(\boldsymbol{(0,0)}\) y - intercept: \(\boldsymbol{(0,0)}\) asymptote: \(\boldsymbol{y = 1}\) Domain (interval): \(\boldsymbol{(-\infty,\infty)}\) Range (inequa…
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day 1 - exponential functions practice for ( y = 2^x + 1 ): x - interce…
Let's tackle the first function \( y = 2^x + 1 \) step by step: ### x - intercept: To find the x - intercept, we set \( y = 0 \) and solve for \( x \). So, \( 0=2^x + 1 \) \( 2^x=…
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graph the following features: - slope = 2 - y-intercept = -2
The line $y=2x-2$ is graphed by plotting the y-intercept $(0, -2)$, using the slope to find a second point $(1, 0)$, then drawing a straight line through these points and extendin…
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determine the end behavior of the graph. use -> and ∞, you may copy and…
As \( x\to -\infty \), \( f(x)\to\infty \); as \( x\to\infty \), \( f(x)\to\infty \)
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simplify the following expression. -1 - (-590.173) a. -591.173 b. -589.…
D. 589.173
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1710_roller coaster the path of a roller coaster after it has reached t…
A relative minimum in this roller coaster context means that at a specific distance (along the x - axis, distance in feet) from the start of the roller - coaster's path (after the…
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(06.03) which system of equations is represented by the graph? options:…
d. \(y = x-4\), \(y=\frac{x - 4}{x + 2}\)
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question 2 of 10 what are the x-intercepts of the graph of the function…
D. (-7, 0) and (4, 0)
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determine the domain and range of the function. (options are presented …
1. Domain: b. \( x \in \mathbb{R} \) (all real numbers) 2. Range: c. \( y \in (0, \infty) \) (\( y > 0 \))
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3. what system divides power between the federal and state governments?…
3. C. Federalism 4. D. Necessary and Proper Clause 5. B. It expanded the use of federal powers 6. D. Gibbons v. Ogden 7. C. It establishes federal law as the highest law 8. B. The…
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graph the following features: • slope = 3 • y-intercept = 1
The line $y=3x+1$ is graphed by plotting the y-intercept $(0,1)$, using the slope to find a second point $(1,4)$, then drawing a straight line through these points and extending i…
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determine the end behavior of the graph. use -> and ∞, you may copy and…
As \( x \to +\infty \), \( f(x) \to +\infty \); as \( x \to -\infty \), \( f(x) \to +\infty \)
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question 2 (2 points) determine whether the function represents exponen…
a. Exponential Growth
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7. target d using the graph, determine the domain and range of the func…
Domain: $(-\infty, \infty)$; Range: $(-\infty, \infty)$
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6. target i a function f(x) is graphed. which equation best describes t…
C. \(f(x)=x^{3}+3x^{2}-4x\)
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5. target b evaluate the expression. find ( f(-3) ) for ( f(x) = 2x^3 -…
\( -99 \)
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evaluate. $7^3 = \\square$
\(343\)
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the path of a roller coaster after it has reached the top of the first …
D. 250
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1710_roller coaster the path of a roller coaster after it has reached t…
C. 100
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evaluate. $2^4 = \\square$
16
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3\\cdot 2^{\\frac{x}{5}} = 150\ which of the following is the solution …
A. $x = 5 \log_{2}(50)$
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18\\cdot 2^{5t} = 261\ what is the solution of the equation?\ round you…
$t \approx 0.772$
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read the information in the chart. | | dates of exploration/ colonizati…
The Spanish, French, and British all had economic interest in the Southeast.
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simplify the following expression. -127.762 - 68.296 a. 8.83 b. -197.05…
D. -196.058
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evaluate. write your answer as a decimal or whole number. $(8.1)^3 = \\…
\(531.441\)
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evaluate. \\(9^3 = \\square\\)
\(729\)
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match the insurance term with its definition premium deductible limit i…
To solve this, we match each insurance term with its correct definition: 1. **Premium**: The definition "your monthly bill or 'subscription' to the insurance policy" fits because …
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evaluate. $8^2 = \\square$
\(64\)
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although exercise has many health benefits, it should be limited becaus…
stress. The claim that exercise should be limited for this reason is incorrect.
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the war sacrifices of mr. spagg | reading quiz 1. which best describes …
To solve these reading comprehension questions, we analyze each based on the story "The War Sacrifices of Mr. Spagg" (assuming "Spagg" is a typo for "Spugg"): ### Question 1: Tone…
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evaluate. $5^3 = \\square$
\(125\)
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what was the importance of jacksonian democracy? it tackled the growing…
D. It increased the number of common men holding office.
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evaluate. write your answer as a decimal or whole number: \\((0.82)^3 =…
\(0.551368\)
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evaluate the following. (a) \\(|-7| + 5 = \\square\\) (b) \\(|-7 + 5| =…
(a) 12 (b) 2
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the function g (graphed below in blue) is a transformation of function …
B. $f(x) - 4$
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question 3 1 point a penguin dives into the sea from its starting posit…
$y = -3x + 2$
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the function f (graphed below in blue) is a transformation of function …
$\boldsymbol{g(x)-2}$
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“hamilton was no fan of the articles.... he knew we needed a federal go…
Denied Powers (The Articles of Confederation created a very weak national government with limited powers.)
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a wall is being painted with a mural designed on a coordinate plane wit…
$y-5=8(x-3)$
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question 2 which is the equation of the line in point slope form that p…
B. $y-6 = \frac{-2}{5}(x+5)$ (Note: correcting the typo in the original option; the correct x-term should be $x - (-5) = x+5$, and the slope is $\frac{-2}{5}$)
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which are equations of the given line in point slope form? select all t…
E. $y+2=-(x+3)$
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although exercise has many health benefits, it should be limited becaus…
cause abundant stress. Excessive exercise can have negative effects, but the claim that exercise "should be limited" generally due to abundant stress is false.
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28. independent states that agree to form a(n) ___ may still retain the…
d. confederation ### Question 29
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y = 3x² + 12x + 8 xis of symmetry: vertex: ( , ) max or min value: x | …
Axis of Symmetry: $\boldsymbol{-2}$ (correct as given) Vertex: $\boldsymbol{(-2, -4)}$ (correct as given) Max or Min Value: $\boldsymbol{Min}$ (corrected from Max) Table y-values:…
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what is the horizontal asymptote of the rational function \\( f(x) = \\…
\( y = \frac{a}{d} \)
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list all the asymptotes of the following function, then graph the funct…
(Asymptotes): D. \( x = 3, x = -3 \)
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y = x² - 2 y = 7 the system of equations has the solutions (-a, b) and …
B. 3
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6. what are the coordinates of the vertex of the quadratic function $y …
d. $(-2, 9)$
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9. an exponential function is graphed on the grid. which function is be…
A. $f(x) = 10(0.5)^x$
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in the tidal area of a certain city, a sinusoidal function $f(x)=a\\sin…
A. $4.17\sin(b(x + c)) + d$
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graph the following features: • y-intercept = 1 • slope = $-\frac{5}{3}$
The graph is a straight line passing through the points (0, 1) and (3, - 4) (or (-3, 6)) with a slope of $-\frac{5}{3}$ and y - intercept at (0, 1). The equation of the line is $y…
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a. $f(x)$ is increasing and positive on the interval $(-infty, 3)$. b. …
B. \( f(x) \) is decreasing and positive on the interval \((-\infty, 3)\).
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choose the characteristic that represents the graph of the radical func…
(Assuming we are to evaluate option A and it's incorrect, but since the full options are not shown, if we assume the correct option is, for example, if there was an option like "f…
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graph the following features: • y-intercept = 2 • slope = $-\frac{6}{5}$
To graph the line: 1. Plot the point \((0,2)\) (the y - intercept). 2. Use the slope \(m =-\frac{6}{5}\) to find another point (e.g., from \((0,2)\), move 5 units right and 6 unit…
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which statement best describes your ability to choose sports and exerci…
., adapting activities to their needs). Option B is unrealistic, as not everyone can participate at maximum intensity due to physical limitations, fitness level, or health conditi…
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the function $f(x)=-sqrt{x}$ is represented by the graph. what is the r…
\(\{y|y\leq0\}\)
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suppose that the function ( f ) is defined, for all real numbers, as fo…
1. Graph: (See step-by-step graph construction below) 2. Is the function continuous? Yes
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how does black use history to make his case more persuasive? he quotes …
C. He shows that the Bill of Rights was added to limit government power and protect the press.
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state laws also explain how local governments are set up and operated. …
a. using the same basic principles as guidelines. ### Question 2
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function operations instruction active some special cases $f(x)=x^2$ wh…
\( 3f(x) \) (from the options: 3f(x))
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complete the sentence based on the equation shown below. $h(-x - 3) = -…
$h = 8$ because you get one solution when either side of the equation has different constants for the linear variable terms. Dropdown selection: different constants
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passive leisure is just as beneficial as active leisure. please select …
e.g., watching TV, mindless scrolling), which has limited proactive benefits. Thus the statement is false.
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question 23 4 pts you have a credit card that you use regularly for sma…
B. Use less than 30% of the credit limit and pay it off in full every month by the due date
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what is the range of the function $g(x) = |x - 12| - 2$? $\\{y \\mid y …
\(\{y|y\geq - 2\}\) (the second option)
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which graph represents the function $f(x) = |x + 3|$?
The V - shaped graph (the first graph in the given image) represents the function \( f(x)=|x + 3| \). (Assuming the first graph is the V - shaped one and the second is a straight …
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mike is a veterinarian. he is placing a 9-line job ad for an assistant.…
s: a. \(\boldsymbol{0}\) b. \(\boldsymbol{108}\) c. \(\boldsymbol{117}\)
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question 12 4 pts the truth in lending act of 1968 requires creditors t…
B. state monthly finance charge and the Annual Percentage Rate (APR) on the monthly statement.
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simplify \\ln e = \\ln e^{2x} = \\ln 1 = done
$\ln e = 1$ $\ln e^{2x} = 2x$ $\ln 1 = 0$
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4. identify the y - intercept of each of the exponential functions. \\(…
s: - For \( y = 3123(432,543)^x \), the \( y \)-intercept is \( 3123 \) (at the point \( (0,3123) \)) - For \( y = 76(89,047,832)^x \), the \( y \)-intercept is \( 76 \) (at the p…
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4. identify the y-intercept of each of the exponential functions. $3123…
s: - For \( 3123(432,543)^x \), the y - intercept is \( 3123 \). - For \( 76(89,047,832)^x \), the y - intercept is \( 76 \). - For \( 45(54)^x \), the y - intercept is \( 45 \). …
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base your answers to questions 5 and 6 on the passage below and your kn…
5. 1. Congress cannot mandate a national religion. 6. 2. The trial of John Peter Zenger
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evaluate $y = \\ln{(x - 2)}$ for the following values of $x$. round to …
$x=3, y=0$ $x=4, y=0.693$ $x=6, y=1.386$
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add. 4.068 + 15 + 0.105 6.618 19.173 19.83 4.188
19.173 (corresponding to the option: 19.173)
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question 7 add. $15.24 + 5.09$ $\\circ$ $20.33$ $\\circ$ $20.249$ $\\ci…
20.33
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match each expression on the left with an equivalent value on the right…
$15 \cdot 28 \longleftrightarrow 420$ $22 \times 23 \longleftrightarrow 506$ $(39)13 \longleftrightarrow 507$
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evaluate $y = e^x + 1$ for the following values of $x$. round to the ne…
The correct graph is the second one (the middle graph, which shows an increasing exponential curve passing near $(0,2)$, rising steeply for positive $x$, and approaching the x-axi…
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evaluate $y = e^x + 1$ for the following values of $x$. round to the ne…
$x=-2, y \approx 1.135$ $x=1, y \approx 3.718$ $x=2, y \approx 8.389$
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fill in the blank in the sentence below. based on the section \animals …
C. feel and express.
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15. a) graph the function $f(x) = 3(x - 1)^2 - 4$. b) what does $f(-1)$…
### Part a) Graphing \( f(x) = 3(x - 1)^2 - 4 \) This is a quadratic function in vertex form \( f(x) = a(x - h)^2 + k \), where: - Vertex: \( (h, k) = (1, -4) \) - Since \( a = 3 …
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solve the equation 2.03x = 31.1 ( x = 15.3198 ( round to four decimal p…
The correct solution for \(x\) (assuming the equation is \(2.03x^2 = 15.23\) or a similar correction) is \(x\approx2.7391\) (rounded to four decimal places). If we follow the step…
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solve the equation. $2.01e^t = 31.1$ $t = \\square$ (round to four deci…
\(t\approx2.7490\)
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5 which expression is equivalent to \\(sqrt4{xy} cdot sqrt4{2x}\\) wher…
A. \(\sqrt[4]{2x^{2}y}\)