Given the Vertices v1 = (3, 1), v2 = (1, 4), v3 (6, 5). Calculate the normal vectors n1 of vertex = v1. Prove that the normal is perpendicular.

Q: Question 5 (i) Use the diagram below to find sin(0), cos(0) and tan(0). (ii) If sin (500) -1…

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Q: Find the equation of y, given the derivative and the indicated point on the curve. dy dx = 2x - 1 y…

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Q: im not really understanding because its typed

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Q: Solve the differential equation dy da - y²+7xy+16x² x² a. x + y = O b. x Y = ; when x = 1, y = 1 5…

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Q: 6. Which of the following expresses (3√32 + √√8 ) in simplest form ? a) 3√40 b) 6√10 c) 3√2 d) 14√2

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Q: Compute the length of the curve r(t) = (-4t, 5t — 3, -2t + 3) over the interval 0 ≤ t ≤9 L =

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Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) e) y = (52)²x g) y =…

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Q: A particle moves along the x-axis so that its position at time 0 ≤ t ≤ 18 is given b x(t), whose…

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Q: The area of the surface formed by revolving the curve x = 2√1-y in the interval 0 ≤ y ≤ 1 about the…

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Q: Consider the region R bounded by the functions f(x) = 3x and g(x) a. (4,2) b. (4,1) c. (22², ²) C.…

A: Region R is bounded by the functions f(x)=3x, g(x)=x2+2 Their intersection points…

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A: We need to find maxima and minima.

Q: Which of the following is a possible equation for the following trigonometric function?

A: To find which of the given equation is possible equation for the trigonometric function.

Q: Find the difference quotient f(x+h)-f(x) for f(x) = x² - 4x. h

A: Here is the solution:

Q: 5) Calculate the area of the region between the curves: y = 2 = x² and y = x²

A: We can find the area as below.

Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

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Q: Use the matrices below to perform matrix multiplication. B If the operation is undefined, enter NA.…

A: Please see the below picture for detailed solution.

Q: 150 5 -4 -2 100 50 -50 -100 -150 200! 2 4 6 8 Xx

A: We know that, The highest point the graph ever reaches is the absolute maximum. The lowest point the…

Q: The function f(x) = x³ + 7x² + 7x − 25 is graphed below. Plot a line segment connecting the points…

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Q: Solve the differential equation [cos (2y) — 3x²y²] dx + [cos (2y) - 2x sin (2y) - 2x³y] dy - a. sin…

A: Given: cos2y-3x2y2dx+cos2y-2xsin2y-2x3ydy=0

Q: Exercise. Find the curvat 1. R(t) = ti+t²j+t³k

A: R(t)=ti+t2j+t3k Curvature formula κ(t)=R'(t)×R''(t)R'(t)3

Q: 3. Use the graph off to find the followings. a) b) c) 5 4 3 2 1 f(1) f(-2) 32 --14 -2 -3 234 5.X…

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Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

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Q: 21. y = sech(√√x)

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Q: For the following equation, find Answer: dy da || y = -4x5 8x³ + x² +9x

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Q: Calculate (t) when k(t) = r(t) = (6t¯¹, 1, 6t)

A: r(t)=6t-1, 1, 6t Formula for  curvature κ(t)=r'(t)×r''(t)r'(t)3

Q: 3. State the components of a unit vector that is perpendicular to the vector = (5,2,−1).

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Q: A woman standing on a hill sees a flagpole that she knows is 70 ft tall. The angle of depression to…

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Q: Write the interval in set notation. [2, 6) {x | 2 < x ≤ 6} {x | 2 ≤ x < 6}   {x | 2 ≤ x ≤ 6} {x | 2…

A: Write the interval in set notation. [2, 6) {x | 2 &lt; x ≤ 6} {x | 2 ≤ x &lt; 6}   {x | 2 ≤ x ≤ 6}…

Q: A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a…

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Q: -5 -4 -3 -2 -1 E у 6 5 4 3 2 I 1 H - -21 3 -4 -5 -6 1 2 3 4 5 X

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Q: egrate the following by hand, shc 9 (a) 3 3 √x³ - 24+8) dx

A: We can solve this as follows:

Q: = Express the following equation in standard form: y · 2(x + 2)² − 6

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Q: Determine the type of function shown in the graph below. a) Polynomial function Ob) Rational…

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Q: If f(x) Files = Time left 0:5 sin²x and g(x) = 1 + cos²x, how are f'(x) and g'(x) related? Maximum…

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Q: The function f is graphed below. State the values that fulfill the following requirements. If there…

A: Please see the below picture.

Q: Solve (x² 1 + 2y) dx + (1 - x²) dy = 0; when x = 2, y = 1 1) (x + 1 + 2 ln x 1) b. (x + 1) y = (x −…

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Q: or the equation, find the slope m and y-intercept (0, b) (when they exist). (If an answer does not…

A: An equation of the form y=mx+c called slope intercept form of line where slope = m and y-intercept =…

Q: Find the differential dy of the given function. (Use "dx" for dx.) √ dy y = 2√x +

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Q: 2 -1 4 3 N у -1 1 2 X

A: Graph of the function is given, we have to find its domain and range

Q: 2 6) Compute the area bounded by y² + 2y + 4 and y = 4.

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Q: 5y4+7=x4-3y; x=3, y=-2

A: To find slope of a line tangent to the given curve at a given point. To make a sketch of this…

Q: Determine the following limit in simplest form. If the limit is infinite, state that the limit does…

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Q: A fast-food restaurant has a cost of production C(x) = 14x + 108 and a revenue function R(x) = 82.…

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Q: Use summation properties and formulas to rewrite and evaluate the sum. 31 Σ [(3i)² – 6i] - i=1

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Q: Is the following piecewise function continuous? if x < 0 0<if x < 3 if 3 < x f(x) = -3x² x - 3, . -x…

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Q: Exercise. Find the curvature and the radius of curvature at any point. 2. R(t) = e²¹i + (t²-1)j 90#-…

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Q: Find the area of the region bounded by the graphs of the equations. y = 7x² + 3, x=0, x=2, y = 0

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Q: The sequence {(1 + 1)^² +1} 2n O O converges to e² is divergent ez converges to e 2 O converges to e

A: Sequence

Q: Find f(x) if y = f(x) satisfies dy dx 80yx⁹ and the y-intercept of the curve y = f(x) is 6. f(x) =

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= - 4 cos…

A: We  have given polar equation  r=-4cosθ-6sinθ Using cartesian equations x=rcosθ y=rsinθ x2+y2=r2 Put…