Find an equation for the hyperbola that satisfies the given conditions Foci: (+5, 0), vertices: (±3, 0)

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 s t < 1. dy

A: Given: I=∫Cx+3y2dy And x=4t, y=8t  and 0≤t≤1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 7 cos(9x – 10y)j + 3zk. V·(V × F)

A:

Q: Find out whether the series given below converges or diverges. 00 In (n+ 1) Σ n+1 n= 1 Choose the…

A: Here we will find whether series is convergent or divergent,

Q: Use the Integral Test to determine whether the infinite series E is convergent. (Use symbolic…

A: We have to find if the series converges.

Q: Determine the generating function of the following sequence {0, 0, 0, 1, 1, 1, ....}

A:

Q: Suppose y (t) = 3t-6 is the velocity of an object Part A) What is the total displacement of the…

A:

Q: Solve the Laplace Transform of the equation f(t)= te⁻³ᵗcos²2t

A: We have to find the laplace transform of the given function.   f(t)= te⁻³ᵗcos²2t

Q: an arithmetic sequence is 75 and the second term is 11 Find the first term.

A: Here I am providing the handwritten solution

Q: Find the exact arc length of the curve x = + 2) ? from y = 1 to y = 5. Enter the exact answer. L =

A: Given problem:-

Q: What is the angle between the vectors u = and v = ? 213° O 188° O 111° 120°

A: Solution:

Q: nd the volume of the solid generated by

A:

Q: Find all values of x for which the series converges. (Enter your answer using interval notation.)…

A: Given :

Q: es conve n=1

A:

Q: x'y" – xy' + y = In(x)

A:

Q: While standing on a bridge 30.0m above the ground, you drop a stone from rest. When the stone has…

A:

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A:

Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

A:

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A:

Q: 17) Find the area of the serface genereted by revolving tue curr X> 3t, y=2t about fue x-Qx's on tue…

A:

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = - 10…

A:

Q: Can you find the second subpart to this wue

A: This question has been solved completely. Please ask your query clearly.

Q: Describe the graph of the equation. r = (5 – 21) i + 7tj O Itis a line in 2-space through the point…

A:

Q: Evaluate the iterated integral. /4 y cos(x) dy dx 地

A:

Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 %3D O x- y…

A: The solution is given in the next step.

Q: Exercises: Find the derivatives of: 1. 1-y = (secx + tanx)(secx- tanx) 2- y = x2.cotx- x2 4. 1+cscx…

A:

Q: The vat shown in the accompanying figure contains water to a depth of 1.5 m. Find the work required…

A:

Q: QUESTION 10 If you have $51,000 in student loans at an interest rate of 3%, compounded monthly, what…

A: Solution:

Q: d Calculate ri(t) - r2(t)] and (ri(t) × r2(t)] first by differentiating d dt dt the product directly…

A: This is a problem related to vector's dot and cross product. Based on the rule of dit and cross…

Q: n-1 (-3)' is convergent or divergent. If it's convergent, b) Determine whether the series 4" n=1…

A:

Q: Complete parts a through c for the given function. f(x) = 4x° - 5x - 40x° + 5 on [- 3,4] c. Identify…

A:

Q: 13. Solve the following system of equations using either the substitution method or the graphing…

A: Linear equation: Linear equations are first-order equations. An equation with a homogeneous variable…

Q: Use limits to find f'(x) if f(x) = 3x. f'(x) =| (Simplify your answer.)

A: Consider the function  f(x)=3x

Q: Write an equation for the ellipse that has vertices (+7,0) and co-vertices (0, +6). Provide your…

A: Vertices : (7,0) and (-7,0)Co-Vertices: (0,6) and (0,-6)Vertices are of the form : (h±a , k)h+a=7 ,…

Q: d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating d dt the product directly and…

A:

Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

A:

Q: nance. A person wishes to have $27,100 cash for a new car 4 years from now. How much should be…

A:

Q: Find the volume of the solid bounded by the plane z = 10 - 5x - 8y and the coordinate planes in the…

A:

Q: Find the velocity, speed, and acceleration of a particle moving with position function r(t) = (3t² –…

A: Velocity: Let r(t) denote a differentiable vector-valued function that represents a particle's…

Q: п a) Σ-1 n=1 n2 b) Ση-1 ι=1 (2")²

A:

Q: cos x sinx dx- 3 COS

A:

Q: Find the arc length of the graph of r(t) = = ev2'i + e¬V2'j+ 2tk, 0<t < v2 ln 7 NOTE: Enter the…

A:

Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8xy? = 2y6 +…

A: We need to find the surface integral.

Q: Sketch the region whose area is represented by the iterated integral. dyds un

A: Option C is correct.As lower limit in inner integration is tanx2 which you can see in the graph.if…

Q: (x – 2)y' + y = e“, y(3) = e³ +1

A:

Q: a) Find the average acceleration in the first 3 seconds. b) The particle changes direction twice.…

A: Here I am providing my handwritten solution.

Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti + tj dt

A:

Q: 2 en Does the series converge or diverge? 1+ e 2n n=1 Choose the correct answer below. O A. The…

A: ∑n=1∞ 2en1+e2n=2e1+e2, 2e21+e4, 2e31+e6This is not a geometric series; as there is nocommon ratio…

Q: If the demand equation is D(x) = 180 - 6.3x and the supply equation is S(x) = 8.2x + 3, find the…

A: If the demand equation is D(x) = 180 - 6.3x and the supply equation is S(x) = 8.2x + 3, then we have…

Q: Determine the interval (s) on which the vector-valued function r(t) = ti + Vt + 1j + (t2 + 1)k is…

A:

Q: 1. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

A: