Calculus
Limits, derivatives, optimization, and behavior of functions.
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thaddeus wants to attend a sports camp this spring that costs $190.00 f…
$\$42.85$
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01-22 square root test find the inverse of the following function. $f(x…
\( f^{-1}(x)=3-\sqrt{\frac{x - 4}{2}} \)
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question 2-11 if $f(x) = -2x + 3$, what is $f(4)$? -5 4 5 11
-5 (Option: -5)
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transformations of quadratic functions christian is rewriting an expres…
the value of $a$ remains the same
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solving quadratics with square roots (lev question examples solve the f…
\(\pm 3\)
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what are the coordinates of the vertex of the function $f(x)=x^2 - 12x …
(6, -31)
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what are the coordinates of the vertex of the function $f(x)=x^2 - 8x +…
$(4, 7)$
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determine the vertex form of ( g(x) = x^2 + 2x - 1 ). which graph repre…
Vertex form: $g(x) = (x+1)^2 - 2$ The correct graph is the middle (second) one.
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what is true about the function $h(x) = x^2 + 20x - 17$? choose two cor…
To graph the function $h$, shift the graph of $f(x) = x^2$ left 10 units and down 117 units. The vertex of $h$ is $(-10, -117)$.
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what is the sum of 2,043.2 + 3,120.6? enter the answer in the box.
5163.8
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select the correct answer. which statement is true? a. inexhaustible re…
D. Exhaustible resources are scarce.
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describing a quadratic function use the drop - down menus to describe t…
The vertex of $g$ is $\boldsymbol{(7, -50)}$ The axis of symmetry is $\boldsymbol{x=7}$ To graph the function $g$, shift the graph of $f = x^2$ **7 units to the right and 50 units…
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add. 4.264 +7.529 enter the answer in the box.
$11.793$
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add. 3.247 +6.781 enter the answer in the box.
10.028
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two gymnasts are running toward each other in a floor routine, and they…
5 seconds
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question if \\(cos x = \\frac{3}{10}\\), then what is the positive valu…
$\frac{\sqrt{65}}{10}$
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scan through the article.......this is a very misunderstood concept. su…
The "made in America" idea has both positive and negative aspects. Positively, it supports domestic jobs, security, and ethical production. Negatively, it can limit choice and inc…
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(2×8) - 9 + 7
14
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16÷2×4 - 3
29
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activity 1 write a sentence that has the following elements. 1. phrase …
1. The bright red cardinal perched on the old oak branch. (phrase: "the old oak branch") 2. When the bell rings, we will head to the cafeteria. (dependent clause: "When the bell r…
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10 $6\\frac{2}{5} - 3\\frac{3}{4}$
\(2\frac{13}{20}\)
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23+(30÷10)×4
35
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7 $7\frac{2}{5}-3\frac{1}{2}$
\(3\frac{9}{10}\)
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6 ( 3\frac{1}{6} - 1\frac{3}{4} )
\(1\frac{5}{12}\)
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40+(72÷9)÷8
41
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3 (2\frac{1}{8} - \frac{3}{4})
\(1\frac{3}{8}\) (or \(\frac{11}{8}\))
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7×(7 - 4)÷3
7
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2. $y = -\frac{4}{3}x + 1$
Slope \( m=-\frac{4}{3} \), y - intercept \( b = 1 \) If the intended question is different (e.g., find x - intercept, graph the line, solve for x when y = 0, etc.), please provid…
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graph 1. $y = \\frac{1}{2}x - 3$
To graph the linear equation \( y = \frac{1}{2}x - 3 \), we can use the slope - intercept form of a linear equation \( y=mx + b \), where \( m \) is the slope and \( b \) is the y…
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solving systems of equations by graphing\t\t\t\t\tname: \t\t\t\t\t\t\t\…
The solution is \( (-2,1) \) ### Problem 2:
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why are tradeoffs necessary? advertisers promote products. every produc…
Resources are limited.
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type the correct answer in the box. use numbers instead of words. what …
100
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peoples wants are unlimited. this fact means that which of the followin…
scarcity
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what number makes the equation true? $53.01 \\times 10^3 = ?$ a. 530.1 …
D. 53,010
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type the correct answer in the box. use numbers instead of words. what …
4870
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graph the function. $f(x)=2\\sqrt{x + 3}$ plot four points on the graph…
Leftmost point: $(-3, 0)$ Additional point 1: $(-2, 2)$ Additional point 2: $(1, 4)$ Additional point 3: $(6, 6)$ (Plot these points and draw a smooth curve starting at $(-3,0)$ a…
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find the domain of the function. \\( g(x) = sqrt{-x} - 8 \\) write your…
$x \leq 0$
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which is equivalent to $216^{\\frac{1}{3}}$?\ \\bigcirc 3\ \\bigcirc 6\…
B. 6
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exercise 4. (2 p) a company produces two different types of products (a…
The maximum profit is 1100 euros, achieved when producing 100 units of product A and 300 units of product B.
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write the equation of the line in fully simplified slope - intercept fo…
$y = -\frac{1}{2}x - 6$
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unit 4 lesson 7 homework period the function $f(x)=\\frac{2}{3}x - 8$ i…
1. The solution point is $(9, -2)$ 2. $x = 9$ 3. The solution point is $(-6, -12)$ 4. $x = -6$
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in 1215, the magna carta limited the english king’s power, but in 1689,…
The important document was the English Bill of Rights.
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directions: use the reading to fill in the blanks. 1. in the early 1800…
s: 1. judicial 2. John Adams; Judiciary (or if strictly 1789 Act, still John Adams as the president leaving in 1801 and the 1789 Act established the court system) 3. fifteen 4. Se…
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7. which of the following graphs would fit the system of equations? y =…
a) (the graph labeled a)
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squaring numbers a) find the values of the following. 1) $7^2$ 2) $13^2…
## Part A 1) 49 2) 169 3) 16 4) 625 5) 1764 6) 100 ## Part B 1) 25 2) 2401 3) 289 4) 441 5) 9 6) 1156 ## Part C 1) iii) 400 2) i) 1,936
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use the figure below to answer the question that follows. the graph of …
A. The graph of \( g \) is identical to the graph of \( f \).
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a bank looks to attract investors. they are offering 9.5% annual intere…
\(\$48463.85\) (Note: If we calculate more precisely, \(e^{1.14}\approx e^{1.14}\approx3.126703744\), then \(15500\times3.126703744 = 15500\times3.126703744=48463.908032\approx484…
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you purchase a new house for $240,000 today. if you live in that house …
$\$837682.29$
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you purchase a $142.83 ticket for your favorite band. you remember your…
\$696.01
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your uncle says that when he was 10, he used to go down to the fast - f…
$\$14.86$
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evaluate. \\(\\frac{6!10!}{8!8!}\\) simplify your answer as much as pos…
\(\frac{45}{28}\)
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an island is 7 km due north of its closest point p along a straight sho…
8.967 km
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question find the area of the rectangle of largest area that has its ba…
$5832$
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describe the end behavior of the following graph: enter your response h…
As $x \to +\infty$, $y \to -\infty$; as $x \to -\infty$, $y \to -\infty$
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what is the range of this graph? options: -1 ≤ y < ∞ -∞ < y ≤ 0.5 -∞ < …
-1 ≤ y < ∞
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what is the range of the function? all ______ numbers
All real numbers greater than or equal to -2
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2. decimals, fractions, integers score ____/84 or ______% a. decimal ca…
All the handwritten answers for the decimal addition and subtraction problems are correct. The total possible score for this section is 84, so the score is 84/84 or 100%.
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a gardener has 88 yd of fencing and wants to fence off a rectangular en…
The dimensions are 22 yards (perpendicular to the wall) and 44 yards (parallel to the wall), which gives the maximum area.
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an expression is shown. \\(\frac{12}{7} \times \frac{2}{3}\\) what is t…
C. \(\frac{24}{21}\)
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systems a. whole number calculations multiply score_____/50 or_____% sc…
--- ## Multiply Answers: 2 Digit Numbers: 1080, 221, 2418, 3850 3 Digit Numbers: 19344, 396740, 249676, 86250 4 Digit Numbers: 2492680, 29543040, 53939600, 20262181 ## Divide Answ…
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question 10 of 10 type the correct answer in each box. use numerals ins…
\(\frac{9}{40}\)
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question 7 of 10 type the correct answer in each box. use numerals inst…
\(5\frac{5}{7}\) (So the first blank is \(5\), the numerator of the fraction part is \(5\), and the denominator of the fraction part is \(7\))
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find the dimensions of the rectangle of largest area that has its base …
The rectangle has a base of length $10$ and height of $150$, so the dimensions are $\boldsymbol{10 \times 150}$.
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question 6 of 10 type the correct answer in each box. use numerals inst…
\(\frac{1}{36}\)
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type the correct answer in each box. use numerals instead of words. if …
\(1\frac{1}{9}\) (So the first blank is \(1\), the numerator of the fraction part is \(1\), and the denominator of the fraction part is \(9\))
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write an equation for the function graphed below y =
$y=\frac{2x}{x^2 - 4}$
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write an equation of the line that passes through (-4, -1) and is perpe…
$y = -\frac{3}{4}x - 4$
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what is the end behavior of this function? options: as ( x \to infty ),…
As $x \to \infty, f(x) \to \infty$ As $x \to -\infty, f(x) \to -\infty$
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write an equation of the line that passes through (1,2) and is parallel…
$y = -5x + 7$
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complete the input - output table based on this graph. write your answe…
Input 0: Output = 3 Input 8: Output = 11 (So the blanks are: [0] → 3, [8] → 11)
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determine an equation for the pictured graph. write your answer in fact…
\(y=-x^{2}(x + 2)(x - 1)\)
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question 4 based on the graph above, estimate (to one decimal place) th…
-2.0
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write an equation for the function graphed below y = question help: vid…
$y=\frac{x-2}{(x+2)(x-2)}$ simplified to $y=\frac{1}{x+2}$ with a hole at $x=2$ (or written as $y=\frac{x-2}{x^2-4}$)
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11. solve: $\\log_{3} 4 + \\log_{3}(x - 5) = 3$
$\frac{47}{4}$
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10 multiple choice 1 point what is the inverse of the given function? $…
A. $y = \sqrt{x} - 3$
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8 multiple choice 1 point given $f(x) = -sqrt{x - 2} + 5$, what is the …
Domain: $x \leq 5$ Range: $y \geq 2$
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6 multiple choice 1 point the table includes values of a square root fu…
$y = 2\sqrt{x}$
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5 multiple choice 1 point given $f(x) = 4sqrt{x} - 7$, identify the min…
y = -7
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4 multiple choice 1 point a function is defined by $y = \\sqrt{x - 4}$.…
$y = x^2 + 4; x \geq 0$
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perform the indicated operation. if possible, reduce the answer to its …
\(\frac{1}{2}\)
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6. add 16 + (-9). 7. evaluate a - b for a = -7 and b = 14. -7 - 14 = -21
\(7\) ### Problem 7: (Verification)
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in exercises 23–30, condense the logarithmic expression. (see example 3…
23. $\log_{10}\frac{7}{10}$ (or $\log 7 - 1$) 24. $\ln 3$ 25. $\ln 24$ 26. $\log 22$ 27. $\log_5 (4\sqrt[3]{x})$
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question 3 consider the function $f(x) = x^2 e^{6x}$. $f(x)$ has two in…
$C = \frac{-2-\sqrt{2}}{6}$, $D = \frac{-2+\sqrt{2}}{6}$ - $(-\infty, C)$: Concave Up - $(C, D)$: Concave Down - $(D, \infty)$: Concave Up
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question 6 given the function ( g(x) = 6x^3 - 27x^2 - 72x ), find the f…
At $x = 4$ the graph of $g(x)$ is concave up At $x = 4$ there is a local minimum
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sketch a graph of $f(x)=\\begin{cases}-1.5x - 5&\\text{if }x\\leq - 2\\…
The graph consists of: 1. A line segment/ray for $y=-1.5x-5$ with a closed dot at $(-2, -2)$, passing through $(-4, 1)$, extending left. 2. A horizontal segment for $y=1$ with an …
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question 5 given the function ( g(x) = 6x^3 + 30x^2 - 90x ), find the f…
$g'(x) = 18x^2 + 72x - 90$ $g''(x) = 36x + 72$ $g''(1) = 108$ At $x=1$ the graph of $g(x)$ is concave up At $x=1$ there is a local minimum
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question 3 consider the function $f(x) = x^3 e^{0x}$ $f(x)$ has two inf…
$C = \frac{-3-\sqrt{57}}{4}$, $D = \frac{-3+\sqrt{57}}{4}$ $(-\infty,C)$: concave up $(C,D)$: concave down $(D,\infty)$: concave up --- For Question 4:
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consider the function $f(x)=x^{2}e^{3x}$. $f(x)$ has two inflection poi…
$C=\boldsymbol{\frac{-2-\sqrt{2}}{3}}$, $D=\boldsymbol{\frac{-2+\sqrt{2}}{3}}$ - $(-\infty, C)$: Concave Up - $(C, D)$: Concave Down - $(D, \infty)$: Concave Up --- For the second…
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question 2 given ( f(x) = 2x^3 + 12x^2 + 5x + 3 ) find where ( f(x) = 0…
$x = -2.00$ At $x = 0.5$ the function is concave up At $x = 6.5$ the function is concave up
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match each piece of derivative information with what it tells us about …
- $f'(x)$ is positive → b. The graph of $f(x)$ is increasing - $f'(x)$ is negative → f. The graph of $f(x)$ is decreasing - $f''(x)$ is positive → d. The graph of $f(x)$ is concav…
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find the derivative of the function.\\( g(t) = \\frac{16 \\log_{4}(t)}{…
$\boldsymbol{\frac{16(1 - \ln(t))}{t^2\ln(4)}}$
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3) name the event described. 1. peaceful change in power after a heated…
1. Peaceful Presidential Power Transition (e.g., U.S. Post-Election Transfer of Power) 2. Alien and Sedition Acts (1798)
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find the derivative of the function. \\( y = log_8(6x + 1) \\) \\( y = …
1. $\frac{6}{(6x+1)\ln 8}$ 2. $\frac{2x-9}{(x^2-9x)\ln 2}$
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y = 2x² - ln(x), (1, 2) (a) find an equation of the tangent line to the…
$y = 3x - 1$ *(Note: Part (b) requires a graphing utility to complete, which cannot be done in this text format, but the equation for the tangent line to graph is provided above)*
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joels turn: from \\(\frac{8}{12}\\), joel throws the disc \\(\frac{6}{1…
\(\frac{8}{12}+\frac{6}{12}=\frac{14}{12}=\frac{7}{6}\), and \(\frac{7}{6}>1\)
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consider the following.\\( y = \\ln(x^9),\\ (1, 0)\\)\\(\\text{(a)}\\) …
(a) $y' = \frac{9}{x}$ Slope of tangent line: $9$ Equation of tangent line: $y = 9x - 9$ (b) When graphing, plot the function $y=\ln(x^9)$ (equivalent to $y=9\ln(x)$ for $x>0$) an…
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b) $p = 3x^2 - 15$ | x | p | |----|----| | 4 | | | 0 | | | 12 | | | | -…
Pour \( x = -4 \), \( P = 33 \) ; Pour \( x = 0 \), \( P = -15 \) ; Pour \( x = 12 \), \( P = 417 \) ; Pour \( P = -12 \), \( x = \pm1 \) ; Pour \( P = 177 \), \( x = \pm8 \) ; Po…
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find the derivative of the function.\\( f(x) = 8x^2 ln(8x) \\)\\( f(x)=…
$f'(x) = 16x\ln(8x) + 8x$
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2. (0 / 0.25 points) find the derivative of the function. $f(x) = \\ln(…
For $f(x)=\ln(9x)$: $f'(x)=\frac{1}{x}$ For $y=(\ln x)^6$: $y'=\frac{6(\ln x)^5}{x}$
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test review #3, chapter 5 score: 6.5/37 answered: 6/37 question 7 given…
The y-intercept is $0$ The x-intercepts is/are $-3, 0, 4$ When $x \to \infty$, $y \to \infty$ When $x \to -\infty$, $y \to -\infty$