X-1 y-3 Given that L: k and M: 4x + ky – 3 = 0 then find the value(s) 16 of k such that the two lines L and M are perpendicular.

Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: Three vectors are given by: J = 2î – k K = 2î – ĵ+ 2k L= 2î – 3} Determine: (i) K•L x J; and (ii)…

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Q: The graph of e(t) -(2 sedt), 6 tant)) for 0st< can aino be described in the form y/(x). This problem…

A: We use the formula. Sec2t-tan2t=1

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

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Q: Written Homewo 1) Find the zeros and maximum value of r 2+4 sin 0.

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Q: uation of motion in the form x(t) = Ae™it sin( V2 – 2?t + w), which ft

A: answer is in next step

Q: 6. sin v- -2 cos Va + C %3D 4x2 1. Ja-8 dx = 18 (1-8x)4 (1-8x3)4 8. Se*dx =+ %3D In e

A: As per the instruction, we will be answering only the first three subparts. For (6),    ∫sinxxdxLet…

Q: A ball is thrown vertically upward from the top of the house 110 ft high with an initial velocity of…

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Q: 2 sec" x AX JS -sec? x

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Q: a)True b)False 2/ Answer the following: (A) Find the solution of this equation y=+y-6y = 0. roncform…

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Q: the mapping notation for this function 2. Given the function F(x) -4 *+2 al Determine the mappina…

A: we have  f(x)=4123x+3-2 the domain of the given function is (-∞,∞)and range of the given function is…

Q: Find the x-value maximizing the shaded area on the interval 0 < x < 18. One vertex is on the graph…

A: First  I have found the Area of the shaded region region then find the critical point and then find…

Q: dV = vt+1+t where V 4. The volume of a balloon is increasing according to the formula dt cm³ is the…

A: To solve the given differential equation and find an expression  for V(t).

Q: Let C(x) =x +4x+1 dollars be the cost function, where the x represents the quantity. The !3!…

A: 1) Here, to find the 11th item.  Now, the cost of x quantity is given by: C(x)=25x2+4x+1

Q: // Find the Area bounded by: x = -y2 and x = y- 2

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Q: 5. [4 log x + 1] dx

A: Student has specifically asked for the solution to the Question (5). Hence answer to that problem is…

Q: Find the area, A, of the region enclosed by the cardioid r = 8+ 8 cos 0. 96 л (B 52 A © 48 n (D) 100…

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Q: Find the smallest value of x for which the series (x+ 124)" 2in(n) n 2 is conditionally convergent.…

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Q: 13. sec*0 sin 8 de

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Q: 4. Find the arc length of r = cos? (0/2), 0 s 0 s 2n.

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Q: 2.) Suppose E is the solid which is inside the sphere x + y² + z° = 4_and above the plane z = v3 .…

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Q: Si s(2x)dx = 23. If f is a continuous fiunction and if F'(x) = ƒ(x) for all real numbers x, then (A)…

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Q: Use power series to show that sinh(z) + cosh(x)= e".

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Q: 24. Given z = 6x°y-e", calculate or z. A) 12y–x'e" B) 12y-ye" C) 12y-e" ху D) 12x - хуе"

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Q: The derivative of f(x)= (x2+2x)(x²-2x) is a. 4x3-8 O b. x-4x2 с. none d. 3.

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Q: Q2// Solve the following differential equation: e2y dx + 2(xe2y – y)dy = 0

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Q: Consider a triangle where A = 30°, a = 1.5 cm, and b 1.2 cm. %3D (Note that the triangle shown is…

A: Explained below

Q: Given the equation x In(y) dz = z Arctan(3y). Assuming z as a function of variables x and y, find ar

A: To partially differentiate the function z with respect to x.

Q: Sketch the graph of the cardioid r = 1 + cosθ and the circle r = 3cosθ. Shade the region that is…

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Q: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the…

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Q: Problem 3. Sketch the region enclosed by the curves y = 6x, y=4x², and find the area of that region.…

A: We can solve as follows

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x) sin 1 (x) xp

A: ∫cosxsin16x dx

Q: Question 3 How much work is required to pump all the water from a right circular cylindrical tank,…

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Q: Find the x-value maximizing the shaded area on the interval 0 < x < 18. One vertex is on the graph…

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Q: Use the polygon law of addition to draw the resultant vector ( å + b) + ở for the following yectors.

A: The given vectors are added

Q: Consider the series n+5 Determine whether the series converges, and if it converges, determine its…

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Q: Find the n-th Taylor polynomials for 1 about x = 3 and express it in f(æ) x + 2 sigma notation.

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Q: 1. Find the derivative of the following: (Simplify your final answers.) sech h. j(r) = e (Using…

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Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: "If a function is continuous at some point then it must be differentiable at that point". Do you…

A: No, i am not agree. If function is differentiable then it continuous , but not vice versa. For…

Q: Evaluate: S Vx(x – 5)dx

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Q: 1. Suppose a car is travelling on a straight road and s(t) is the distance travelled after For…

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Q: 1. lim 32-3 +5 2. lim log, (x-8x 1) 3. lim (In 2x +5) + 4 Write your final answer using 4 decimals

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Q: A ball is thrown vertically upward from the top of the house 112 ft high with an initial velocity of…

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Q: Given: re + In(x - y) xe*? Find dy/dx. 2ry(z=y)+z* 1+(z=v}(2»² +1)e| dy dr 2r(z-y)-z1z…

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Q: Determine a. (Give your answer as a whole or exact number.)

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Q: 5. The velocity function of a moving particle on a coordinate line is v (t) = t³ + 6t² + 11t + 6.…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: Sketch the graph the integrands and use areas to evaluate the integrals. V16 – x² dx

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Q: Directions: Solve the following using the theorems on differentiation. 1. Evaluate x5dx 2. Evaluate…

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Q: Answer the question. Show ALL your steps in your calculations. Answer in complete sentences. 8…

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