H.W: find the angle between the planes x + y = 1 and 2x + y- 2z = 2

Q: Find T(t) and N(t) at the given point. r(t) = 10 cos(t)i + 10 sin(t)j + tk; t = 2 TE) -| 6) =

A: we have to find unit tangent vector and normal vector.

Q: Consider the plane curve given by the parametric equations x = t² + 22t - 23 y = t² + 22t - 5 What…

A:

Q: If f(x) = 6(a-3/+7), find f'(2). Find f'(5).

A:

Q: Write the following expression as a single definite integral of the form [²f(x) dx + [²³1(x) dx - [~…

A: Given query is to find the value of the integral.

Q: Use the indicated method to approximate the area under the curve f(x) = x³ + 28 on the interval [-3,…

A:

Q: (b) Given the demand function P = 120 – 3Q, fixed cost, FC of 50 and variable cost, VC of 5 per unit…

A: Find your answer below

Q: 5. J sinx cos²x dx V1 − cosx -

A:

Q: 4+ 2t + et dt

A:

Q: Suppose that f(x, y) is differentiable at the point (3, 1) with f(3, 1) = 4, fx (3, 1) = 2, and fy…

A:

Q: 7. Find the partial fraction decompositions of the following rational expressions. a) b) (x²+11x) dx…

A:

Q: y? = x and y2 = 2 – x %3D

A:

Q: D(x) = 62-0.1x

A: answer is in next step

Q: The traffic flow rate past a certain point on a highway is q(t) = 1300 + 2200t – 390,² where t is in…

A:

Q: Evaluate the function at the indicated value of x =1. f(x)=loggx 8 -8 - 1011 8 0

A:

Q: 2x-5y ≥10 y-axis 4 3 2 1 -54-3-2-1 1 2 3 4 5 6 6 5 N -3 -4 -5 -6 x-axis

A:

Q: Evaluate F. dr. F(x, y) = 7xi + 4yj C: r(t) = ti + V4 - tj, -1 sts

A:

Q: Find the centroid of the given region. y = 2-x? y = x A (3/22,45/61) В) (5,15) c) (5/14,38/35)…

A: Centroid is x¯,y¯ , where, x¯ = 1A∫ab xfx-gx dx  and y¯ = 1A∫ab 12 fx2-gx2 dxand A = ∫ab f(x)-g(x)…

Q: How much work is required to pump all the water from a right circular cylindrical tank, that is 8…

A:

Q: he conclusion of Green's Theorem by evaluating both sides of each of the two forms of Green's…

A:

Q: Find the first four terms of the Taylor expansion of the solution to the given differential equation…

A:

Q: 2. Given the function f(x) = 2x² + 3x + 1, a. Use the secant method to find the instantaneous rate…

A:

Q: Find the formula for the nth term of the arithmetic sequence.  Use the formula to find the 20th term…

A:

Q: A2. (a) (i) Find the future value of £2000 when it grows at an annually compounded rate of 5% for 10…

A: To find the future value of £2000 when it grows at an annually compounded rate of 5% for 10 years.…

Q: X 75 ft 0 A pole stands 75 feet tall. An angle is formed when wires of various lengths of a feet are…

A:

Q: In the simple model of a national economy:

A: answer is in next step

Q: 2. [x² √x + 1 dx

A:

Q: Find for the equation below. dy dt

A:

Q: 3. A container in the shape of a (right) cylindrical can with an open top of volume 87 cm³ is to be…

A:

Q: Given the graph of the function f(x), answer the following question. -30 B C F -20 -10 A D E 4 -10…

A:

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 3 cos…

A:

Q: Find the limit. If you L'Hopitals Rule, make sure to justify why you can use i use lim 2?e

A: We have to find the limit.

Q: Solve for the Maclaurin series. You can write the first 5 terms or express in summation notation…

A: Maclaurin series is expansion of function at x= 0.

Q: Ex: Show that if v, u, w are any vectors, then (H.W.) ux (v x w) + v x (w x u) +w x (u x v) = 0.

A: Dot Product Property :- a.b = b.a = a*b*cosθ

Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: x = 4…

A:

Q: Find the area between the innér and outer loops of the limaçon r = 2 – 4 sin .

A: This is a problem related to area of the polar curve. based on the graph of limacon curve we will…

Q: Find an equation of the tangent line to the given curve at specified point. (1, 1/4).

A:

Q: 1. Evaluate the Riemann sum for f (x) = x² , 1 < x < 3, with three subintervals, using left…

A:

Q: Evaluate the integral of the following using Miscellaneous Substitution X Sdx 1+x 5.

A:

Q: inverse laplace (7s-2)/(25-s^2)

A:

Q: Use the Fundamental Theorem of Calculus to find the "area under the curve" of -² + 7x between x = 2…

A: The region is bounded by -x2+7x between x=2 to x=5

Q: If q'(t) is the growth rate of a population of a fish population in fish per month, what does…

A:

Q: 구. ( 34 Cxtd) ax An 14 X? (X-1)

A:

Q: 1. Use the limit definition of derivative (no shortcuts!) to find the derivative of f(x) = 3x² + 2x.

A: The formula for derivative of function f(x) using limit is given by:…

Q: · ln(1+x) a) dx f (1+x)7 u= du = b) f(2x + 1) tan-¹ √√x dx U= du = c) f x² sin(2x) dx U= du = dv =…

A: I have performed integration by parts for the part a) and for the rest I have mention the u and dv…

Q: The population of a slowly growing bacterial colony after t hours is given by p(t) = 5t² + 31t +…

A: The objective of the question is determine the growth rate.

Q: X : Let f(x) be a function defined by f(x) = 1

A:

Q: L(25 — х?)3/2. |dx

A:

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. Σ+1+1, k+5 k(k…

A:

Q: Perform

A:

Q: If 3x² + 2x + xy 2 and y(2) -7, find y' (2) by implicit differentiation.

A: