Math Statement

Problem 26501

Simplify the expression: (8u4v6u3v32v37uv4)(4u3v38v34uv45u4v)+(3uv48u3v3v3+4u3v4)(-8 u^{4} v - 6 u^{3} v^{3} - 2 v^{3} - 7 u v^{4}) - (-4 u^{3} v^{3} - 8 v^{3} - 4 u v^{4} - 5 u^{4} v) + (3 u v^{4} - 8 u^{3} v^{3} - v^{3} + 4 u^{3} v^{4}).

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Problem 26502

Find the derivative f(π)f^{\prime}(\pi) for the function f(x)=11+cosxf(x)=\frac{1}{1+\cos x}.

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Problem 26503

Calculate 323^{2} and simplify your answer.

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Problem 26504

Factor the expression 2x3+6x28x242 x^{3}+6 x^{2}-8 x-24.

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Problem 26505

Rewrite the quadratic x2+8x3x^{2}+8x-3 in vertex form y=(x+h)2+ky=(x+h)^{2}+k by completing the square. Choose a step:
1. y=x2+8x+838y=x^{2}+8x+8-3-8
2. y=x2+8x+83+8y=x^{2}+8x+8-3+8
3. y=x2+8x+16316y=x^{2}+8x+16-3-16
4. y=x2+8x+163+16y=x^{2}+8x+16-3+16

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Problem 26506

What interval does the inequality x1x \leq -1 represent?

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Problem 26507

Calculate (8)2(-8)^{2}. What is the result?

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Problem 26508

Simplify the expression: 7x33\sqrt{\frac{7 x^{3}}{3}}

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Problem 26509

Calculate (7)2(-7)^{2}. What is the result?

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Problem 26510

What interval does the inequality x5x \geq 5 represent?

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Problem 26511

Calculate (38)2\left(\frac{3}{8}\right)^{2}.

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Problem 26512

Solve the inequality 5z+63z4-5z + 6 \geq -3z - 4 and express the solution in interval notation.

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Problem 26513

Simplify (12)5=\left(-\frac{1}{2}\right)^{5}=\square (What is the result?)

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Problem 26514

Find the value of the variable var after executing: var = 100; var = var + 100; var = var + var.

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Problem 26515

Determine the slope, mm, of the tangent line to the curve y=7+5x22x3y=7+5 x^{2}-2 x^{3} at x=ax=a.

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Problem 26516

Decompose the function 1+xcos(x)1+x \cos (x) into its even and odd parts.

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Problem 26517

Calculate the value of 4+844 + 8 \cdot 4. What is the result?

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Problem 26518

Decompose sin2(y)8y4sin(y)\sin^{2}(y) - 8y^{4}\sin(y) into even and odd functions.

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Problem 26519

Evaluate: 8+2527=-8 + 2 \cdot 5^{2} - 7 =

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Problem 26520

Simplify: 64+86=6 \cdot 4 + 8 \cdot 6 =

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Problem 26521

Solve the inequality x+15x + 1 \geq 5 and express the solution in interval notation.

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Problem 26522

Evaluate: 75(8+6)=7 - 5(8 + 6) =

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Problem 26523

Find the value of csc(1305)\csc (-1305).

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Problem 26524

Divide 1.9 by 0.76.

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Problem 26525

Solve the inequality x+15x + 1 \geq 5 and express the solution in interval notation.

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Problem 26526

Evaluate: 366(610)2=-36-6(6-10)^{2}=

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Problem 26527

Evaluate: (20÷5)3+92÷27(20 \div 5)^{3}+9^{2} \div 27

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Problem 26528

Solve for xx: 220,000x+475=0\frac{220,000}{x+475}=0

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Problem 26529

Evaluate: 3+2[1+(18÷32)]-3+2\left[-1+\left(18 \div 3^{2}\right)\right]

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Problem 26530

Calculate 4(13)54 - (-13) - 5.

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Problem 26531

Calculate: 300.4215.960.213=300.42 - \frac{15.96}{0.213} =

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Problem 26532

Simplify: 1624÷4(4)2+21=16 - 24 \div 4(-4)^{2} + 21 =

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Problem 26533

Calculate the expression: 1217(8)12 - 17 - (-8).

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Problem 26534

Calculate: (15÷5)+3(97)2=(15 \div 5)+3(9-7)^{2}=

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Problem 26535

Find the distance traveled if speed is 45 miles/hour for 2/3 hour. Use d=rtd = rt.

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Problem 26536

Calculate (5)3+15÷3(-5)^{3} + 15 \div 3. What is the simplified result?

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Problem 26537

Calculate 0.01800.00590.03168\frac{0.0180-0.0059}{0.03168}.

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Problem 26538

Calculate 52(25)\frac{5}{2}-\left(-\frac{2}{5}\right).

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Problem 26539

Evaluate a) (8)2(-8)^{2}, b) (8)2-(-8)^{2}, and c) 82-8^{2}. What are the results?

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Problem 26540

Evaluate these expressions for x=8x = -8: a) x2x^{2}, b) x2-x^{2}, c) (x)2(-x)^{2}.

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Problem 26541

Convert the equation x4y=4x - 4y = -4 to slope-intercept form (y=mx+by = mx + b).

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Problem 26542

Evaluate a) x2x^{2}, b) x2-x^{2}, and c) (x)2(-x)^{2} for x=8x = -8. What are the results?

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Problem 26543

Evaluate 9z6-9z - 6 for z=3z = 3. What is the result?

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Problem 26544

Evaluate the piecewise function f(x)f(x) where f(9)f(-9) and find f(4)f(4).

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Problem 26545

Evaluate r2s2r^{2}-s^{2} for r=6r=-6 and s=7s=-7. What is r2s2=?r^{2}-s^{2}=?

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Problem 26546

Calculate (47)2\left(\frac{4}{7}\right)^{2}.

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Problem 26547

Evaluate: 3+2[2+(45÷32)]-3 + 2[-2 + (45 \div 3^{2})]

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Problem 26548

Find the velocity of a particle with displacement s=2t2s=\frac{2}{t^{2}} at t=a,t=1,t=2,t=3t=a, t=1, t=2, t=3 (in m/s\mathrm{m/s}).

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Problem 26549

Calculate 11211^{2} and provide the simplified answer in the box: \square.

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Problem 26550

Find the critical points of f(x,y)=x2+2xy+2y28x+2yf(x, y)=x^{2}+2xy+2y^{2}-8x+2y and classify each as max, min, or saddle.

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Problem 26551

Calculate (9)2(-9)^{2}. What is the result?

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Problem 26552

Simplify: 618÷6(5)2+86 - 18 \div 6(-5)^{2} + 8

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Problem 26553

Solve the inequality 4x>8-4x > 8 and express the solution in interval notation.

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Problem 26554

Evaluate: 6+3529=-6 + 3 \cdot 5^{2} - 9 =

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Problem 26555

Simplify: 55+46=5 \cdot 5 + 4 \cdot 6 =

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Problem 26556

Evaluate: 336(610)2-33 - 6(6 - 10)^{2}. What is the result?

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Problem 26557

Calculate: (4÷2)+4(82)2(4 \div 2) + 4(8-2)^{2}. What is the result?

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Problem 26558

Solve the inequality 5x30-5 x \leq 30 and express the solution in interval notation.

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Problem 26559

Find f+gf+g, fgf-g, fgfg, and fg\frac{f}{g} for given functions f(x)f(x) and g(x)g(x) in three cases.

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Problem 26560

Evaluate r2s2r^{2}-s^{2} for r=3r=-3 and s=4s=-4. What is the result?

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Problem 26561

Find f+gf+g, fgf-g, fgfg, and fg\frac{f}{g} for f(x)=3x+4f(x)=3x+4 and g(x)=2x1g(x)=2x-1.

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Problem 26562

Find critical points of t(x,y)=x312xy+y3t(x, y)=x^{3}-12xy+y^{3} and classify as max, min, or saddle.

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Problem 26563

Evaluate a) x2x^{2}, b) x2-x^{2}, and c) (x)2(-x)^{2} for x=8x = -8. Find values for a), b), and c).

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Problem 26564

What interval does the inequality 3x<6-3 \leq x < 6 represent?

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Problem 26565

Calculate 3+96 3 + 9 \cdot 6 . What is the result?

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Problem 26566

Evaluate: (35÷7)3+92÷27(35 \div 7)^{3}+9^{2} \div 27

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Problem 26567

Minimize the cost function C(x,y)=3000+600x2+700y2C(x, y) = 3000 + 600x^2 + 700y^2 for pounds of sulfur (xx) and lead (yy) removed daily.

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Problem 26568

Find the implicit derivative of ycosy=x+1y - \cos y = x + 1.

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Problem 26569

Evaluate: 75(9+8)=7 - 5(9 + 8) =

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Problem 26570

Given f(x)=2x5f(x)=2x-5 and g(x)=4x2g(x)=4x^{2}, find: a. f+gf+g, b. fgf-g, c. fgfg, d. fg\frac{f}{g}.

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Problem 26571

Calculate 51,59922,78251,599 - 22,782 and check if it is approximately 33,00033,000.

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Problem 26572

Find the following for f(x)=2x5f(x)=2x-5 and g(x)=4x2g(x)=4x^{2}: a. f+gf+g, b. fgf-g, c. fgfg, d. fg\frac{f}{g}.

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Problem 26573

Find prices p1p_{1} and p2p_{2} for Ultra Mini and Big Stack such that q1=0q_{1}=0 and q2=0q_{2}=0 using given demand functions.

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Problem 26574

Find expressions equivalent to (5g+3h+4)2(5 g+3 h+4) \cdot 2. Choose all that apply: A (5g+3h)8(5 g+3 h) \cdot 8, B (5g+3h)6(5 g+3 h) \cdot 6, C None.

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Problem 26575

Solve the inequality 2x+54>x23+2\frac{2 x+5}{4}>\frac{x-2}{3}+2 and express the solution in interval notation.

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Problem 26576

Which expressions equal x+2y+x+2x + 2y + x + 2? Select all that apply: A 2(x+y+1)2(x+y+1) B 2x+4y+42x + 4y + 4 C None.

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Problem 26577

Prove the trigonometric equation: θsin(1n)x1x2=tan1(x)\theta \sin \left(\frac{1}{n}\right) \frac{x}{\sqrt{1-x^{2}}} = \tan^{-1}(x).

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Problem 26578

Find expressions equivalent to 2(4f+2g)2(4 f+2 g). Choose 3: A 8f+2g8 f+2 g, B 2f(4+2g)2 f(4+2 g), C 8f+4g8 f+4 g, D 4(2f+g)4(2 f+g), E 4f+4f+4g4 f+4 f+4 g.

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Problem 26579

Given matrix AA and vectors uu and vv, find T(u)T(u) and T(v)T(v) where T(x)=AxT(x) = A x.

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Problem 26580

Find f(4)f^{\prime}(-4) for f(x)=4x23xf(x)=4 x^{2}-3 x using the difference quotient and limit as h0h \rightarrow 0.

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Problem 26581

Find the following for f(x)=x4f(x)=x-4 and g(x)=xg(x)=\sqrt{x}: a. f+gf+g, b. fgf-g, c. fgfg, d. fg\frac{f}{g}.

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Problem 26582

Round the sum of 5.63+2.15+16.395.63 + 2.15 + 16.39 to the nearest integer.

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Problem 26583

Find (fg)(x)(f \circ g)(x), (gf)(x)(g \circ f)(x), and (fg)(3)(f \circ g)(3) for f(x)=2xf(x)=2x, g(x)=x+5g(x)=x+5.

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Problem 26584

Given the matrix AA and vectors uu and vv, find T(u)T(u) and T(v)T(v) where T(x)=AxT(x)=Ax. Simplify your answers.

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Problem 26585

Find the xx-intercept and yy-intercept of the line 3x2y=183x - 2y = -18 and use them to graph the line.

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Problem 26586

Solve for xx in the equation 5x=9x165 x=9 x-16.

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Problem 26587

Find all x\mathbf{x} in R4\mathbb{R}^{4} such that Ax=0A \mathbf{x} = \mathbf{0} for the matrix A=[1271103401231574]A=\begin{bmatrix} 1 & 2 & 7 & -1 \\ 1 & 0 & 3 & -4 \\ 0 & 1 & 2 & 3 \\ -1 & 5 & 7 & 4 \end{bmatrix}. Choose A, B, C, or D.

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Problem 26588

Show that multiplication is commutative by proving qc=cqq \cdot c = c \cdot q for variables 'q' and 'c'.

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Problem 26589

Solve the inequality for yy. 225y18-2-\frac{2}{5} y \geq-18
Simplify your answer as much as possible.

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Problem 26590

Solve the inequality for xx. 14x+817\frac{1}{4} x+8 \leq 17
Simplify your answer as much as possible.

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Problem 26591

Solve the inequality for ww. 1383w>1913-\frac{8}{3} w>19
Simplify your answer as much as possible.

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Problem 26592

Answer the following. (a) A certain solution has a hydrogen Ion concentration of 9.14×1059.14 \times 10^{-5} moles per liter. Write this number in standard not (b) An African bush elephant can weigh up to 28,000 pounds. Write this number in scientific notation. (a) [I moles per liter ×\square \times{ }^{\square} (b) \square pounds

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Problem 26593

Graph the line. y=2x6y=2 x-6 Explanation Check

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Problem 26594

1. In Exercises 53-60, use transformations to describe how the graph of the function is related to a basic trigonometric graph. Graph two periods.
53. y=sin(x+π)y=\sin (x+\pi)
54. y=3+2cosxy=3+2 \cos x
55. y=cos(x+π/2)+4y=-\cos (x+\pi / 2)+4
56. y=23sin(xπ)y=-2-3 \sin (x-\pi)
57. y=tan2xy=\tan 2 x
58. y=2cot3xy=-2 \cot 3 x
59. y=2secx2y=-2 \sec \frac{x}{2}
60. y=cscπxy=\csc \pi x

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Problem 26595

Let gg be a.function defined for all x0x \neq 0, such that g(5)=3g(5)=-3, and the derivative of gg is given by g(x)=x2x2xg^{\prime}(x)=\frac{x^{2}-x-2}{x} for all x0x \neq 0. A. Find all values of xx for which the graph of gg has a horizontal tangent, and determine whether gg has a local maximum a local minimum, or neither at each of these values. Justify your answers. B. On what intervals, if any, is the graph of gg concave up? Justify your answer. C. Write an equation for the line tangent to the graph of gg at x=5x=5. D. Does the line tangent to the graph of gg at x=5x=5 lie above or below the graph of gg for x>5x>5 ? Why?

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Problem 26596

Question 1 (a) Rationalize the denominator and simplify 23113+331+3\frac{2 \sqrt{3}-1}{1-\sqrt{3}}+\frac{3 \sqrt{3}}{1+\sqrt{3}}. [5 marks] (b) If w=4+7iw=4+7 i, express w+1ww+\frac{1}{w} in the form a+bia+b i where aa and bb are real. [5 marks]
Question 2 Given that f(x)=x+5f(x)=\sqrt{x+5} and g(x)=ln(x+5)g(x)=\ln (x+5). (i) Sketch the graph of f(x)f(x). (ii) State the domain and range of f(x)f(x). (iii) Find f1(x)f^{-1}(x) and (gf1)(x)\left(g \circ f^{-1}\right)(x). [10 marks] Question 3 (a) Given that the 5th 5^{\text {th }} term of an arithmetic progression is 21 and its 10th 10^{\text {th }} term is 41 , find (i) the common difference, dd and the first term, aa. (ii) the sum of first 20th 20^{\text {th }} term. [7 marks] (b) Expand (23x)8(2-3 x)^{8} in ascending power of xx up to the term in x3x^{3}. [3 marks]
Question 4 (a) Given that A=(2132)\mathbf{A}=\left(\begin{array}{cc}2 & -1 \\ 3 & 2\end{array}\right) and B=(a1b1)\mathbf{B}=\left(\begin{array}{ll}a & 1 \\ b & 1\end{array}\right) where aa and bb are real. Find the values of aa and bb such that AB=BA\mathbf{A B}=\mathbf{B A}. [6 marks] (b) If P=(3243)\mathbf{P}=\left(\begin{array}{ll}3 & -2 \\ 4 & -3\end{array}\right), show that the inverse matrix of P\mathbf{P} is also P\mathbf{P}. [4 marks]
Question 5 (a) Given the parametric equations x=t3tx=t^{3}-t and y=t2+ty=t^{2}+t where t>0t>0.
Find dydx\frac{d y}{d x} in terms of tt. [5 marks] (b) Evaluate xx25dx\int x \sqrt{x^{2}-5} d x by using the substitution u=x25u=x^{2}-5. [5 marks]

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Problem 26597

Evaluate the integral. (Use C for the constant of integration.) ln(x)x2dx\int \frac{\ln (x)}{x^{2}} d x

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Problem 26598

Factor the expression completely. x2y5+x4x^{2} y^{5}+x^{4}
Answer Attempt iout of 2

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Problem 26599

Grades 41
Announcements IXL Learning iReady Question 13 5 pts
Which equation correctly represents the line in slope-intercept form of y+4=2(x3)?y+4=2(x-3) ?
Enter your answer like this: y=3x+7y=3 x+7 (this is just an example, not the answer). y=y= \square Next

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Problem 26600

Question
Factor the expression completely. 5xx25 x-x^{2}
Answer Atsmpt sout of 2

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