Q: a) Find the area of the triangle determined by the given point P₁(1, 2, 4), P2(1,-1, 3), P(-1,-1,2)
A: As per Bartleby guideline, only the first question has been answered. Please repost mentioning the…
Q: Solve the given initial-value problem. y(x) = 7e y" + 6y' - 7y= 11e2x, y(0) = 1, y'(0) = 1 2x -7.x +…
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Q: (B): If A = 2i +3j - 4k; B = 3i-4j+5k and C=i+j-k, find: (ii) B.C (iii)A. (B+C)and (A + B).C (iv)…
A: Given: A→=2i+3j−4k;B→=3i−4j+5k and C→=i+j−k We know that x1i +y1j+z1k·x2i +y2j+z2k = x1x2+y1y2+z1z2
Q: Solve the given initial-value problem. y(x) = y" + 6y' 7y= 11e²x, y(0) = 1, y'(0) = 1 11e2x -7.x 7e…
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Q: doesn't this mean there are no critical points
A: Given the function fx,y=10x2-5y2
Q: Q2: Solve the following integrals: (1) 7x²+14x+15 (x²+3)(x+7) dx ; (2) sin6 x+cos6 x sin ³ x cos³ x…
A: According to our guidelines, we can answer only one question or three subparts of a question.other…
Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j+5k 4i + 5j-6k ;
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Q: Discuss the topic from algebra you used in completing this exercise. Give an example of a business…
A: Concept: Algebra: The area of mathematics known as algebra aids in the representation of…
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Q: Solve the initial value problem 25y" - 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t) = How does the…
A: We have to solve the initial value problem 25y'' - 40y' + 16y = 0 y(0) = 2 & y'(0) = 3
Q: First, compute the gradient of the function f(x,y) = 4+5x²-3y². Then evaluate it at the point…
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Q: 1-). 25 2-) 3+4i 3-1
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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…
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A: The given function is; f(x)=(-x+1)/x3 over the interval [-3,-1].
Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y = 11e2x, y(0) = 1, y'(0) = 1 -7.x 2x 7e…
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Q: dy Q5: Find for the following functions: (3) y = ex.sin² x In√x
A: We can solve this as follows:
Q: aluate the following integral in spherical coordinates. This integral calculates the volume of the…
A: See this solution in below
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Q: The radius of a right circular cone is increasing at the rate of 6cm/sec while its altitude is…
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Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) dx ; (2) f sin x+cos x dx sin³ x…
A: We will use partial fraction to solve the first part of the question.
Q: Find the cross products uxv and vxu for the the vectors u=2i-j-2k and v= i +3j-2k.
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Q: -2- 0 y = g(x) 4 7 x
A: To evaluate the integral.
Q: + 2 .4 i ti ti ti ti + i _ ។ { / - 1 "
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Q: The figure to the right shows the area of regions bounded by the graph of f and the x-axis. Evaluate…
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Q: (A): Solve the following linear equations by Cramer's rule: x + y + 2z=1 2x-y-z = 0 = 4 x +2y-z
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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x 2…
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Q: Find the trigonometric integral. (Use C for the constant of integration.) [" (cos(20)) (sin(0) +…
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Q: 2 x²log₂ (x) dx S
A: Please show complete solution. (Use integration by parts)
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A: Given:
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A: We need to find integral.
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A: Given : The curve is to be fitted R = Ae(Bt) Taking log both side log10(R) = log10 A + Bt log10…
Q: 4 (A): If A 2 2 1 Find AB and AC. 01 0; 1-2 -1 1. 2 B = 2 ܚ ܨܢ ܝ 1 ܚܕ ܨܐ ܝܕ -2 -2 and -1 2 1 C: 11…
A: Here, the given matrices are: A=420210-2-11, B=2312-2-2-121, C=31-3026-121
Q: 9. f dx 3x²√√25-x² 10. √ √² + 2tdt 11. f 3x+1 -dx 3x³-2x²-4 12. x²(x-1)(x+2) dx
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Q: A boat purchased for $25,000 depreciates exponentially. After one year, the car is valued at…
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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 2 (1) limx-o[: 1-cos x sin²x (2)…
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Q: Find the area of the given region. y = sin(x) y 2 R|4 + + T Зл T
A: In this question we have to find the area of the given region.
Q: (B): Find the tangent equation to the curve y = sin² x at point x = = 33.
A: The curve y=sin2x at point x=π3
Q: Compute the indefinite integral of the following function. r(t) = (13 cost,7 cos 5t,3 sin 6t)
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Q: Test the series below for convergence using the Ratio Test. Σ n=1 n! The limit of the ratio test…
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Q: Q3/ A. For the following function f(x). Find: i. iii. f(x) = x² + 1 The slope of the f(x) by using…
A: We need to find out the slope using the definition.
Q: Q5: Find for the following functions: dx (1) In (x - y) = xy + y³ ; (2) y = tan³√/cot(7x);
A: Given :lnx-y=xy+y3y=tan3cot7x
Q: Describe the domain and range of the function. xy x-y z Domain: 0 {(x, y); y # 0} 0 {(x, y): x*y} O…
A: To find domain and range of the given function.
Q: Evaluate the integral and check your answer by differentiating. x8+8x5 - 1 x7 S dx = +C
A: To find out the integration.
Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) x + y lim (x,y) → (0, 0) x²…
A: To evaluate: lim(x,y)→(0,0)x+yx5+y
Q: Find a differential equation of the following family of curves whose solution is: 1. A family of…
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Q: LI) Prove that (3
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Q: A cylindrical tube expands as its radius r and height h increase at the rate of 2 in/min and 4…
A: Basic product rule of differentiation is used.
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- If r(t) = cos(7t)i + sin(7t)j – 3tk, compute the tangential and normal components of the acceleration vector. COS Tangential component ar(t) Normal component an(t) =If r(t) = cos(2t)i + sin(2t)j + 3tk, compute the tangential and normal components of the acceleration. vector. Tangential component at(t) Normal component an(t) = =If r(t) = cos(lt)i + sin(lt)j - 4tk, compute the tangential and normal components of the acceleration vector. Tangential component aÃ(t) = ¯ Normal component an(t) =
- If r(t) = cos(2t)i + sin(2t)j – 4tk, compute the tangential and normal components of the acceleration vector. Tangential component ar(t) = Normal component a(t) =The motion of a point on the circumference of a rolling wheel of radius 2 feet is described by the vector function r(t) = 2(23t sin (23t))i + 2(1 - cos(23t))j - Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) =If r(t) = 8ti + t²j – 3tk, compute the tangential and normal components of the acceleration vector. Tangential component ar (t) Normal component an(t)
- Find the directional derivative of the function at the point Pin the direction the unit vector u = cos ôi + sin 0j. Sketch each the graph of the function, t point P, and the unit vector u. 2. f(x,y) = sin(2x + y), P(0, n), 0 = -.The motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function r(t) = 4(12t - sin(12t))i + 4(1 − cos(12t))j Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = =A charged particle begins at rest at the origin. Suddenly, a force causes the particleto accelerate according to the vector function a(t) = ⟨ sin(t) , 6t , 2cos(t)⟩Find functions for the velocity, speed and position of the particle at time t
- If r(t) = cos(6t)i + sin(6t)j — 2tk, compute the tangential and normal components of the acceleration vector. Tangential component ar(t) = = Normal component an(t): =Find Components of the Acceleration For the curve defined by 7(t) = (e-t cos(t), eʻ sin(t)) find the unit tangent vector, unit normal vector, normal acceleration, and tangential acceleration at t = 3 T(플) - N(플) - 3 3 AN =Find the tangential and normal components of acceleration for F(t) = (5 cos(t), 7t², 5 sin(t)). Answer: ä(t) = a +aN where a7 aÑ Submit Question and