Triangle ABC has vertices A(4, 7, 7), B(1, 6, 5), and C(–2, 9, 8). Which kind of triangle is ΔABC? Justify your answer.

Q: Find the antiderivtive: 3x5+2x²+3 x8 - dx = + C

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Q: Consider the equation x² + y³ + zª − 8xyz = z². Find z point (1,1,1). at the

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Q: Consider the following position function. Find (a) the velocity and the speed of the object and (b)…

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Q: (b) x2n - 2y5n x5n + 4y=n 1/3

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Q: Given the series Σ find the ratio (Express numbers in exact form. Use symbolic notation and…

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Q: Suppose that the mass in a mass-spring-dashpot system with m = 10, c = 7, and k = 1 is set in motion…

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Q: A graphing calculator is recommended. Graph the function in each of the given viewing rectangles.…

A: The given function kx=132x4-x2+2. We have to sketch the graph of the function in the given viewing…

Q: Evaluate the definite integral 3x³-4x² x² -dx

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Q: Evaluate ff xydA, where R = {(x, y) : ²+¹ ≤ 1, x ≥ 0, y ≥ 0}. 36 R

A: First, we need to find the limits of integration for x and y. The region R is the interior of the…

Q: Evaluate the expressions. (Simplify your answers completely. Use only positive exponents in your…

A: Algebra

Q: f g is a differentiable function, find an expression for the derivative of each of the following…

A: Given query is to find indicated derivative.

Q: Solve using Substitution

A: Use appropriate substitution and solve the definite integral.

Q: Find (5 cos(x) + 6 sec²(x)) dx (5 cos(x) + 6 sec²(x)) dx = +C

A: Integration

Q: Suppose that f(x, y) = x + y and the region D is given by {(x, y) | −3 ≤ x ≤ 1, −3 ≤ y ≤ 1}.

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Q: Find the area enclosed by the curve x = t² - 2t y = √t and the Y axis.

A: Eliminate the parameter t and draw the graph then find the definite integration to get the area.

Q: Compute the gradient of the following function and evaluate it at the given point P. g(x,y)=x²-3x²y…

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Q: IP 4-91/2 I |

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Q: Find the limit by rewriting the fraction first. xy-y-2x + 2 X-1 lim (x,y) →(1,9) x #1

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Q: Using the Inverse Function Theorem, what is (h−1)′(−8) given that h(x)=−3x+7/2x+4? Note that…

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Q: The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV =…

A: The pressure, volume, and temperature of a mole of an ideal gas are related by the  equation…

Q: Can you explain the reversing step (first step) in detail?

A: Given Integral:- ∫02∫y2ex2dxdy

Q: 13. Find the unit tangent and the principal unit normal vectors at the given points. r(t) = (-4cos…

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Q: A = (5,-2), B = (-1,-4) AB=(x, y) X= type your answer... y= type your answer...

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Q: Evaluate the limit using L'Hôpital's Rule. 8 0-2 HIL lim x 0 4(e- e *) sin(2x)

A: To evaluate the limit of the function

Q: Consider the following position function. Find (a) the velocity and the speed of the object and (b)…

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Q: 2 An object is moving with a uniform acceleration a = 2ms-², determine the functions for: a)…

A: We will find the required.

Q: Use the first derivative to find all critical points and use the second derivative to find all…

A: Given:   fx=x4-18x2+4 To Find:  By using the first derivative test to find all critical points  and…

Q: Estimate the time for the population to reach 60,000. (Round your answer to two decimal places.) hr

A: Given query is to find the time for population to reach 60000.

Q: A police car is located 30 feet to the side of a straight road. A red car is driving along the road…

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that f(9) = 13, f(13) = 3, f'(13)=9, f'(9) = 7…

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Q: Let F = (2xy + z²x²,2xz) and let C be the circle r(t) = (5 sin t,3 sin t,6 cos t), for 0 st≤ 2.…

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Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise.…

A: Green's Theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA And use the equation of the line when it passes through…

Q: Find the length of the curve over the given interval.

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Q: tion about the origin. hat is the 13. Let T: R2 R2 be the linear transformation such that T(e₁) and…

A: Please see the below picture for detailed solution.

Q: y = In(5x), y = 1, y = 4, x = 0; Sketch the region. 3 1

A: As mentioned we have to only sketch the graph based pn given boundations.

Q: Find the volume of the solid obtained by rotation the region bounded by y=√(x), x=0, x=4, y=0 about…

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Q: Find the solution to the IVP y" + y = f(x), with y(0) = 1, y'(0) = −1, where 0 x 3π f(x) = 0 using…

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Q: Solve equation (10) from Section 7.4 + ["i(t) dr = E(t) (10) L+Ri(t) + dt subject to i(0) = 0 with…

A: The given differential equation is: Ldidt+Ri(t)+1C∫0t i(τ) dτ=E(t)

Q: From the properties of exponential functions, the graph of f(x)=ax always passes through the point…

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Q: Find • 1 1 f²f² (5x + 2y) dxdy 0

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Q: The plane containing the point (0,-1,-8) and parallel to the plane 3x - 6y + 2z = -2 has equation…

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Q: A tank contains 100 gal of fresh water. A solution containing 5 lb/gal of soluble lawn fertilizer…

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Q: Maximizing the Volume of a Box A box with an open top is to be constructed from a square piece of…

A: Four square pieces at the corners of a square cardboard of size 12 × 12 Inches  And it was made into…

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: The base of a solid is the region in the first quadrant bounded by the graph of y = 1- and the 2-…

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Q: sides of the box costs 20¢/ft2. Find the dimensions of the least expensive box that can be…

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Q: Let P(x)= 2x3-5x2-4x+3.  a) List all possible rational zeros of P.  b) Find the complete…

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Q: 5) Differentiate f(x) = √3x² + 4x.

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Q: The graph of y = f(x) (solid) and y = g(z) (dashed) is shown -6 -5 4 -3 -2 f(x) lim 2+1 9(2) 6-8 0…

A: solution: Given graph,

Q: Suppose that f(x, y) = eª/y on the domain D = {(x, y) | 0 ≤ y ≤ 1,0 ≤ x ≤ y³}. D Q Then the double…

A: The given function is: fx,y=exy 0≤y≤1, 0≤x≤y3 To find ∫∫Dfx,ydxdy