Find the dimensions of a rectangle with area 1,728 m² whose perimeter is as small as possib m (smaller value) m (larger value)

Q: Vadas/3-V169 3. Construct a sign analysis for the second derivative function and then use it to…

A: Explanation of the answer is as follows

Q: #6 Suppose the position of a projectile is expressed by the vector-valued function Describe how you…

A: As per Bartley guidelines we are supposed to answer only three subparts of one question per post.…

Q: Find 2u, -3v, u + v, and 3u - 4v for the given vectors u and v. (Simplify your answers completely.)…

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Q: √(√x³ - 2 1/2 + √²) d dax In x++²x+ }\x² +C √√(x³)x=√x + √√2x+C

A: SOLUTION-

Q: Find the area of the region bounded by y = x³ - 8 the x-axis and the y axis. 1/3 3 1/9 9 None of the…

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Q: If u and are orthogonal to each other, then u x O True False = 0.

A: Given :u→ and v→ are orthogonal

Q: 1 - ₁ - £x² = 1 + x + x² + X x=0 +++1-23-²² 3! sin x-(-1). cos x=(-1)- -(-1*- 1 - 2 + 1 - 4 - =…

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Q: 5. Find the telescoping sum 2 k=3(k+1)(k-2)

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: 2. Evaluate the following 3. S²³S² (5x³y² + 3x) dy dx 3 3 9. O

A: ∫03∫01(5x2y3+3x) dy dx

Q: a. y = 3et-2 et +1

A:

Q: 1. Simplify. Write "undefined" for expressions that are undefined. -3 1-6 0 {}} 4 3 5 3 4.) +

A: To simplify the given expression.To write "undefined" for expressions that are…

Q: Find all local maxima, local minima, and saddle points (if any) of the following function. If these…

A: A detailed solution is given below.

Q: Let f(x, y) = 10-3r² +4. (a) Find the gradient Vƒ(2,-3) of f at the point P(2,−3). (b) Find the…

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Q: termine the absolute maximum and minimum values of f(x) = cos²x-cosx the interval 0≤x≤ 2π.

A: Please refer to the image below

Q: In 7 + 4√3 2.63391 ≈

A: The given expression is  ln7+43

Q: 12. Find the equation of the tangent line to the polar curve r = 2-sin(0) at 0 = 1/3. Draw.

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use a double integral to find the area inside one leaf of r=3sin2*theta

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Q: Question 8 A manufacturer has determined that the total cost C of operating a factory is C = 0.5 x²…

A: At what level of production will be average cost per unit

Q: For the function f(x) = 2x², make a table of slopes of secant lines and make a conjecture about the…

A: Slope= df/dx

Q: VII. - ) Let C be the curve consisting of the line segment from (0,0) to (2,0), the the portion of…

A: Given that a curve consisting a line segment from (0,0) to (2,0) and a portion of circle from (2,0)…

Q: Evaluate the following integral: a.) SIS z ln y tan z dV if S = {(x, y, z) = R³ : − 1 ≤ x ≤ 0, e ≤ y…

A: S is a rectangular cuboid, hence limit of each individual are independent so the integral are…

Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x² -…

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Q: x² +9 √(x² - 1)(x^² + 4) In 1x + 11 + In |x-1| + tan-¹) + C Option 1 In x +11+ In |x-1|-tan ¹ () + C…

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Q: The current population of a certain bacteria is 2050 organisms. It is believed that bacteria's…

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Q: Let p(t) represent the population of a major city t years after 1950, as shown in the table and…

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Q: Solve for the slope of each of the given point of a function

A: Given that,

Q: Evaluate f(x³ -x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

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Q: There are 30 emoticons. If 15 of the emoticons show hapinnes, 10 show confusion and 5 show anger,…

A: The answer is given below:

Q: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y² +…

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Q: Determine if the function is continuous on the given interval. - 1. f(x) = √x² – 25 ; [−6, −5] 2.…

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Q: Find the vertical asymptote of the following function. X - 1 f(x) = 2x + 18 X =

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Q: Determine the interval(s) where f(x)-In (5x+10) is continuous. It is continuous in the interval

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Q: Let r(t)=(3-2 cost)i + (2+2 sin t)j. Find the arc length parametrization in term of the arc length…

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Q: Find dy/dx, if y= (3+cos x) ^(2x+1)

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Q: Find derivative of each; A) m(t)= In(4t^3+tan(5t)) B) h(x)= 4sin^8(5x+1)

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Q: Find the area (in square units) bounded by the parabolas x² + 2y - 8 = 0. a. 7.10 sq. units b. 7.01…

A: Here we have to find the area bounded by the parabola.

Q: Find in the parametric equation d'y dx² x = 5 sin² t y = 2 cost 0≤t≤ 2π.

A:

Q: Find the volume of the solid generated by revolving the region bounded by y = 2x, y=0, x=0, and x =…

A: The given lines are y=2x, y=0, x=0 and x=4.   So, the bounded region is as shown below. Apply the…

Q: Find an equation of the plane tangent to the following surface at the given point. yz e x² + +42=0;…

A: The given equation is;  yzexz+42=0; (0,-7,6).

Q: 4. 2-5 2 -1

A: Given: ∆=|2-52-1|

Q: VI. Consider the conservative vector field 1. F(x, y, z) = (z cos(rz) -y sin(ry), 2y cos(ry) - ry²…

A: Solved below.

Q: 26. *2# 70 x² sin x dx

A:

Q: Find the general solution of the following DE. xy² (y')² + y(x - 1)y' - x³ = 0

A: The given differential equation,    xy2y'2+yx4-1y'-x3=0

Q: 1/2 x3 1-x4 1/2 √3 - 2/2 √2/560 16 Option 1 1/11 Option 3 1 15 2 16 dx 1 Option 2 Option 4 15 8 √15…

A: Given, ∫012x31-x4dx

Q: Find an equation of the plane tangent to the following function at (0, 0): O z = 9 O 2x +2y+z-7=0 O…

A:

Q: 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

A: Given problem:- 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

Q: 1. Find of ахду OF f(x,y) = xy (x+y-1) -x2

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Q: xy² (xdy + ydx) = (xy - 2)dy

A: We have to solve given Questions.