Find an equation of the plane that passes through the points (-6, 1, 1), (0, 3, 5), and (1,0, –1). Equation:

Q: Find the area of a triangle PQR, where P = (2, – 3, – 4), Q = ( – 6, – 2, – 6), and R = (5, 6, – 6)

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Q: 1 (a) log16 2 = 4' That is, write your answer in the form A" = C. Then А |, B = and C 1 (b) log, 16…

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Q: Evaluate the integral. [TI/3 2 sin(0) + 2 sin(0) tan2(0) sec2(0) de Step 1 2 sin(0) + 2 sin(0)…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: 1 Using u = 1 + 2x6, then the integral | x°(1+ 2x6)5 dx becomes 12 us du- This evaluates as 5+1 1 12…

A: Follow next step

Q: A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms…

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Q: u = 7i + 5j + k v = i+j+ 8k w = i+ 2j + 5k nd the volume. i

A: Given query is to find the volume.

Q: By expressing the product as a sum, 2cos(3x)cos(4x)= ?

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2r sinh(r – 1) +2 – r %3D has a critical number…

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Q: average cost per gigabyte of RAM can be approximated by the function C(t)= 8,500,000(0.65)^ t, where…

A: Given query is to find the the average cost of ram for the given time.

Q: A box with a square base and open top must have a volume of 13,500 cm. Find the dimensions of the…

A: Given query is to find the sides of the box

Q: The thermometer reading 70oF is placed in an oven preheated to a constant temperature. After 1⁄2…

A: The temperature of the oven is 390°F

Q: a) How many 3-digit positive integers are there with odd digits?

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Q: TEST 1. DETERMINE WHETHER EACH OF THE FOLLOWING FUNCTI a. CONTINUOUS b. DIFFERENTIABLE 1. f(x) = 5x-…

A: To determine whether the given functions are continuous and differentiable or not.

Q: Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are…

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Q: x2 1. Let f(x) = 3Vx² – 1 and g(x) x4 – 81 (a) Determine the domain of f and g. (b) Compute gof and…

A: Find domain.  According to guidelines we solve only first question.

Q: Find two unit vectors in 2-space that make an angle of 45° with 8i + 3j. NOTE: Enter the ezact…

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Q: Complete the parametric equations for the line where the planes 8x + 13y – z = 27 and 9x + 15y – 12z…

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Q: Let g be a function that is defined for all x, x # 2, such that g(3)% = 4 and the derivative of g is…

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Q: 2. Evaluate the following limits. x+ 1, if x 1 c. lim f(x) a. lim f(x) b. lim f(x) x→1+ x→1- X→1

A: Explained below

Q: 28. f,(2,4) if f(x, y) = x* In y

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Q: Find the distance between the parallel planes – 2x + y + z = 0 and - 10x – 5y – 5z – 11 = 0. - NOTE:…

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Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

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Q: Find the derivative: y = (3x² – 2x) Væ5 – 2x + 2 %3D

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Q: During the summer months Terry makes and sells necklaces on the beach. Last summer she sold the…

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Q: Graph the following vector addition: + Start from the origin. One vector to show One vector to…

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Q: -3/2 dx S(35 + 4x – 4x²)

A: Explained below

Q: ind equations of the following. 2(x- 8)2 + (y- 4)2 + (2 - 7)2 - 10, (9, 6, 9)

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Q: Solve the differential equation. dP 3 Р(4) — 20 dx Using sqrt{t} for Vt. P(t)= 6sqrt{t} +8 O P(t)=…

A: Given query is to solve the differential equation.

Q: 2. Evaluate the following limits. x2-4x+4 a. lim x→5 x*-8x³+24x²–36x+16

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Q: Given –6i is a root, determine all other roots of f(x) = x + 2x² + 36x +72. x= -6, ±2i x = -2, +6 x…

A: Given query is to find the other two roots.

Q: n: - 4.r? with f'(x) = (x+ 2)2 r(r+8)(r – 2) (x + 2)3 8(7.r – 4) - f(r) = and f"(x) = %3D %3D %3D…

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Q: Find the vector component of v = (4, - 1, 7) along b (3, 6, -6) and the vector component of v…

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Q: Given that arcsec e) + (x – y²)² = 2. (a) Find dy using implicit differentiation. dx dy using…

A: Given,            arcsecyx+x2-y232=2

Q: Find the derivative of the function described. (Rx5) 1. у %3D (2х + 3) (5х — 4) y = | Зх-1 2. f (x)…

A: Let's find.

Q: For the function f(x) = -x^3 + 1.5x^2 - 4: a. Find the critical number of the function and…

A: We will use critical points for calculation

Q: rational functions solve suppose it costs C dollars ( in billions) to build X miles of a wall…

A: A)C(x)=0.425 x1954-xwhere, x is the miles of the wall.cost to build 1000 miles of…

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (– 8,…

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Q: At which points on the curve y = 1 + 60x3 - 2x5 does the tangent line have the largest slope? 1 5…

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Q: DIFFERENTIAL EQUATIONS Solve the following application problems. *show the every details of your…

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Q: Evaluate the integral. 10) 5x2 V5 + 3x3 dx

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Q: Find the equation of the tangent line at the given point on the curve. 3y - Vx = 23, (16,3) y =

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Q: The student should answer the question below: Evaluate the given equation: | ydA where T is the…

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Q: Given: a, =4, d=-1 Answer the following questions. Part: 0 / 2 Part 1 of 2 (a) Write the first five…

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Q: The dimensions of avectargubr region are varying with the bimeltsaccoding 1-2728 cmfsee and wa3t+6…

A: L= 2t2-8w= 3t+6Let A be the area of rectanglegiven : dAdt= 360 cm2/sec   A= L×wA=(…

Q: In 6 19) ex dx In 3

A: ∫ ex dx = ex +C

Q: 7. Х Arcsec (2х) dx 3 (4x2 – 1)7

A: The objective of the question is evaluate the indefinite integral.

Q: Let g be a function that is defined for all x, x # 2, such that g(3) = 4 and the derivative of g is…

A: Here, g(3)=4 & g'(x)=x2-16x-2, x≠2

Q: sin t 11) dt (5 + cos t)6 A) (5 + cos 5 + C B) (5 + cos t)5 +C 1 7(5 + cos t)7 D) 5(5 + cos + C

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Q: If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) =…

A: Average Cost = C(x)x. Marginal Cost = C'(x)