Math Statement

Problem 3501

16+17=\frac{1}{6}+\frac{1}{7}= \square (Type an integer or a simplified fraction.)

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Problem 3502

dxdy=Axwithx(0)=x0\frac{dx}{dy} = Ax \quad \text{with} \quad x(0) = x_0 where A=[32121232],x0=[1212]A = \begin{bmatrix} -\frac{3}{2} & \frac{1}{2} \\ \frac{1}{2} & -\frac{3}{2} \end{bmatrix}, \quad x_0 = \begin{bmatrix} \frac{1}{2} \\ \frac{1}{2} \end{bmatrix}

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Problem 3503

Evaluate the integral. sec(9x5)tan(9x5)dx\int \sec (9 x-5) \tan (9 x-5) d x
Determine a change of variables from x to u . Choose the correct choice below.

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Problem 3504

Choose the statement(s) that correctly describe the system. {2x+z=06x+yz=64x+y+z=0\left\{\begin{array}{rr} 2 x+z= & 0 \\ 6 x+y-z= & -6 \\ 4 x+y+z= & 0 \end{array}\right.
Select all that apply. The system's complete solutian can be written as (5+3a3,3a3,a)\left(\frac{5+3 a}{3}, \frac{3-a}{3}, a\right), where aa is any real number. The system has a unique solution. The system has no solution. The system has infinitely many solutions. The system is consistent. One solution is (1,2,2)(-1,2,2). The system is dependent. The system's complete solution can be written as (2+6a,2a,a)(2+6 a, 2-a, a) where aa is any real number.

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Problem 3505

Which expression represents the determinant of A=[6742]A=\left[\begin{array}{cc}-6 & -7 \\ -4 & -2\end{array}\right] ? det(A)=(4)(7)(6)(2)\operatorname{det}(A)=(-4)(-7)-(-6)(-2) det(A)=(4)(7)+(6)(2)\operatorname{det}(A)=(-4)(-7)+(-6)(-2) det(A)=(6)(2)(4)(7)\operatorname{det}(A)=(-6)(-2)-(-4)(-7) det(A)=(6)(2)+(4)(7)5\operatorname{det}(A)=(-6)(-2)+(-4)(-7)^{5}

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Problem 3506

Evaluate the expression for y=19y=19 and z=4z=4. Simplify your answer. yzy3=\frac{y z-y}{3}= \square
Submit

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Problem 3507

Evaluate C5z+7z2+2z3dz\oint_{C} \frac{5 z+7}{z^{2}+2 z-3} d z, where C:z2=2\mathrm{C}:|z-2|=2.

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Problem 3508

Solve: 2<3x+61-2<3 x+6 \leq-1
The answer is \square <x<x \leq \square

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Problem 3509

Let α0\alpha \neq 0 and β0\beta \neq 0 be real nonzero constants. Define the following real symmetric matrices (1) A1=(ααααααααα)A_{1}=\left(\begin{array}{ccc}\alpha & -\alpha & \alpha \\ -\alpha & \alpha & \alpha \\ \alpha & \alpha & \alpha\end{array}\right), (2) A2=(αβββαβββα)A_{2}=\left(\begin{array}{ccc}\alpha & -\beta & -\beta \\ -\beta & \alpha & -\beta \\ -\beta & -\beta & \alpha\end{array}\right), (3) A3=(αββββαββββαββββα)A_{3}=\left(\begin{array}{cccc}\alpha & -\beta & -\beta & -\beta \\ -\beta & \alpha & -\beta & -\beta \\ -\beta & -\beta & \alpha & -\beta \\ -\beta & -\beta & -\beta & \alpha\end{array}\right), (4) A4=(αβαββαβααβαββαβα)A_{4}=\left(\begin{array}{cccc}\alpha & -\beta & \alpha & -\beta \\ -\beta & \alpha & -\beta & \alpha \\ \alpha & -\beta & \alpha & -\beta \\ -\beta & \alpha & -\beta & \alpha\end{array}\right) (5) A5=(αβ0000αβ0000αβ0000αβ0000α)\quad A_{5}=\left(\begin{array}{lllll}\alpha & \beta & 0 & 0 & 0 \\ 0 & \alpha & \beta & 0 & 0 \\ 0 & 0 & \alpha & \beta & 0 \\ 0 & 0 & 0 & \alpha & \beta \\ 0 & 0 & 0 & 0 & \alpha\end{array}\right)
Solve the following first order homogeneous systems of differential equations (1) ddtu=A1u\frac{\mathrm{d}}{\mathrm{d} t} \mathrm{u}=A_{1} \mathbf{u} (2) ddtu=A2u\frac{\mathrm{d}}{\mathrm{d} t} \mathbf{u}=A_{2} \mathbf{u} (3) ddtu=A3u\frac{\mathrm{d}}{\mathrm{d} t} \mathrm{u}=A_{3} \mathrm{u} (4) ddtu=A4u\frac{\mathrm{d}}{\mathrm{d} t} \mathbf{u}=A_{4} \mathbf{u} (5) For the system u=A5u\mathbf{u}^{\prime}=A_{5} \mathbf{u}, find a solution of the form u(t)=eat(ξ+ηt)\mathbf{u}(t)=e^{a t}(\xi+\eta t) where ξ\xi and η\eta are real nonzero constant vectors. Let α0,β0\alpha \neq 0, \beta \neq 0 and γ0\gamma \neq 0 be real nonzero constants. Let μ\mu be a real constant. Define the following real matrices (1) B1=(0110)B_{1}=\left(\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right), (2) B2=(0ββ0)B_{2}=\left(\begin{array}{cc}0 & \beta \\ -\beta & 0\end{array}\right), (3) B3=(αββα)B_{3}=\left(\begin{array}{cc}\alpha & \beta \\ -\beta & \alpha\end{array}\right), (4) B4=(0αβα0γβγ0)B_{4}=\left(\begin{array}{ccc}0 & \alpha & \beta \\ -\alpha & 0 & \gamma \\ -\beta & -\gamma & 0\end{array}\right) (5) B5=(μαβαμγβγμ)B_{5}=\left(\begin{array}{ccc}\mu & \alpha & \beta \\ -\alpha & \mu & \gamma \\ -\beta & -\gamma & \mu\end{array}\right).
Solve the first order homogeneous linear differential equations (6) ddtu=B1u\frac{\mathrm{d}}{\mathrm{d} t} \mathbf{u}=B_{1} \mathbf{u} (7) ddtu=B2u\frac{\mathrm{d}}{\mathrm{d} t} \mathbf{u}=B_{2} \mathbf{u} (8) ddtu=B3u\frac{\mathrm{d}}{\mathrm{d} t} \mathrm{u}=B_{3} \mathrm{u} (9) ddtu=B4u\frac{\mathrm{d}}{\mathrm{d} t} \mathbf{u}=B_{4} \mathbf{u} (10) ddtu=B5u\frac{\mathrm{d}}{\mathrm{d} t} \mathbf{u}=B_{5} \mathbf{u}

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Problem 3510

Solve: 1<5x821<5 x-8 \leq 2 The answer is \square <x<x \leq \square

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Problem 3511

Use Gauss-Jordan elimination to solve the system. {x+y=02x+y+z=1y+2z=11\left\{\begin{array}{rlr} x+y & =0 \\ 2 x+y+z & = & -1 \\ y+2 z & = & -11 \end{array}\right.

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Problem 3512

Find (fg)(x)(f \circ g)(x) given the functions f(x)=1xf(x)=\frac{1}{x} and g(x)=1x+9g(x)=\frac{1}{x+9}. Simplify your answer. (fg)(x)=x+9x(f \circ g)(x)=\frac{x+9}{x} (fg)(x)=1x2+9x(f \circ g)(x)=\frac{1}{x^{2}+9 x} (fg)(x)=x+9(f \circ g)(x)=x+9 (fg)(x)=1x+9(f \circ g)(x)=\frac{1}{x+9} (fg)(x)x1+9x(f \circ g)(x) \fallingdotseq \frac{x}{1+9 x}

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Problem 3513

Choose the statement(s) that correctly describe the system. {3x+z=212x+yz=1912x+y+z=17\left\{\begin{array}{rr} 3 x+z= & 2 \\ 12 x+y-z= & 19 \\ 12 x+y+z= & 17 \end{array}\right.

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Problem 3514

Choose the augmented matrix for the system of linear equations. {3x+y+z=010x10z=0x+10y+3z=10\left\{\begin{array}{c} 3 x+y+z=0 \\ 10 x-10 z=0 \\ x+10 y+3 z=10 \end{array}\right.

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Problem 3515

What is the domain and range of arccos(x)\arccos (x) and arcsin(x)?\arcsin (x) ?
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12pt • Paragraph

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Problem 3516

1. [-/1 Points] DETAILS MY NOTES
Fill in the blank. For the function y=asin(bxc),cby=a \sin (b x-c), \frac{c}{b} represents the \qquad ---Select one cycle of the graph of the function. Need Help? Read It Watch It

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Problem 3517

14x+3>5x+21 OR 13+6x13x614 x+3>5 x+21 \text { OR }-13+6 x \geq 13 x-6
Clear All Draw: \square

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Problem 3518

Evaluate the expression for r=2r=-2. Simplify your answer. r11r+15=\frac{r-11}{r+15}= \square
Submit

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Problem 3519

If f(x)=xcos1(3x+2)63x2f(x)=x \cos ^{-1}(3 x+2)-\sqrt{6-3 x^{2}}, find f(x)f^{\prime}(x)

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Problem 3520

Find the period and amplitude. y=6cos4xy=6 \cos 4 x period \square amplitude \square

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Problem 3521

Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.) n=0(1)n192n+1(2n+1)\sum_{n=0}^{\infty}(-1)^{n} \frac{1}{9^{2 n+1}(2 n+1)}

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Problem 3522

Find the exact value. log103log103=\begin{array}{c} \log 10^{3} \\ \log 10^{3}= \end{array}

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Problem 3523

ppose that the function gg is defined as follows. g(x)={2 if 2.5<x1.51 if 1.5<x0.50 if 0.5<x<0.51 if 0.5x<1.52 if 1.5x<2.5g(x)=\left\{\begin{array}{cc} -2 & \text { if }-2.5<x \leq-1.5 \\ -1 & \text { if }-1.5<x \leq-0.5 \\ 0 & \text { if }-0.5<x<0.5 \\ 1 & \text { if } 0.5 \leq x<1.5 \\ 2 & \text { if } 1.5 \leq x<2.5 \end{array}\right.
Graph the function gg. Explanation Check

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Problem 3524

Find the exact value. log0.0001log0.0001=\begin{array}{l} \log 0.0001 \\ \log 0.0001= \end{array}

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Problem 3525

Use a calculator to find the common logarithm. log(22)\log (22)
The answer is \square . (Round to four decimal places as needed.)

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Problem 3526

g) xx2+1x+4=2x26x+8\frac{x}{x-2}+\frac{1}{x+4}=\frac{2}{x^{2}-6 x+8}

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Problem 3527

Balancing chemical equations with interfering coemicents
Balance the chemical equation below using the smallest possible whole number stoichiometric coefficients. Fe(s)+O2(g)+H2O(l)Fe(OH)2(aq)\mathrm{Fe}(s)+\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{Fe}(\mathrm{OH})_{2}(a q)

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Problem 3528

Let a,ha, h, and kk be arbitrary real numbers with a0a \neq 0, and let ff be the function given by the rule f(x)=a(xh)2+kf(x)=a(x-h)^{2}+k.
Which of the following statements are true about ff ? Select all that apply.
A. The graph of y=f(x)y=f(x) is a line.
B. If a>0a>0, then ff has a global maximum. C. The graph of y=f(x)y=f(x) is a parabola. D. An extreme value occurs at the point (h,k)(h, k). E. If a>0a>0, then ff has a global minimum. F. The maximum value of f(x)f(x) is hh. G. None of the above
Next we use some calculus to develop familiar ideas from a different perspective. To start, treat a,ha, h, and kk as constants and compute f(x)f^{\prime}(x). f(x)=f^{\prime}(x)=\square
Find a critical value of ff. (This will depend on at least one of a,ha, h, and kk.) Critical value == \square Assume that a<0a<0. Make a derivative sign chart for ff. Based on this information, classify the critical value of ff as a maximum or minimum. A. maximum B. minimum C. neither

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Problem 3529

f(x)=4+6x47xf(x)=\frac{4+6 x}{4-7 x}
For each of the following, enter DNE if no such answer exist. Enter multiple values in a comma-separated list. Enter intervals using interval notation, including the union symbol when entering multiple intervals if necesary.
2. Determine all critical xx-value (s)(s) of f(x)f(x).

Critical value(s): \square b. Determine the interval(s) where f(x)f(x) is increasing.
Increasing: \square c. Deternine the interval(s) where f(x)f(x) is decreasing.
Decreasing: \square d. Deremine the xx-coordinate(s) of all local maxima of f(x)f(x). z-value(s) of local maximas: \square e. Detertmine the xx-coordinate of all local minima of f(x)f(x).
I valuer(s) of local minimas \square f. Determine che interval(s) where f(x)f(x) is concave up.
Concave up \square g. Deermine the interval(s) where f(x)f(x) is concave down.
Concave down: \square h. Deernine the xx-value(s) of all inflection point(s) of f(x)f(x). z-value(s) of inflection point(s): \square i. Deternine all horizonal asymptote(s) of f(x)f(x). y=y= \square j. Decermine all vertical asymprote( (x)(x) of f(x)f(x). \square
1. Use all of the preceding information to shecth a graph of f(x)f(x) on your own paper. Change the following to Yes when you're done.

Graph complete: \square 1

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Problem 3530

Consider the function f(x)=2x3+6x290x+7,5x4f(x)=2 x^{3}+6 x^{2}-90 x+7, \quad-5 \leq x \leq 4.
Find the absolute minimum value of this function. Answer: \square Find the absolute maximum value of this function. Answer: \square
Note: You can earn partial credit on this problem.

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Problem 3531

Factor by grouping. 24x315x2+8x524x315x2+8x5=\begin{array}{l} 24 x^{3}-15 x^{2}+8 x-5 \\ 24 x^{3}-15 x^{2}+8 x-5= \end{array}

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Problem 3532

Find the critical points and determine if the function is increasing or decreasing on the given intervals. y=3x4+6x3y=3 x^{4}+6 x^{3}
Left critical point: c1=c_{1}= \square Right critical point: c2=c_{2}= \square The function is: ? on (,c1)\left(-\infty, c_{1}\right). ? on (c1,c2)\left(c_{1}, c_{2}\right). ? on (c2,)\left(c_{2}, \infty\right).

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Problem 3533

Find the critical point and determine if the function is increasing or decreasing on the given intervals. y=x2+2x+7y=-x^{2}+2 x+7
Critical point: c=c= \square The function is: ? on (,c)(-\infty, c). ? on (c,)(c, \infty).

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Problem 3534

Find all critical points of the function f(x)=x23x+3f(x)=x^{2}-3 x+3 x=x=
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Problem 3535

Rework problem 18 from section 6.1 of your text, involving two constants, cc and dd. Use the following matrix equation instead of that found in your text to find the values of cc and dd which make the equation true. c[95]+d[21]=[11463]c\left[\begin{array}{l} -9 \\ -5 \end{array}\right]+d\left[\begin{array}{l} 2 \\ 1 \end{array}\right]=\left[\begin{array}{l} -114 \\ -63 \end{array}\right] (1) To make this equation true, set c=c= \square (2) And set d=d= \square Submit answer Next item

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Problem 3536

Complete the factoring. x2+10x+24x^{2}+10 x+24 x2+10x+24=(x+4)(x^{2}+10 x+24=(x+4)( \square )

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Problem 3537

Factor the polynomial. r2+9r+8r^{2}+9 r+8
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The answer is \square (Factor completely.) B. The polynomial is prime.

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Problem 3538

(1 point) Setup the Riemann sum abf(x)dx=limnk=1nf(xˉk)Δx\int_{a}^{b} f(x) d x=\lim _{n \rightarrow \infty} \sum_{k=1}^{n} f\left(\bar{x}_{k}\right) \Delta x for the given integral. Answer: 38x3dx=limnk=1n\int_{3}^{8} x^{3} d x=\lim _{n \rightarrow \infty} \sum_{k=1}^{n}

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Problem 3539

Determine whether the relation y=6x+12 y = 6x + 12 defines y y as a function of x x . Also, provide the domain of the function.

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Problem 3540

11. A model rocket is fired. For the first 10 seconds of its flight, the engine is firing. The height, hh metres, of the rocket above the ground during this time is given by the function: h=3t2+60th=-3 t^{2}+60 t, where tt is the time in seconds. a) Determine the maximum height the rocket reaches. b) At what time is the rocket 10 m above the ground?

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Problem 3541

Homework Part 1 of 2
Solve by the elimination method. Also determine whether the system is consistent or inconsistent and whether the equations are dependent or independent. 3x6y=152x4y=10\begin{array}{l} 3 x-6 y=15 \\ 2 x-4 y=10 \end{array}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is only one solution. The solution of the system is \square (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions of the form ( xx. \square ). (Simplify your answer.) C. There is no solution.

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Problem 3542

Part 2 of 3
Use the Substitution Formula, abf(g(x))g(x)dx=g(a)g(b)f(u)\int_{a}^{b} f(g(x)) \cdot g^{\prime}(x) d x=\int_{g(a)}^{g(b)} f(u) du where g(x)=ug(x)=u, to evaluate the following integral. 1102lnxxdx\int_{1}^{10} \frac{2 \ln x}{x} d x

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Problem 3543

If x3+63xy2=1sin(2x5)x^{3}+6-3 x y^{2}=-1-\sin \left(2 x^{5}\right), find dydx\frac{d y}{d x} when x=1,y=2x=1, y=2.

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Problem 3544

Factor the given polynomial completely. If the polynomial cannot be factored, say that it is prime. x22x63x^{2}-2 x-63
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. x22x63=x^{2}-2 x-63= \square B. The polynomial is prime.

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Problem 3545

Factor completely. a2+8ad+7d2a^{2}+8 a d+7 d^{2}
Select the correct choice below and fill in any answer boxes within your choice. A. a2+8ad+7d2=a^{2}+8 a d+7 d^{2}= \square B. The polynomial is prime.

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Problem 3546

ASKYOUR TEACHER V(t)=75(1t32)20t32V(t)=75\left(1-\frac{t}{32}\right)^{2} \quad 0 \leq t \leq 32. (a) Find V(0)V(0) and V(32)V(32). V(0)=galV(32)=gal\begin{array}{l} V(0)=\square \mathrm{gal} \\ V(32)=\square \mathrm{gal} \end{array} (b) What do your answers to part (a) represent? V(32)V(32) represents the the time when the tank is empty, and V(0)V(0) represents the time when it is full. V(0)V(0) represents the time when the tank is empty, and V(32)V(32) represents the time when it is full. V(0)V(0) represents the initial rate at which the water is leaking, and V(32)V(32) represents the rate at which it is leaking when 32 gallons have drained. V(0)V(0) represents the initial volume, and V(32)V(32) represents the final volume. V(32)V(32) represents the initial volume, and V(0)V(0) represents the final volume. (c) Make a table of values of V(t)V(t) for t=0,8,16,24,32t=0,8,16,24,32. (Round your answer to three decimal places.) \begin{tabular}{|c|c|} \hlinett (in minutes) & V(t)V(t) (in gallons) \\ \hline 0 & \square \\ 8 & \square \\ 16 & \square \\ 24 & \\ 32 & \\ \hline \end{tabular} (d) Find the net change in the volume VV as tt changes from 0 min to 32 min .

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Problem 3547

Function AA and Function B are linear functions. Function AA Function B y=2x1y=2 x-1 \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-7 & -21 \\ \hline 4 & 12 \\ \hline 6 & 18 \\ \hline \end{tabular}
Which statement is true?
The slope of Function A is greater than the slope of Function B.
The slope of Function AA is less than the slope of Function B.

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Problem 3548

Find the inverse of the function and differentiate the inverse in two ways. (i) Differentiate the inverse function directly. (ii) Use ddxf1(x)=1f[f1(x)]\frac{d}{d x} f^{-1}(x)=\frac{1}{f^{\prime}\left[f^{-1}(x)\right]} to find the derivative of the inverse. f(x)=4x+9,x94f(x)=\sqrt{4 x+9}, x \geq-\frac{9}{4}
The inverse of f(x)f(x) is f1(x)=y294f^{-1}(x)=\frac{y^{2}-9}{4}, \square x0x \geq 0 \text {. } for all xx. x90x \geq 90

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Problem 3549

Which expression represents the inverse of the matrix below? [1312]\left[\begin{array}{cc} 1 & 3 \\ -1 & 2 \end{array}\right] 15[2311]\frac{1}{5}\left[\begin{array}{cc}-2 & -3 \\ 1 & -1\end{array}\right] 11[2311]\frac{1}{-1}\left[\begin{array}{cc}-2 & -3 \\ 1 & -1\end{array}\right] 11[2311]\frac{1}{-1}\left[\begin{array}{cc}2 & -3 \\ 1 & 1\end{array}\right] 15[2311]\frac{1}{5}\left[\begin{array}{cc}2 & -3 \\ 1 & 1\end{array}\right]

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Problem 3550

The graph of f(x)=1xf(x)=\frac{1}{x} is shown below. Let gg be a transformation of f(x)=1xf(x)=\frac{1}{x} such that the graph of ff is shifted down 2 and right 4. Draw the graph of y=g(x)y=g(x) and write its formula below.
Clear All \square Write the formula for of g(x)g(x) below.

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Problem 3551

If AA and BB are matrices and AB=IA B=I, which of the following represents the value of BB ? A=[1438]A=\left[\begin{array}{cc} -1 & 4 \\ -3 & 8 \end{array}\right] [141342]\left[\begin{array}{cc}\frac{1}{4} & 1 \\ -\frac{3}{4} & -2\end{array}\right] [141342]\left[\begin{array}{cc}-\frac{1}{4} & -1 \\ \frac{3}{4} & 2\end{array}\right] [213414]\left[\begin{array}{cc}-2 & 1 \\ -\frac{3}{4} & \frac{1}{4}\end{array}\right] [213414]\left[\begin{array}{rr}2 & -1 \\ \frac{3}{4} & -\frac{1}{4}\end{array}\right]

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Problem 3552

Find the domain of the function. (Enter your answer using interval notation.) f(x)=1x5f(x)=\frac{1}{x-5} \square

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Problem 3553

Factor the trinomial completely. 7v2+52v+217 v^{2}+52 v+21
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 7v2+52v+21=7 v^{2}+52 v+21= \square B. The polynomial is prime.

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Problem 3554

1. You are given that 5xf(x)dx=35\int_{-5}^{x} f(x) d x=35 and 510f(x)dx=52\int_{-5}^{10} f(x) d x=52. What is the value of 2104f(x)dx?\int_{2}^{10} 4 f(x) d x ?

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Problem 3555

Factor completely. 9a249t29 a^{2}-49 t^{2}
Select the correct choice below and fill in any answer boxes within your choice. A. 9a249t2=9 a^{2}-49 t^{2}= \square B. The expression is prime.

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Problem 3556

Factor the following. 49x2+56x+1649 x^{2}+56 x+16
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 49x2+56x+16=49 x^{2}+56 x+16= \square B. 49x2+56x+1649 x^{2}+56 x+16 is prime.

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Problem 3557

y15=1812\frac{y}{15}=\frac{18}{12}

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Problem 3558

120=3.5z\frac{1}{20}=\frac{3.5}{z}

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Problem 3559

Listen
USING TOOLS Use technology to solve the system of linear equation 1.6x3.2y=242.6x+2.6y=26\begin{array}{l} -1.6 x-3.2 y=-24 \\ 2.6 x+2.6 y=26 \end{array}

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Problem 3560

Solve the following system of equations. 4x+7y=118x4z=246y4z=22\begin{aligned} 4 x+7 y & =-11 \\ 8 x-4 z & =-24 \\ 6 y-4 z & =-22 \end{aligned}
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution. The solution is \square . \square D) \square (Type integers or simplified fractions.) B. There are infinitely many solutions. The solutions are \square , z) (Type integers or simplified fractions.) C. There is no solution.

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Problem 3561

Consider the following expression. 2b+6a+5+7a2 b+6 a+5+7 a
Select all of the true statements below. 2b2 b is a factor. 6a6 a and 7a7 a are like terms. 2b2 b is a coefficient. 5 is a constant. 2b2 b is a term.
Try again f these are true.

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Problem 3562

7. 8 \longdiv { 2 , 3 4 5 }

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Problem 3563

8(1+6)(9v+4)8(1+6)(9 v+4) lect all of the true statements below. In (9v+4),9v(9 v+4), 9 v is a constant. 8 is a factor. (9v+4)(9 v+4) is written as a sum of three terms. In 9v,99 v, 9 is a coefficient. 1 and 6 are like terms.

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Problem 3564

Question
Solve for x . 28x=23\frac{28}{x}=\frac{2}{3}

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Problem 3565

(1 point) Setup the Riemann sum abf(x)dx=limnk=1nf(xˉk)Δx\int_{a}^{b} f(x) d x=\lim _{n \rightarrow \infty} \sum_{k=1}^{n} f\left(\bar{x}_{k}\right) \Delta x for the given integral. Answer: 02(3xx2)dx=limnk=1n\int_{0}^{2}\left(3 x-x^{2}\right) d x=\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \square
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Problem 3566

A population numbers 19,000 organisms initially and grows by 17.4\% each year. Suppose PP represents population, and tt the number of years of growth. An exponential model for the population can be written in the form P=abtP=a \cdot b^{t} where P=P=

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Problem 3567

Give the domain and range for the rational function. Use interval notation. f(x)=1(x7)2+5f(x)=\frac{1}{(x-7)^{2}}+5

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Problem 3568

If sin(α)=35\sin (\alpha)=\frac{3}{5} where 0<α<π20<\alpha<\frac{\pi}{2} and cos(β)=1517\cos (\beta)=\frac{15}{17} where 3π2<β<2π\frac{3 \pi}{2}<\beta<2 \pi, find the exact values of the following. (a) sin(α+β)\sin (\alpha+\beta) (b) cos(αβ)\cos (\alpha-\beta) \square Submit Answer

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Problem 3569

6. [-/1 Points]
DETAILS MY NOTES MARSVECTORCALC6 2.6.013.
Find a unit vector normal to the surface cos(xy)=ez2\cos (x y)=e^{z}-2 at (1,π,0)(1, \pi, 0). \square
Additional Materials eBook

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Problem 3570

Express as a single logarithm. logb(61)+logb(84)logb(61)+logb(84)=\log _{b}(61)+\log _{b}(84) \quad \log _{b}(61)+\log _{b}(84)=

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Problem 3571

9x2+42x+4909 x^{2}+42 x+49 \leq 0

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Problem 3572

Use long division to divide. Express any numbers as integers or simplified fractions. (x5+5x4+10x218x15)÷(x2+3)=\left(x^{5}+5 x^{4}+10 x^{2}-18 x-15\right) \div\left(x^{2}+3\right)=

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Problem 3573

Multiplying Polynomials Name Date
Find esech proelerce. 1) 6r(2x+3)12r2+18r\begin{array}{l} 6 r(2 x+3) \\ 12 r^{2}+18 r \end{array} 3) 2x(2x3)4x26x\begin{array}{r} 2 x(-2 x-3) \\ -4 x^{2}-6 x \end{array} 5) (2n+2)(6n+1)12n2+14n+2\begin{array}{l} (2 n+2)(6 n+1) \\ 12 n^{2}+14 n+2 \end{array} 7) (x3)(6x2)(x-3)(6 x-2) 6x220x+66 x^{2}-20 x+6 9) (6p+8)(5p8)(6 p+8)(5 p-8) 30p28p6430 p^{2}-8 p-64 11) (2a1)(8a5)(2 a-1)(8 a-5) 16a218a+516 a^{2}-18 a+5 2) 7(5v8)35v56\begin{array}{l} 7(-5 v-8) \\ -35 v-56 \end{array} 4) 4(v+1)4v4\begin{array}{r} -4(v+1) \\ -4 v-4 \end{array} 6) (4n+1)(2n+6)8n2+26n+6\begin{array}{r} (4 n+1)(2 n+6) \\ 8 n^{2}+26 n+6 \end{array} 8) (8p2)(6p+2)(8 p-2)(6 p+2) 48p2+4p448 p^{2}+4 p-4 10) (3m1)(8m+7)(3 m-1)(8 m+7) 24m2+13m724 m^{2}+13 m-7 12) (5n+6)(5n5)25n2+5n30\begin{array}{l} (5 n+6)(5 n-5) \\ 25 n^{2}+5 n-30 \end{array} -1-

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Problem 3574

Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area 0.8170. z=z= \square (Type an integer or decimal rounded to two decimal places as needed.)

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Problem 3575

Use the Standard Normal Table or technology to find the zz-score that corresponds to the following cumulative area. 0.90060.9006
The cumulative area corresponds to the z-score of \square (Round to three decimal places as needed.)

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Problem 3576

Condense eaun eapressioninto a single Jogar ithm and Simplify. a. 12log9+2logx+logy\frac{1}{2} \log 9+2 \log x+\log y b. log5122log52+log5x\log _{5} 12-2 \log _{5} 2+\log _{5} x

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Problem 3577

Find the values of xx that give critical points at y=ax2+bx+cy=a x^{2}+b x+c, where a,b,ca, b, c are constants. Under what conditions on a,b,ca, b, c is the critical value a maximum? A minimum? x=x=
Use the drop-down menus to indicate whether the critical value is a maximum or a minimum under certain conditions.
The critical value is a Choose one \square if a<0a<0 and a Choose one if a>0a>0.

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Problem 3578

Consider the following function. h(z)=1z+5z2 for z>0h(z)=\frac{1}{z}+5 z^{2} \text { for } z>0
Select the exact global maximum and minimum values of the function. The global maximum of h(z)h(z) on z>0z>0 is 110+125\frac{1}{10}+125, the global minimum is 103+543\sqrt[3]{10}+\sqrt[3]{\frac{5}{4}} The global maximum of h(z)h(z) on z>0z>0 does not exist, the global minimum is 103+523\sqrt[3]{10}+\sqrt[3]{\frac{5}{2}} The global maximum of h(z)h(z) on z>0z>0 is 110+125\frac{1}{10}+125, the global minimum is 53+543\sqrt[3]{5}+\sqrt[3]{\frac{5}{4}} The global maximum of h(z)h(z) on z>0z>0 does not exist, the global minimum is 103+543\sqrt[3]{10}+\sqrt[3]{\frac{5}{4}}

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Problem 3579

Find f+g,fg,fg\mathrm{f}+\mathrm{g}, \mathrm{f}-\mathrm{g}, \mathrm{fg}, and fg\frac{\mathrm{f}}{\mathrm{g}}. Determine the domain for each function. f(x)=x;g(x)=x20f(x)=\sqrt{x} ; g(x)=x-20 (f+g)(x)=(f+g)(x)= \square (Simplify your aniswer.)

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Problem 3580

10+83÷1610+8^{3} \div 16

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Problem 3581

(39)+(+59)(-39)+(+59)

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Problem 3582

ections: Use algebra (not graphing) to find the circumcenter of the triangle whose tices are given. A(8,2)A(-8,2) - A(10,10)A(10,10) (2325)2.)B(4,6)(23-25)_{2 .)} B(-4,6)
B (5,5)(5,5) C(10,14)C(10,14) 3.) (2,4)(2,4)

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Problem 3583

[(7)(5)](6)[(-7)-(5)]-(-6)

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Problem 3584

Solve using the substitution method. 5x7y=415x+53=y\begin{array}{l} 5 x-7 y=-41 \\ 5 x+53=y \end{array}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution of the system is \square . (Type an ordered pair.) B. There are infinitely many solutions in the form ( xx, \square ). C. There is no solution.

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Problem 3585

(126)52(12-6) \cdot 5^{2}

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Problem 3586

1. The sequence an=3n2+11n3a_{n}=\frac{3 n^{2}+1}{1-n^{3}} (A) converges to 0 . (B) converges to -1 . (C) converges to -2 . (D) is divergent.
2. The sequence an=(1)n5n3n72na_{n}=(-1)^{n} \frac{5^{n} 3^{n}}{7^{2 n}} (A) converges to 1 . (B) converges to 0 . (C) converges to 2 . (D) is divergent.
3. The sequence an=3n+1n+1a_{n}=\frac{3^{n}+1}{n+1} (A) converges to 1 . (B) converges to 0 . (C) converges to 2 . (D) is divergent.

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Problem 3587

Find f+g,fg,fg\mathrm{f}+\mathrm{g}, \mathrm{f}-\mathrm{g}, \mathrm{fg} and fg\frac{\mathrm{f}}{\mathrm{g}}. Determine the domain for each function. f(x)=6x+1,g(x)=x+6f(x)=6 x+1, g(x)=x+6 (f+g)(x)=7x+7(\mathrm{f}+\mathrm{g})(\mathrm{x})=7 \mathrm{x}+7 (Simplify your answer.) What is the domain of f+gf+g ? A. The domain of f+gf+g is {\{\quad. (Use a comma to separate answers as needed.) B. The domain of f+gf+g is (,)(-\infty, \infty). (Type your answer in interval notation.) C. The domain of f+gf+g is \varnothing. (fg)(x)=(f-g)(x)= \square (Simylify your answer.)

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Problem 3588

40 Solve each equation. c) cos2(2x+π6)=12\cos ^{2}\left(2 x+\frac{\pi}{6}\right)=\frac{1}{2}

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Problem 3589

Question 4 of 15, Step 1 of 1 3/153 / 15 Correct
Solve the following logarithmic equation, using a calculator if necessary to evaluate the logarithm. Write your answer as a fraction or round your answer to two decimal places. log8(2x8)=2\log _{8}(2 x-8)=2
Answer How to enter your answer (opens in new window) Keypad Keyboard Shortcuts x=x=

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Problem 3590

13x=1\frac{1}{3} \cdot x=1

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Problem 3591

Solve the formula S=RVR+7S=\frac{R V}{R+7} for the variable VV. V=V=

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Problem 3592

Graph the function rule. y=2x+1y=2 x+1

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Problem 3593

Solve the system by substitution. 3x6y=455y=x\begin{array}{r} -3 x-6 y=45 \\ -5 y=x \end{array}

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Problem 3594

Question 7 of 15, Step 1 of 1 6/15 Correct
Write the following logarithmic equation as an exponential equation. Do not simplify your answer. 2x=log19(3.6)2 \mathrm{x}=\log _{19}(3.6)
Answer

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Problem 3595

Consider the following relation. 5y+x=2x+(x3)2-5 y+\sqrt{x}=2 x+(x-3)^{2}
Step 3 of 3 : Determine the implied domain of the function found in the first step. Express your answer in interval inotation.
Answer

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Problem 3596

Save \& Exit Certify Lesson: 7.4 Logarithmic Properties and Mo... BRYCE GUILLORY Question 3 of 15, Step 1 of 1 2/15 Correct
Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1 . All exponents should be positive. ln(z)+ln(14)\ln (\mathrm{z})+\ln (14)
Answer Keypad Keyboard Shortcu1

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Problem 3597

Factor. 4964u249-64 u^{2}

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Problem 3598

Factor. 49x29y249 x^{2}-9 y^{2}

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Problem 3599

c) (102)112(56)8=\binom{10}{2} \cdot 1^{1^{2}} \cdot\binom{5}{6}^{8}=

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Problem 3600

1. Evaluate the following limits: a) limx55xx25x\quad \lim _{x \rightarrow 5} \frac{5 x-x^{2}}{\sqrt{5}-\sqrt{x}}.

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