Let ā = ( – 5, — 4, 5) and - 4, 5) Find the projection proja b 6 and 7 = (3, 1, 0). =< of b onto a. V

Q: 11. a) By solving some equations with some unknowns, determine whether it is possible to write [5,…

A: To determine whether it is possible to write the vector [5, -10, 1] as a linear combination of [4,…

Q: Which of the following functions have at least one asymptote? ¡)f(x)=-x f(x): ii) ²/ x ›-() f(x)=…

A: and The line x=L" data-mce-style="box-sizing: border-box; margin: 0px; padding: 0px; font-style:…

Q: 19-38 Evaluate the integral.

A:

Q: 4. Let = and (a) Find 7+7 and 27-37. Write the result both in terms of components and standard…

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Q: Me number of mosquitoes in a field after a major rainfall is modeled by the function M defined by…

A: Here we given a function M described here models the quantity of mosquitoes in a field following a…

Q: y" - 6y' + 8y = 0

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Q: If y = (sin x)², then find O O dy dx (sin x)ª (x cot ä + ln(sin x)) (sin x)” (x cos x + sin x) (sin…

A:

Q: Evaluate the definite integral. Use a graphing utility to verify your result. (Round your answer to…

A: Explanation of the answer is as follows

Q: State the range for the function f(x) = -e* + 2:

A: Find range and choose the correct option

Q: Let à = ā ( – 5, — 4, 5) and b Find the projection of b onto a. proja b = (3, 1, 0). V

A:

Q: By observation, are any of the members of the truss shown zero-force members?

A: Truss structure is given

Q: (b) Describe the relationship between each pair of planes, and determine any intersection: (i)…

A: (i)Here we have given a equations of pair of plane.Now, comparing their coefficients and constants…

Q: Solve the equation: sin(2x) - cos(2x) = 1 over the interval [0, 2π).

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Q: Given the function f(x)=x²-3 a. What is the domain for f(x) What is the range for f(x) b. Find f¹(x)…

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Q: 8. Three forces of 5N, 8N, and 10N are at equilibrium. Determine the angle between the two largest…

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Q: Convert the given angle to decimal degrees. Round to 4 decimal places 10°12’25” =

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Q: Decompose the following fraction using a long division: 5x³ + 2x² - 38x - 21 x² - 9 a = b = 5 0 C =…

A: The given term is; (5x3+2x2-38x-21) /(x2-9).

Q: Find an equation of the tangent line and normal line to the curve 2 of f(x) f(x). = X -√x + 5x² at…

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Q: Solve the given system of equations. Sy=11x + 20 y=-2+11x O (1,-1) no solution O (1,1) O (2, 2)

A: When, (Ratio of coefficient of x )=( ratio of coefficient of y)≠(ratio of constant terms)then,…

Q: Determine whether the alternating series converges. 5 ln k k Σ( -1)*. k=3

A:

Q: Part A: Determine the interval of convergence of the power series for h.

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Q: gallons, 12,000 gallons, and 24,000 gallons. How many of each type of tank car should be leased? Let…

A: Let x1 be the number of cars with a 6000 gallons capacityx2 =The number of cars with a 12000 gallon…

Q: Find the area between the graph of x = 2y + 3 and the y-axis on the interval [0, 2]. 4 3 2 1 -2 -1₁⁰…

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Q: 5. Find the magnitude of the resultant force and the angle it makes with the positive x-axis. у л 0…

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Q: Suppose f(3) = 2, f'(3) = f'(x) > 0 and f"(x) < 0 for all x. (a) When is f(x) increasing?

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Q: Use Lagrange multipliers to find the points on the cone z² = x² + y² that are closest to the point…

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Q: (3) Compute the value of Ay and the value of dy for the function below; f(x). Let the variable x go…

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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: 4. a) b) Let x = 2ī + 3j - k, y = i- j + 4k and 2 = −3ỉ + j. Express the vector x + 2y - 37 in terms…

A: Let , and (a) To express the vector  in terms of vectors  and .(b) To determine .Note: Since the…

Q: 10. Given X(7,3) and Y(-6,2), find the coordinates of any point Z such that XZ XY = 41. .

A:

Q: Question 2 Solve cot 8- sin 8 1+cos ( = √2 for 0 ≤ 0 ≤ 2π.

A:

Q: 3. Differentiate sin a 1+cos z with respect to x and hence, find S -dx 1+cos a

A: We need to first differentiate then solve integration.

Q: In Exercises 17-22, use the nth Term Divergence Test (Theorem 4) to prove that the following series…

A: The given series is:

Q: Draw a sketch of the graph of f(x) = 2√x + 1 − 1. Explain the trans- formations of the graph of…

A: Explaination of the answer is as follows

Q: Use the convolution theorem to find the inverse Laplace transforms of: (a) F'(s) = (8² +9) ² (b)…

A: Given

Q: 3) A metal box is constructed, and it's planned to have dimensions of 120 cm by 50 cm by 75 cm. If…

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Q: Question 5 Using Cramer's rule to solve the following system of equations, what are ? 4x + 3y + 12z…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: Consider the following cost function. a. Find the average cost and marginal cost functions. b.…

A: C(x) = 0.04x^3 +0.02x^2 +30x +90, 0&lt; x &lt; 1500, a = 1000The marginal cost function is the first…

Q: ii. Consider the following differential equation: d²x dx dt² +5+8x = f(x) where f(x) is the input…

A:

Q: the definition of continuity to f(x)=5r-2² at z=0

A: This is question of calculus.Here function is given We have to check it's continuity.Using…

Q: Find the tangential and normal components of the acceleration vector. r(t) = cos(t) i + sin(t) j +…

A: We have to find the tangential and normal components of the acceleration…

Q: 23. (In x)² dx

A: We are required to find:

Q: The count in a bacteria culture was 900 after 15 minutes and 2000 after 35 minutes. Assuming the…

A:

Q: 6. Explain in words how a student would determine the magnitude of the vector P[2, 3, 1]. There is…

A: To determine the magnitude of a vector P[2, 3, 1], a student would follow a simple set of steps. 1.…

Q: Use partial fractions to find the indefinite integral. (Remember to use absolute values where…

A:

Q: Find the linearization of the function ƒ (x) = = L(x) ab B (-2)x-3 X -1.1 86 -1.01 a -1.001 √a |a|…

A: The given function

Q: Determine the set of points at which the function is continuous. f(x, y) = x²y³ 6x² + y² 1 •{(x y) |…

A:

Q: Compute two fully factored derivatives and determine the exact coordinates of any points of…

A: To compute two factored derivatives and to determine the exact coordinates of any points of…

Q: 1) Find: lim x→ 4 x² - 16

A: We are required to find: