If sin x = sin y = a and cos x = cos y = b, then cos (x - y) is equivalent to A. OB. C. D. b²-a² b²+ a² 2b-2a 2b + 2a

Q: A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r…

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Q: Given the vectors u=-i-3j and w=-7i+5j, find -4u and u-w. Write your answers in the form ai+bj.

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Q: Find the slope of the following lines.

A: see below the answer and calculation

Q: If 0 satisfies the inequalities sin (0) > 0, sin(0) cos(0) > 0, in which quadrant must lie? 1.…

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Q: 4. 3 2 (D+D²_5D+3) y = 0

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Q: Solve the logarithmic equation for x. (Enter your answers as a comma-separated list.)  log(4x + 3)…

A: Use the basic property of log function.

Q: Find the linear approximation to the function f(x) = 3x + 4 at a =3, [0,6].

A: Linear approximation formula f(x) = f(a) + ( x-a )f'(a) Given f(x) = 3x + 4

Q: Find the gradient of the function y at x = 4.

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Q: (b) F(t)=(e²¹)i + (2e²¹ +5)j + (2e²¹ -20)k for 0≤1≤ In 2

A: As we know that: The expression for the length of vector-valued curve in the interval a≤t≤b is:…

Q: = x³ +. 5. f(x) = 忘 3x = y + 4 = U x + 2y 6=0

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Q: * 36, got 6=-8, 311/2<0² 2π1₁ eSC

A: given cot(∅)=-8tan(∅)=1cot(∅)=-18∅=tan-1-18∅=352.8749837o

Q: 2. A 71.6m tower is to be constructed on a hill with a slope of 15.6°. Both cables make a 42.5°…

A: We will use sin Rule to find the length of each cable.

Q: 9y" y(0) = 2 y'(0) = -1 12y + 4y = 0

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Q: A box with a volume of 8m³ is to be constructed with a gold-plated top, silver-plated bottom, and…

A: Given:         Assuming the box is a cube.         The volume of cube = side³           side3=8…

Q: 4. TT/6 t sin

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

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Q: (²cos(x)) = 2cos(x) — 4xsin(x) – x² cos(x) Otrue O false

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Q: Evaluate the integral 9 3 12 SS S 00 4y 9 3 12 SSS 0 0 4y (Type an exact answer.) 3 cos (x²) 4√2 3…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the funct 8 + sec(6t) dt…

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Q: 2) Solve the given Variable separable DE 1) x cos² y dx + tany dy =0

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Q: The region W lies below the surface f(z,y)-8e (3) and above the disk z² + y² ≤ 16 in the zy-plane.…

A: We have to find the area and volume integrals.

Q: Suppose wexy + yz² while x(s, t) = s+t, y(s, t) = cos(s), and z(s, t) = est. Determine Əw Əw and Əs…

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Q: The total cost (in hundreds of dollars) of producing x calculators per day is given by the equation.…

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

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Q: 26. tan ³0 sec ³0 de

A: Topic = Integration

Q: Use polar coordinates to find the volume of the solid bounded by the parabolas z = 3x² + 3y² and z =…

A: The solid is bounded by the curves:z=3x2+3y2        and          z=4-x2-y2

Q: Consider the point (음, %) Fort 1. Find (sc (t) A).& 10 22-1 B) 은 C) - 음 이응 Ja 100 0)-10 F) - g) none…

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Q: Describe (don't sketch) the "level curve" defined by sin(√x² + y²) = 1.

A: Given:      sinx2+y2=1⇒x2+y2=sin-1(1)⇒x2+y2=π2+2πn⇒x2+y2=π24+2π2n+4π2n2

Q: Solve the logarithmic equation for x, as in Example 7. (Enter your answers as a comma-separated…

A: Note: Since the student has posted multiple questions and does not mention any specific question, so…

Q: A function contains the following ordered pairs. ((0, -8), (1, -6), (3, -2), (4, 0), (5, 2)) Which…

A: To find the function: Find a general rule satisfied by all the elements .

Q: 1. | xe3xdx

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Q: Let F(x, y, z) = x³i+y³j+z³k. Compute the following: (i) V.F (ii) V X F

A: i) Given:       Fx,y,z=x3i+y3j+z3k then         ∇·F=∂∂xx3+∂∂yy3+∂∂zz3                 =3x2+3y2+3z2…

Q: 6. 2 S²³ x5 ln x d

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Q: Find a power series representation for the function. 8 + Χ (1 − x)2 f(x) Σ( 1) η Determine the…

A: The given function is: f(x)=8+x(1-x)2

Q: a. Find a curve with a positive derivative through the point (1,1) whose length integral is given…

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Q: Calculate the double integral S fæ cos(2x + y) dA where R is the region: 0 ≤ x ≤ 7,0 ≤ y ≤ 4

A: The given integral is: ∫∫R x cos(2x+y) dA       where R is the region:  0≤x≤π6,   0≤y≤π4

Q: An object is projected directly upward from the ground with an initial velocity of 128feet per…

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Q: 2. Evaluate = I= √²² + y² + 2² av where E is the region enclosed by the the sphere x² + y² + 2² =z.…

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Q: Use a trigonometric identity to evaluate the integral. [tan²(x) dx = +C

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Q: Consider two nonnegative numbers x and y where x + y = 13. What is the minimum value of 2x² + 12y?…

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Q: The linear approximation at where A is: and where B is: = 0 to sin (3x) is A + Bx

A: We need to find Linear approximation.

Q: ૨ 2 (D² -2D +10) y =0

A: Solution : Given that DE is

Q: (6) Determine if the alternating series converges Σ(-1)"+1. ∞ n=2

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Q: Let Give the 2,1 entry of 4-¹. a) 0-¹ b) 0¹/2 c) 03/2 d) 0-5 e) 0-2 f) O None of the above. 02 2 A-1…

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Q: Esc [3] Use a first derivative test with a well written conclusion to state the local min and max…

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Q: 21. Find the volume of the solid bounded above by the surface z = ryery and below by the rectangle…

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Q: Let y = 3x². Find the change in y, Ay when x = 3 and Ax = 0.3 Find the differential dy when x = 3…

A: The given function y=3x2 We have to find ∆y and dy.

Q: 2. Use Euler's method to approximate the first three steps of a ten-step approximation to dy 2x+1…

A: Use Euler's method to approximate the first three steps of a ten-step approximation to the solution…

Q: 2700 360 * 31, cos 0 = 1/8, 311/2 <0 < 2 ४ 1% کے too (1) ³+ (8) ²

A: given  cos∅=183π2&lt;∅&lt;2π there for ∅ is in 4 quadrant in 4 quadrant sin∅ is negative and tan∅ is…

Q: Solve the following differential equation: [e2y − y cos(xy)]dx + [2xe2y − x cos(xy) + 2y]dy = 0

A: e2y − y cosxydx + 2xe2y − x cosxy + 2ydy = 0