Math Statement

Problem 15201

1). Find the coordinates of the vertex of the following quadratic functions: [3K] b).. y=4x216x+7y=4 x^{2}-16 x+7

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Problem 15202

on 12. Homework YOUR SCORE: 8 Simplify. 60 1b1 b 1c1 c 1d (e) (a3)+(a5)=(a-3)+(a-5)= 1 g 2a 2b 2 e 2f2 f 2 g
Answer: \square GRADE ANSWER

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Problem 15203

12) Sketch the function y=[(x2)]4+12y=-[(x-2)]^{4}+12. Use the mapping formula applied to 5 key points to sketch [A-5] 13) Write the equation of the transformed parent function y=x3y=x^{3}. [A-5]
Simplify your answer. Show your work.

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Problem 15204

Perform the indicated operation. Simplify the result if possible. 6yd2fl×46 \mathrm{yd} 2 \mathrm{fl} \times 4

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Problem 15205

4. Write each of the following as a simplified rational expression. a) c2c+26\frac{c}{2}-\frac{c+2}{6} b) a+23+a35\frac{a+2}{3}+\frac{a-3}{5} c) t24t35\frac{t-2}{4}-\frac{t-3}{5} d) 2y34y+47\frac{2 y-3}{4}-\frac{y+4}{7} e) 2x3352x9\frac{2 x-3}{3}-\frac{5-2 x}{9} f) x4+x+36+3x2\frac{x}{4}+\frac{x+3}{6}+\frac{3 x}{2}
5. Simplify the following. a) 2y552-\frac{y-5}{5} b) 3a+4121\frac{3 a+4}{12}-1 c) t7tt33\frac{t}{7}-t-\frac{t-3}{3}

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Problem 15206

1. Circle all of the following polynomials that are DEGREE 2: [1 mark] 2x+34x2+3x1(x+3)(x2)(x+4)28\begin{array}{llll} 2 x+3 & -4 x^{2}+3 x-1 & (x+3)(x-2) & (x+4)^{2}-8 \end{array}

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Problem 15207

Aufgabe 2 Untersuchen Sie rechnerisch, ob der Graph der Funktion f achsensymmetrisch zur y-Achse oder punktsymmetrisch zum Ursprung ist. a) f(x)=x4x2f(x)=x^{4}-x^{2} b) f(x)=sin(2x)f(x)=\sin (2 x) c) f(x)=cos(x)+1f(x)=\cos (x)+1 d) f(x)=4xf(x)=\frac{4}{x} e) f(x)=2x3+3xf(x)=\frac{2}{x^{3}}+\frac{3}{x} f) f(x)=x3x5f(x)=x^{3} \cdot x^{5}
Aufgabe 3 Untersuchen Sie, ob der Graph der Funktion f eine Symmetrie zum Koordinatensystem aufweist. Überprü̈ Sie Ihr Ergebnis mit einem Funktionenplotter. a) f(x)=sin(1x)f(x)=\sin \left(\frac{1}{x}\right) b) f(x)=(x2)2+1f(x)=(x-2)^{2}+1 c) f(x)=sin(x)cos(x)f(x)=\sin (x) \cos (x) d) f(x)=(sin(x))2f(x)=(\sin (x))^{2} e) f(x)=x1x2f(x)=\frac{x-1}{x^{2}} f) f(x)=x21x2f(x)=\frac{x^{2}-1}{x^{2}}

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Problem 15208

1. Risolvi l'equazione: x+5=(2x5)(x+5)x+\sqrt{5}=(2 x-\sqrt{5})(x+\sqrt{5}).

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Problem 15209

6 What is the difference: 45(710)\frac{-4}{5}-\left(\frac{-7}{10}\right) ? 6. \qquad A) 32\frac{-3}{2} B) 310\frac{3}{10} C) 110\frac{-1}{10} D) 32\frac{3}{2}
7. What -is the product 14×(35)\frac{1}{4} \times\left(\frac{-3}{5}\right) ?
7. \qquad A) 320\frac{-3}{20} B) 29\frac{-2}{9} C) 320\frac{3}{20} D) 720\frac{-7}{20}

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Problem 15210

You can drag the values to rearrange them! x16=624x=??\begin{array}{l} \frac{x}{16}=\frac{6}{24} \\ x=\square ? ? \end{array}

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Problem 15211

3. Evaluate: A) 119+(176)\frac{11}{9}+\left(\frac{-17}{6}\right) \quad (2 marks)

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Problem 15212

\begin{align*} 2x &= 4 + 2 \\ 1 + X Y \end{align*}

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Problem 15213

{2x3)2=4x12\{2 x-3)^{2}=4 x^{12}

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Problem 15214

2. Solve the following: 4sinxcosx+3=04 \sin x \cos x+\sqrt{3}=0 given 0x<2π0 \leq x<2 \pi 4sinxcosx+3=04(sinxcosx)+3=0\begin{array}{l} 4 \sin x \cos x+\sqrt{3}=0 \\ 4(\sin x \cos x)+\sqrt{3}=0 \end{array}

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Problem 15215

6. Prove the Trig Identities. a. cosθ×tanθ=sinθ\cos \theta \times \tan \theta=\sin \theta

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Problem 15216

2. Divide: x32x2x\frac{x^{3}-2 x^{2}}{x}
3. Divide: 12x3+6x23x\frac{12 x^{3}+6 x^{2}}{3 x}
4. Divide: 15x2y3+5xy5xy\frac{15 x^{2} y^{3}+5 x y}{5 x y}
5. Divide: 8x34x24x2\frac{8 x^{3}-4 x^{2}}{4 x^{2}}

Part B: Medium-Challenging Division
6. Divide: 3x3+x2xx+1\frac{3 x^{3}+x^{2}-x}{x+1}
7. Divide: 4x48x3+2x22x2\frac{4 x^{4}-8 x^{3}+2 x^{2}}{2 x^{2}}
8. Divide: x33x2+3x1x1\frac{x^{3}-3 x^{2}+3 x-1}{x-1}
9. Divide: 6x47x3+x2+x2x2\frac{6 x^{4}-7 x^{3}+x^{2}+x}{2 x^{2}}
10. Divide: x45x2+4x21\frac{x^{4}-5 x^{2}+4}{x^{2}-1}

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Problem 15217

b) cos10cos7sin10sin7\cos 10^{\circ} \cos 7^{\circ}-\sin 10^{\circ} \sin 7^{\circ} cos(10+7)2cos\cos (10+7)-2 \cos d) sinπ3cosπ4cosπ3sinπ4\sin \frac{\pi}{3} \cos \frac{\pi}{4}-\cos \frac{\pi}{3} \sin \frac{\pi}{4}

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Problem 15218

sin(π3π4)2sin(4π123π12)\sin \left(\frac{\pi}{3}-\frac{\pi}{4}\right)-2 \sin \left(\frac{4 \pi}{12}-\frac{3 \pi}{12}\right) \rightarrow
Simplify and then give an exact value for each expression. a) cos25cos5sin25sin5\cos 25^{\circ} \cos 5^{\circ}-\sin 25^{\circ} \sin 5^{\circ} cos25cos5sin25sin5cos(25+5)8cos(30)32\begin{array}{l} \cos 25^{\circ} \cos 5^{\circ}-\sin 25^{\circ} \sin 5^{\circ} \\ \Rightarrow \cos (25+5)-8 \cos \left(30^{\circ}\right) \rightarrow \frac{\sqrt{3}}{2} \end{array} d) cos7π12cosπ3+sin7π12sinπ3\cos \frac{7 \pi}{12} \cos \frac{\pi}{3}+\sin \frac{7 \pi}{12} \sin \frac{\pi}{3}

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Problem 15219

limx1x3+x2+x+1x+1\lim _{x \rightarrow-1} \frac{x^{3}+x^{2}+x+1}{x+1}

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Problem 15220

3.32. Në qoftë se densiteti i XX është f(x)=1,0<x<1f(x)=1, \quad 0<x<1 gjeni E[etX]E\left[e^{t X}\right]. Kryeni llogaritjet për të gjetur E(Xn)E\left(X^{n}\right).

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Problem 15221

Welche Zahlen darfst du nicht für die Variablen einsetzen? a) 4xx(x+2)\frac{4 x}{x(x+2)} c) 9x(x+3)(x2)\frac{9-x}{(x+3)(x-2)} e) 3(x2)(x1)\frac{3}{(x-2)(x-1)} g) 1x(x2)\frac{1}{x(x-2)} b) 2+xx(x4)\frac{2+x}{x(x-4)} d) 4x5(x5)(x+2)\frac{4 x-5}{(x-5)(x+2)} f) 2x(x2)(x+2)\frac{2-x}{(x-2)(x+2)} h) 4+x(x1)(x+1)\frac{4+x}{(x-1)(x+1)}

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Problem 15222

2. Calculate [H3O+],[ClO4]\left[\mathrm{H}_{3} \mathrm{O}^{+}\right],\left[\mathrm{ClO}_{4}\right] and [OH][\mathrm{OH}] in an aqueous solution that is 0.150 M in HClO4(aq)\mathrm{HClO}_{4}(\mathrm{aq}). Is the solution acidic or basic?
3. Calculate, [OH],[K+]\left[\mathrm{OH}^{-}\right],\left[\mathrm{K}^{+}\right]and [H3O+]\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]in an aqueous solution that is 0.250 M in KOH(aq)\mathrm{KOH}(\mathrm{aq}). Is the solution acidic or basic?
4. Compute [Ca2+],[OH]\left[\mathrm{Ca}^{2+}\right],\left[\mathrm{OH}^{-}\right]and [H3O+]\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]for a solution that is prepared by dissolving 0.600 g of Ca(OH)2\mathrm{Ca}(\mathrm{OH})_{2} in enough water to make 0.500dm30.500 \mathrm{dm}^{3} of solution.

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Problem 15223

Exerace 市II: 4m<2,+5<n<8;1<a3<2-4 \leqslant m<-2,+5<n<8 ; 1<a_{-3}<2 2) Encadrer 1m+n;nm;mn;m2;m2n31 m+n ; n \cdot m ; m n ; m^{2} ; \frac{m^{2}}{n-3} 2) Mortier que 5<a<4-5<a<-4. 3) Verifier que 0<a+n2<20<\sqrt{\frac{a+n}{2}}<\sqrt{2}

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Problem 15224

[1,+[[1,+\infty[ J (x1)+lnx0(x-1)+\ln x \geqslant 0 is

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Problem 15225

14(2x3)dx\int_{1}^{4}\left(2-\frac{x}{3}\right) d x using Diemann Sum

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Problem 15226

(x1)+lnx0(x-1)+\ln x \geqslant 0 if

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Problem 15227

Select the correct answer.
Determine which equation has the same solutions as the given equation. x210x11=0x^{2}-10 x-11=0 A. (x10)2=36(x-10)^{2}=36 B. (x5)2=21(x-5)^{2}=21 C. (x5)2=36(x-5)^{2}=36 D. (x10)2=21(x-10)^{2}=21

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Problem 15228

find the derivative of (x+c)ex(x+c) e^{x}

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Problem 15229

f(x)=(x3+3x+8)3f(x)=\left(x^{3}+3 x+8\right)^{3} f(x)=f(1)=\begin{array}{l} f^{\prime}(x)= \\ f^{\prime}(1)= \end{array}

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Problem 15230

Let f(x)=x+1xf(x)=x+\sqrt{1-x} Find the local maximum and minimum values of ff using both the first and second derivative tests. Which method do you prefer? (That last question can be treated as rhetorical)
Below, type none if there are none. Points with local maximum values \square Points with local minimum values \square
Note: You can earn partial credit on this problem. Preview My Answers Submit Answers

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Problem 15231

Compute the following limits using L'Hospital's rule if appropriate. Use INF to denote oo and MINF to denote limx177x21=limxtan1(x)(1/x)7=\begin{array}{l} \lim _{x \rightarrow 1} \frac{7^{\infty}-7}{x^{2}-1}=\square \\ \lim _{x \rightarrow \infty} \frac{\tan ^{-1}(x)}{(1 / x)-7}= \end{array} \square
Note: You can earn partial credit on this problem.

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Problem 15232

Consider the limit limx0sin2(8x)1cos(8x)\lim _{x \rightarrow 0} \frac{\sin ^{2}(8 x)}{1-\cos (8 x)}
To simplify this limit, we should multiply numerator and denominator by the expression \square After doing this and simplifying the result we find that the value of limit is \square
Note: You can earn partial credit on this problem. Preview My Answers Submit Answers

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Problem 15233

NYA Module 7: Problem 11
For each of the following forms determine whether the following limit type is indeterminate, always has a fixed finite value, or never has a fixed finite value. In the first case answer IND, in the second enter the numerical value, and in the third case answer DNE. To discourage blind guessing, this problem is graded on the following scale 09 correct = 01013 correct =.31416 correct =.51719 correct =.7\begin{array}{l} 0-9 \text { correct = } 0 \\ 10-13 \text { correct }=.3 \\ 14-16 \text { correct }=.5 \\ 17-19 \text { correct }=.7 \end{array}
Note that l'Hospital's rule (in some form) may ONLY be applied to indeterminate forms.
1. \infty^{-\infty}
2. 0\infty^{-0}
3. \infty^{\infty}
4. 1\infty^{1}
5. π\pi^{\infty}
6. 11^{\infty} 7.107.1^{0}
8. 0\infty^{0}
9. π\pi^{-\infty} 10.10 . \infty \cdot \infty
11. 0\frac{0}{\infty}
12. 1\frac{1}{-\infty} 13.013.0 \cdot \infty
14. 0\frac{\infty}{0}
15. 11^{-\infty} 16.116.1 \cdot \infty
17. \infty-\infty 18.0018.0^{0} \square 19.019.0^{\infty} \square 20. 00^{-\infty}

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Problem 15234

Q9) [4,3[4,3 K] Simplify. State any and all 2x2+5x+34x24x15÷3x2+2x12x2+3x20\frac{2 x^{2}+5 x+3}{4 x^{2}-4 x-15} \div \frac{3 x^{2}+2 x-1}{2 x^{2}+3 x-20}

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Problem 15235

f(x)=2x3+x225x+12x3 f(x) = \frac{2x^3 + x^2 - 25x + 12}{x - 3}

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Problem 15236

7. Evaluate: log8(1128)\log _{8}\left(\frac{1}{128}\right)

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Problem 15237

 caushy y3xy+4x2y=0x>0\begin{array}{l}\text { caushy } \\ y^{\prime \prime}-\frac{3}{x} y^{\prime}+\frac{4}{x^{2}} y=0 \quad{ }^{\prime} \quad x^{\prime}>0\end{array}

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Problem 15238

0ex2dx\int_{0}^{\infty} e^{-x^{2}} d x

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Problem 15239

11. Which three of the following show correct calculations for finding 7%7 \% of 900 ? \square 900×7100(900×1%)×7\frac{900 \times \frac{7}{100}}{(900 \times 1 \%) \times 7} \square 900÷7%900 \div 7 \% B
(900×1%)×7(900 \times 1 \%) \times 7
900×0.07900 \times 0.07 D 900×0.07%900 \times 0.07 \% step きiew next step vv

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Problem 15240

4. Expand the following: =25a2=25 a^{2} A. (22)2=(22)^{2}= B. (102)2=(102)^{2}= C. (54)2=(-54)^{2}= D. (59)2=(59)^{2}=

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Problem 15241

Q Q If y1=x^{y_{1}}=x is solution of (x2x)y+xy+y=0\left(x^{2}-x\right) y^{\prime \prime}+x y^{\prime}+y=0 find the General solution

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Problem 15242

Give a vector parametric equation for the line through the point (1,0,4)(-1,0,4) that is parallel to the line 45t,44t,52t\langle 4-5 t, 4-4 t, 5-2 t\rangle : L(t)=L(t)=

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Problem 15243

Estima el cociente. 28.3÷928.3 \div 9 A. 30 B. 10 C. 1 D. 3

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Problem 15244

Estima el cociente. 4.81÷0.974.81 \div 0.97 5 1 0 50

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Problem 15245

You must clearly show your steps for every problem below.
1. Find all distinct (real or complex) eigenvalues of AA. Then find the basic eigenvectors of AA corresponding to each eigenvalue. A=[420206242441616]A=\left[\begin{array}{ccc} 4 & 20 & -20 \\ -6 & -24 & 24 \\ -4 & -16 & 16 \end{array}\right]

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Problem 15246

Estima el cociente redondeando cada número al número entero más cercano. 33.7÷9.533.7 \div 9.5
Escribe tu respuesta en el recuadro.

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Problem 15247

All parts of this question concern the function f(x)=7sinx+3cosxf(x)=7 \sin x+3 \cos x. We will centre our approximation about x=0x=0. (a) Find the smallest positive constant MM that satisfies Mf(k)(t)M \geq\left|f^{(k)}(t)\right| for every possible combination of an integer k0k \geq 0 and an evaluation point t(,+)t \in(-\infty,+\infty).
Hint: A standard trigonometric identity implies that, for a certain angle ϕ\phi, one has f(x)=58sin(x+ϕ)f(x)=\sqrt{58} \sin (x+\phi) for all real xx. Answer, M=M= sqrt58 \square
Let Tn(x)T_{n}(x) be the nnth order Maclaurin expansion of f(x)f(x). Recall the standard decomposition f(x)=Tn(x)+En(x)f(x)=T_{n}(x)+E_{n}(x), in which Lagrange's formula says En(x)=f(n+1)(n+1)!xn+1E_{n}(x)=\frac{f^{(n+1)}}{(n+1)!} x^{n+1} for some tt between 0 and xx. This is valid for every integer n0n \geq 0.
In both parts below, estimate En(x)E_{n}(x) using Lagrange's formula with the constant MM found in part (a). (Use technology as required.) (b) Find the smallest nn for which the polynomial value Tn(0.5)T_{n}(0.5) provides an approximation for f(0.5)f(0.5) that is guaranteed by the Lagrange Remainder Theorem, using the value of MM from befor to be accurate to within 9 decimal places:
Answer: n=n= 10 \square Hint: To guarantee DD correct digits after the decimal point, accounting for rounding, one must have En(0.5)0.5×10D\left|E_{n}(0.5)\right| \leq 0.5 \times 10^{-D}. (c) Suppose n=6n=6 is prescribed. Using the same constant MM as before, find the largest positive number a such that the approximation T6(x)T_{6}(x) for f(x)f(x) is guaranteed to be accurate to within 9 decimal places, for all xx in the symmetric interval (a,a)(-a, a).
Answer: a=a= \square
Remark: Estimations of this type often present a trade-off: getting the best possible bound for MM might allow you to find a simpler estimation (that is, using a smaller-order Taylor polynomial), but finding the best-possible MM can be hard. Sometimes the best use of time is to quickly find a weaker value of MM, and then use a higher-order Taylor polynomial, if the higher-order Taylor polynomial is relatively easy to compute.

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Problem 15248

Wählen Sie bei den folgenden Aufgaben die geeignetste Methode.
7 a) 9x=y+49 x=y+4 3x+y=53 x+y=5 f) 6x4y=106 x-4 y=10 b) x2y=5x-2 y=-5 x2=0,5yx-2=0,5 y g) x+2y=12x+2 y=12

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Problem 15249

650 Hz2=3(343 ms343+11mss)650 \mathrm{~Hz}_{2}=3\left(\frac{343 \mathrm{~ms}}{343+11 \mathrm{mss}}\right)

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Problem 15250

ample 4: Write the equation y=2x83y=|-2 x-8|-3 in the form y=axp+qy=a|x-p|+q, then sketch the graph using transformations.  vertex =(p,q)=(4,3)\begin{aligned} \text { vertex } & =(p, q) \\ & =(-4,3) \end{aligned}

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Problem 15251

Is 672,0886,068-672,088-6,068 positive or negative? positive negative

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Problem 15252

A company determined that the marginal cost, C(x)C^{\prime}(x) of producing the xx th unit of a product is given by C(x)=x34xC^{\prime}(x)=x^{3}-4 x. Find the total cost function CC, assuming that C(x)C(x) is in dollars and that fixed costs are $8000\$ 8000.

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Problem 15253

picy (Max 100\%) 3(12xy)(2x7y)3(12 x-y)(2 x-7 y)

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Problem 15254

g(x,y)=x2y22x;Rg(x, y)=x^{2}-y^{2}-2 x ; R : is the closed region in the xyx y-plane bounded by the graphs y=x2y=x^{2} and y=4y=4. Absolute minimum of -17 at (1,4)(1,4); Absolute maximum of 2 at (1,1)(-1,1)

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Problem 15255

The total cost (in dollars) of producing xx coffee machines is C(x)=1700+50x0.7x2C(x)=1700+50 x-0.7 x^{2} (A) Find the exact cost of producing the 21st machine.
Exact cost of 21st machine == \square (B) Use marginal cost to approximate the cost of producing the 21st machine.
Approx. cost of 21 st machine == \square

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Problem 15256

Consider the surface 9y+6=6xcos(y)e6z9 y+6=6 x \cdot \cos (y) \cdot e^{6 z} at the point P(8,0,0)P(8,0,0). a. Choose the correct equation for the tangent plane to the surface at that point.
Click for List 6x9y+288z48=06 x-9 y+288 z-48=0 b. 6x+9y+288z48=06 x+9 y+288 z-48=0 urface at that point. 6x48=06 x-48=0 6x+9y+288z+48=06 x+9 y+288 z+48=0 6x+48=06 x+48=0 \infty α\alpha Ω\Omega

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Problem 15257

Consider the function f(x)=x5ln(x),15x8f(x)=x-5 \ln (x), \quad \frac{1}{5} \leq x \leq 8. The absolute maximum value is \square and this occurs at xx equals \square The absolute minimum value is \square and this occurs at xx equals \square

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Problem 15258

Find the area of the shaded region. f(x)=x44x3+12x2,g(x)=3x+90f(x)=x^{4}-4 x^{3}+12 x^{2}, g(x)=-3 x+90

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Problem 15259

1. Reduce to lowest terms. a) 3xx3\frac{3 x}{x^{3}} b) 5x510x10\frac{5 x-5}{10 x-10} c) Express 14x\frac{1}{4-x} as a fraction with denominator x4x-4 d) Express as fractions with a common denominator. 2x\frac{2}{x} and 8y\frac{8}{y}

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Problem 15260

The ellipsoid x2+2y2+z2=10x^{2}+2 y^{2}+z^{2}=10 and sphere x2+y2+z23x+y+3z+4=0x^{2}+y^{2}+z^{2}-3 x+y+3 z+4=0 are tangent to each other at a point P(a,b,c)P(a, b, c) where a=2a=2 \text {. }
Find the remaining coordinate values. - b=b= absin(a)xfa^{b} \quad \sin (a) \quad \frac{\partial}{\partial x} f : \infty α\alpha Ω\Omega \square ? - c=c= aba^{b} sin(a)xf\sin (a) \quad \frac{\partial}{\partial x} f \because \infty α\alpha Ω\Omega

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Problem 15261

Calculer l'aire de la région fermée délimitée par les courbes suivantes. f(x)=1x et g(x)=1 sur [12,2]f(x)=\frac{1}{x} \text { et } g(x)=1 \text { sur }\left[\frac{1}{2}, 2\right] \text {. }

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Problem 15262

Évaluer les intégrales suivantes. a) (5x74x3+8x2)dx\int\left(\frac{5 x^{7}-4 x^{3}+8}{x^{2}}\right) d x b) (secxtanxsinx)dx\int(\sec x-\tan x \sin x) d x

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Problem 15263

Prove that cos2ϕ1sinϕ=1+sinϕ\frac{\cos ^{2} \phi}{1-\sin \phi}=1+\sin \phi, where sinϕ1\sin \phi \neq 1, by expressing cos2ϕ\cos ^{2} \phi in terms of sinϕ\sin \phi.

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Problem 15264

Dimostrare che n0,11\forall n \geq 0,11 divide 9n+1+26n+19^{n+1}+2^{6 n+1}

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Problem 15265

a) 12x(5x4) 12x(5x-4)

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Problem 15266

3x[(x3)+y]2y[(y+7)x]3 x[(x-3)+y]-2 y[(y+7)-x]

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Problem 15267

Solve the system by using the substitution method. 5xy=18x=2y+0\begin{array}{l} 5 x-y=18 \\ x=2 y+0 \end{array} (x,y)=((x, y)=( , \square

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Problem 15268

10.5. Which of the following statements are true? A) Let u\mathbf{u} and v\mathbf{v} be any two vectors in Rn\mathbb{R}^{n}. Then uv0\mathbf{u} \cdot \mathbf{v} \geq 0. B) Let u\mathbf{u} and v\mathbf{v} be vectors in Rn\mathbb{R}^{n} such that uv<0\mathbf{u} \cdot \mathbf{v}<0. Then u=cv\mathbf{u}=-c \mathbf{v}, for some scalar c>0c>0. C) Let u\mathbf{u} and v\mathbf{v} be vectors in Rn\mathbb{R}^{n} and let θ,0θπ\theta, 0 \leq \theta \leq \pi be the angle between them. If uv<0\mathbf{u} \cdot \mathbf{v}<0, then π2<θπ\frac{\pi}{2}<\theta \leq \pi. D) Let u\mathbf{u} and v\mathbf{v} be vectors in Rn\mathbb{R}^{n} such that uv=0\mathbf{u} \cdot \mathbf{v}=0. Then either u=0\mathbf{u}=\mathbf{0} or v=0\mathbf{v}=\mathbf{0}.

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Problem 15269

10.6. Find the angle θ,0θπ\theta, 0 \leq \theta \leq \pi between the vectors u=[122] and v=[221]\mathbf{u}=\left[\begin{array}{r} 1 \\ -2 \\ 2 \end{array}\right] \text { and } \mathbf{v}=\left[\begin{array}{r} -2 \\ 2 \\ 1 \end{array}\right]

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Problem 15270

Évaluer les intégrales définies suivantes. a) π4π2sinθecosθdθ\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \sin \theta \cdot e^{\cos \theta} d \theta b) 05x3dx\int_{0}^{5}|x-3| d x

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Problem 15271

Solve the equation for yy. 4x+y=8y=\begin{array}{l} 4 x+y=8 \\ y=\square \end{array}

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Problem 15272

The ellipsoid 2x2+5y2+z2=68552/4412 x^{2}+5 y^{2}+z^{2}=68552 / 441 and sphere x2+y2+z23x4y4z526/441=0x^{2}+y^{2}+z^{2}-3 x-4 y-4 z-526 / 441=0 are tangent to each other at a point P(a,b,c)P(a, b, c) where a=2.a=2 .
Find the remaining coordinate values. - b=b= absin(a)xfa^{b} \quad \sin (a) \quad \frac{\partial}{\partial x} f : \square \square \square \square ? - c=c= absin(a)xfa^{b} \quad \sin (a) \quad \frac{\partial}{\partial x} f \square

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Problem 15273

Solve the inequality. 27y4-\frac{2}{7} y \leq 4
The solution set is {y\{y \mid \square

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Problem 15274

Graph this line using the slope and yy-intercept: y=5x+1y=5 x+1
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Problem 15275

Divide. (7v3x6+24v7x6)÷(4v4x3)\left(-7 v^{3} x^{6}+24 v^{7} x^{6}\right) \div\left(-4 v^{4} x^{3}\right)
Simplify your answer as much as possible.

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Problem 15276

(7.01×103)+(5.6×101)\left(7.01 \times 10^{3}\right)+\left(5.6 \times 10^{-1}\right)
PLY YOUR SKILLS Find the number of second The speed of liaht is appro

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Problem 15277

Graph this line using the slope and yy-intercept: y=35x4y=\frac{3}{5} x-4
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Problem 15278

Use the product rule to simplify the expression. (2y3)(2y3)\left(2 y^{3}\right)\left(2 y^{3}\right)

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Problem 15279

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Solve the system by the addition method 2x+4y=22x4y=2\begin{array}{l} 2 x+4 y=2 \\ 2 x-4 y=2 \end{array}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The sofution set is \{ . (Type an ordered pair) B. There are infinitely many solutions C. There is no solution e this View an example Get more help - Clear all Check answer Search 5:30 PM 11/28/2024

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Problem 15280

Use the power rule and the power of a product or quotient rule to simplify the expression. Assume that all bases are not equal to 0 . (rs)3\left(\frac{r}{s}\right)^{3}

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Problem 15281

Solve the system by the method of your choice. {x=2y+23x+6y=6\left\{\begin{array}{l} x=2 y+2 \\ -3 x+6 y=-6 \end{array}\right.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is exactly one solution. The solution set is }\}. (Simplify your answer. Type an ordered pair.) \square B. There are infinitely many solutions. The solution set is {(x,y)x=2y+2}\{(x, y) \mid x=2 y+2\} or {(x,y)3x+6y=6}\{(x, y) \mid-3 x+6 y=-6\}. C. The solution set is \varnothing.

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Problem 15282

Graph this line using the slope and yy-intercept: y=3x3y=3 x-3
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Problem 15283

Solve the system by the method of your choice. {2x=3y98x=94y\left\{\begin{array}{l} 2 x=3 y-9 \\ 8 x=9-4 y \end{array}\right.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is }\}. (Type an integer or a simplified fraction. Type an ordered pair.) B. There are infinitely many solutions. The solution set is {(x,y)2x=3y9}\{(x, y) \mid 2 x=3 y-9\} or {(x,y)8x=94y}\{(x, y) \mid 8 x=9-4 y\}. C. The solution set is \varnothing.

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Problem 15284

2x+3y+z=5L15x+y+3z=0L2x+2yz=4L3\begin{array}{l}2 x+3 y+z=5 L_{1} \\ 5 x+y+3 z=0 L_{2} \\ x+2 y-z=4 L_{3}\end{array}

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Problem 15285

Use the product rule to simplify the expression. Write the result using exponents. y2y4y2y4=\begin{array}{c} y^{2} \cdot y^{4} \\ y^{2} \cdot y^{4}= \end{array}

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Problem 15286

Simplify: 7.5(13)27.5 \cdot\left(\frac{1}{3}\right)^{2} \square

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Problem 15287

13. One xx-value in the solution to the system of equations y=2x2+2x+ky=2 x^{2}+2 x+k and y=3x2y=3 x-2 is x=52x=\frac{5}{2}. The value of kk must be A. -10 (B.) -12 C. 10 D. 12

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Problem 15288

For f(x)=4x3f(x)=\frac{4}{x-3} and g(x)=1xg(x)=\frac{1}{x}, find the following composite functions and state the domain of each. (a) fgf \circ g (b) gfg \circ f (c) fff \circ f (d) ggg \circ g

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Problem 15289

11. Find constants aa and bb that guarantee that the graph of the function defined by f(x)=ax+53bxf(x)=\frac{a x+5}{3-b x} will have a vertical asymptote at x=5x=5 and a horizontal asymptote at y=3y=-3.

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Problem 15290

Consider the surface at the point P(0,3,0)P(0,3,0). 4z+3=9e9xycos(z)4 z+3=9 e^{9 x} \cdot y \cdot \cos (z) a. Choose the correct equation for the tangent plane to the surface at that point. 243x+9y4z27=0243 x+9 y-4 z-27=0 b. Find a vector v\mathbf{v} that is normal to the surface at that point.

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Problem 15291

5) y=(2x5+3)cosx2y=\left(2 x^{5}+3\right) \cos x^{2} (2x5+3)\left(2 x^{5}+3\right)

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Problem 15292

Hence, or otherwise, solve the following equation, where xRx \in \mathbb{R} : 24x+1=1282^{4 x+1}=128

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Problem 15293

Solve the system using addition/elimination method. If there is exactly one solution, write as an ordered pair. If not, choose one of the other options. {2x2y=123x+5y=20\left\{\begin{array}{l} 2 x-2 y=-12 \\ -3 x+5 y=20 \end{array}\right. One solution: \square No solution Infinite number of solutions

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Problem 15294

Solve the equation analytically. 22x5=162^{2 x-5}=16
The solution set is \square (Simplify your answer.)

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Problem 15295

7. Jonsider the function P(x)=2x28x7P(x)=-2 x^{2}-8 x-7 7a7 a Find the xx-coordinate of the vertex x=x=
Enter your next step here

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Problem 15296

1. [-/1 Points] DETAILS MY NOTES SCALCET9 4.9.006.
Find the most general antiderivative of the function. (Check your answer by differentiation. Use CC for the constant of the antiderivative. f(x)=x27x+8F(x)=\begin{array}{l} f(x)=x^{2}-7 x+8 \\ F(x)=\square \end{array} Need Help? Road It Submit Answer

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Problem 15297

90×90=90 \times 90=

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Problem 15298

sinxcosxtanx=1cos2x\sin x \cos x \tan x=1-\cos ^{2} x

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Problem 15299

Determine the exact value of cscπ6\csc \frac{\pi}{6}. 23\frac{2}{\sqrt{3}} 2 32\frac{\sqrt{3}}{2}

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Problem 15300

Use the equation below to find PP, if a=12,b=4a=12, b=4, and c=15c=15. P=a+b+cP=a+b+c

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