Find the area of one petal of r = 9cos30

Q: f(x) and (f'(x))² into the surface area equation above to find b Surface Area = Lº 2π. = a 5 5 2π…

A: To explain how was the 2 used from 2pie. How is it determined the 2 is needed, when in other cases…

Q: Solve 12 sin² (x) – 5 cos(x) — 9 = 0 for all solutions 0 < x < 2π x = - - Give your answers accurate…

A: x = 0.39π, 0.77πExplanation:

Q: Use integral tables to evaluate the integral. Sx√29x-7dx Click here to view page 1 of the Table of…

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Q: Calculus Math Question. Please help.   Thank you

A: Derivative of y with respect to x is given below Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Find the curve's unit tangent vector. r(t) ti+ k. Osts3 The curve's unit tangent vector is (++ (k.…

A: The given vector valued curve equation is The unit tangent vector given by

Q: A. Find S'(t) B. Find S(20) C. Find S'(20)

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Evaluate the definite integral. 5 L³× √5x² - 4 dx X

A: Answer is  3266​Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Solve dy = ex-y+x²ey dx

A: In this question, we need to solve this problem.

Q: You can see that the amount of medication enters the therapeutic window quickly, but goes below the…

A: Solution is given below Explanation:Step 1: Step 2: Step 3: Step 4:

Q: (d) Horizontal asymptotes. (e) Intervals where f is increasing and decreasing. (f) Local minima and…

A: Given: To Find: To determine the following: (d) Horizontal asymptotes(e) Intervals where f is…

Q: Q2) Find the derivative of f(x)(Hint: use the fundamental theorem of calculus -part f(x)= | 1+2x t…

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Q: The equation r(t) = (2t+3)i + (312-3) j + (3t)k is the position of a particle in space at time t.…

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Q: Homework

A: To minimize total production costs, we need to find the values of L and K that will maximize…

Q: Which of the following statements are TRUE? Select all that apply. If F(x) is an antiderivative of f…

A: To determine the true statements.

Q: With a present value of $130,000, what is the size of the withdrawals that can be made at the end of…

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Q: +x 2 1 dx X

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Q: Solve the given symbolic initial value problem. y''+4y' +13y=38(t-л); y(0)=2, y'(0) =2 y(t) = ☐

A: The given differential equation

Q: Question 6: Find the equations of the tangent and the normal line to the curve g(x) = the point…

A: As we knowThe equation of tangent line at the point with slope  is The equation of the normal line…

Q: 2. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: The equation of  the tangent line to the curve x2+2xy−y2+x=20 at the point (4,8) is…

Q: Let ā = (−4, −5, −3) and 6 = (-5, −4, 4) Find a × 6. V >

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Q: Consider the curve x sin(xy - y2) = x 1. (a) dy dx (b) 913 dx dy

A: Question No. (3);Consider the curve .To find the following:

Q: The equation r(t)=(12 sin t) i+ (4 cos t) j +(8t) k is the position of a particle in space at time…

A: The equation  is the position in space in time . To find the particle's velocity and acceleration…

Q: X 3x2 +5 dx x4

A: To find the indefinite integral and to check the result by differentiation.

Q: Use sigma notation to write the sum.

A: ​[2(1+n3​)2](n3​)+⋯+[2(1+n3n​)2](n3​)=i=1∑n​[2(1+n3i​)2](n3​)​Explanation:Step…

Q: In the mega millions lottery game, a player picks 5 numbers 1-75 and a mega number 1-15. Each ticket…

A: The objective of this question is to calculate the total cost of playing all possible combinations…

Q: Given the points P(-2, 6, -2), Q(5, 7, 2) and R(3, 4, −1). Find the angle, 0, in degrees, that is…

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Q: Let s(t)= v(t) == 6+3 + 45t² + 108t be the equation of motion for a particle. Find a function for…

A: We need to find velocity and acceleration.

Q: Write out the general form of the partial fraction decomposition of the function (as in Example 7).…

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Q: The points A[−1, 1, 1], B[2, 0,3], and C[3, 3, -4]. Show that this triangle is a right-angle…

A: Please see the explanation Explanation:Step 1:

Q: 4) Find the derivative from FIRST PRINCIPLES of √(x) = 2√x (You will need to rationalize the…

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Q: x(t) = 6-7t Find a plane containing the point (-6,-5,-3) and the line y(t) = -6-7t z(t) = 5 - 8t

A: Given that the plane containing the point (−6,−5,−3) and the line {x(t)=6−7ty(t)=−6−7tz(t)=5−8t

Q: Exercise: Solve the equation d³y dx3 +3d²y dx² dx +30 + y = 0

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Q: horizontal asymtotes of  1 (x−3)2

A: The objective of this question is to find the horizontal asymptotes of the function 1/(x-3)^2. A…

Q: Question 4 Consider the curve 5x²+4xy+4y³ = 29125 (a) Show that P(-75,-5) is on the curve i.e., show…

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Q: Where did the 2 go from in 2 pie? I am confused as to why its used sometimes and other times it is…

A: The objective of the question is to find the volume of the solid of revolution formed by revolving…

Q: 1) Write an equation of a function that meets the given conditions (a) x-intercept: (1,0), (3,0);…

A: Given conditionsx-intercept  ,vertical asymptotes , horizontal asymptote x-intercept  ,vertical…

Q: Let f(x)=xex. (Round all answers to four decimal places, if necessary.) (a) Find the interval(s)…

A: The given function is As we knowThe function concaves up when The function concaves down when The…

Q: Find the horizontal and vertical asymptotes of the curve. You may want to use a graphing calculator…

A: x=−1,0,1y=−1Explanation:Given the equation,y=x2−x42+x4​ Solving for horizontal and vertical…

Q: y= (sin(x))6x³-8x+17

A: y=(sin⁡(x))6x3−8x+17Taking natural log both sidesln⁡y=ln⁡[(sin⁡(x))6x3−8x+17]Using logarithm…

Q: please help solve

A: The objective of the question is to find the value of the function y at x=3, given that y is a…

Q: Find equations of the following. y = ln(x+2), (0, 0, 1) (a) the tangent plane × (b) the normal line…

A: a)) x-y+z=1b)) x= -t y= tz= 1-tExplanation:Step 1:Step 2: Step 3: Step 4:

Q: 1. a) y = Differentiate the following and simplify: 2x3. (2x2 - 1 ) 3x²+1.

A: dxdy​=(3x2+1)630x(x3+x+1)(2x3−1)4​Explanation:

Q: Find к for the space curve r(t)=(12 sin t) + (12 cost) j +9tk. K(t)=[ (Type an exact answer, using…

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Q: The graph of the function f on the interval 0 ≤ x ≤ 8 consists of two line segments and one…

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Q: Please don't provide handwritten solution ...

A: Therefore, the required solution is y=3.39−e3.39x​+6.36728745549863034The table is…

Q: At what point on the given curve is the tangent line parallel to the line 3x - y = 6? y = 5 + 2e* -…

A: (x,y)=(ln(6),17−9ln(6))Explanation:

Q: The function f(x)- is concave down on which interval?

A: The function f(x) is concave up on the interval I if f"(x) &gt;0 for all x in I.The function f(x) is…

Q: 2. Write an equation for sine and cosine for the graph below. 5. 0 5 10 15 20

A: We have given a graph of the function and we have to find the corresponding sine and cosine function…

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

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Q: Calculus One Problem. Please help. Thank you.

A: dxdy​=(5x4−10x)cos2x4+(x5−5x2−2)(−8x3sin2x4)Explanation: