Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.) [ (³ - ²/1 ) ²( ² ) d dt

Q: Find the distance between the points with polar coordinates (6, π/3) and (8, 2π/3).

A: formula for distance is  D=(x2-x1)2+(y2-y1)2in rectangular coordinates  x=rcosθ and y=rsinθgiven…

Q: 33. Water is stored in a right circular cone as shown. Water is being added to the cone at a…

A: We have to find rate of change of height of water.

Q: (c) At what points is the height 40 m? (Round your answers to two decimal places.) (x, y) = -52.825…

A: The given equation of the arch:y=211.49-20.96 cosh0.03291765x

Q: Integrate using u-substitution or 2 guys in Jail. fx sin(2x²) dx 5. (4x³-2)7 (24x²)dx

A: (4)   I=∫xsin(2x2)dx∫sinxdx=-cosx+cdxndx=nxn-1

Q: Could you find the equation of the graph?

A: A logarithmic graph is given and we have to find its equation.

Q: Use the method of undetermined coefficients to solve the given nonhomogeneous system. X(t) = dx dt…

A:

Q: 10) a 26 foot lodder bons against a building so that its foot moves away from the building at the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (c) sin 13л 15 COS Зл 15 COS 13п 15 sin 3п 15 Answer: sin 10п 15 = sin (2) 3 2п √√3 =

A:

Q: Determine all values of x. (if any), at which the graph of the function has a horizontal tangent.…

A:

Q: Let f(x,y) = 5xy4 + 5x²y. Find 224 ах = a²fa²fa²f 1 2' ахду' ax2' ay²' and 224 дудх

A:

Q: (D7 + 2D6 + 7D5 + 14D4 + 8D³ + 16D² - 16D - 32) y = 0

A: The given differential equation D2+2D6+7D5+14D4+8D3+16D2-16D-32y=0. We have to find the general…

Q: 15

A:

Q: Solve: y (cosx)= (9+ y²)

A:

Q: 4- Say whether each given sequence is a geometric sequence, or not. Find the common ratio and the…

A:

Q: An airplane flies at an altitude of a = 6 miles towards a point directly over an observer. Consider…

A: According to question,Given data,a = 6 miles,x = 10 miles,Speed of the plane = 400 miles per hour.

Q: Solve the following initial valuc problem using the method of Laplace transforms y" - 4y + 5y = 8c³;…

A:

Q: 6. Given that (a) sin csc x=3, 90° <x<180° find X 3+2√2 6 ×IN Answer: sin- 2

A:

Q: 5 If ["f(x) dx = 8.1 and ["f(x) dx = 3.7, find rox) f(x) dx.

A:

Q: 3) Find curl (xyi + yzj + zxk)

A:

Q: Differentiate: y dy dx 11 In(x) 26

A: Let's find derivative of given both  problem.

Q: The answer

A: We are asked to find the increase in cost if the production level is raised from 1200 units to 1800…

Q: Differentiate the function. F(t) = (3t - 5)² F'(t) =

A: Let's differentiate given function.

Q: Does the series converge conditionally ot absolutely

A:

Q: Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the…

A:

Q: Find the area between the graph of y = 5 - 5x^(2/3) and x-axis and −1≤ x ≤ 8 using properties of…

A:

Q: Find dy/dx. x=tsin(t), y = t² + 5t

A: SOLUTION-

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm/min.…

A:

Q: The marginal cost function C'(x) was defined to be the derivative of the cost function. If the…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Determine the solution of the following differential equations. a) (D² +9) y = 81x² + 14cos3x

A:

Q: The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at…

A:

Q: Solve by separation of variables: dy dx y²-4 x²-1

A: According to our guideline we are supposed to do the only first question if you want any particular…

Q: 1 1 1 은 관 + dt

A:

Q: The farmer knows that the area of the rectangular enclosure must be at least 400 square meters. This…

A:

Q: 3 x³e2x dx

A:

Q: Use graphs to evaluate 2π S 0 sin x dx and 2π So 0 cos x dx.

A: The given integrals ∫02πsinx dx and ∫02πcosx dx. We have to find the value of the integrals using…

Q: Determine the x-value of all critical points for the following function. x² x-3 f(x) = x² x-3 The…

A:

Q: A as it is wishes to manufacture a box with company a volume of 32 ft³ that is open on top and is…

A: Given, Volume of box = 323 ft3 Length is twice of the width. Let, Length of the box = L Width of the…

Q: Find the exact length of the curve. x = e² + e-t,_ y = 5 - 2t, 0 ≤t≤ 2

A:

Q: Find the Laplace transform of f(t)=sin(2t) + cos (21)

A: we know  Lsin(kt)=ks2+k2Lcos(kt)=ss2+k2given  f(t)=sin(2t)+cos(2t)

Q: 5) Given f(2) = 3, f'(2) = | of H(x) = f'(x), thun H'(3) squale, 새ㅎ B) ㅎ 엊 미ㅊ E) |

A: Given query is to find Indicated derivative.

Q: Given the absolute function graphed below, find the following: -3 -12 a) Domain: b) Range: 6…

A: Answering the first three subparts of the question,

Q: U. Solve the given equation 1) sec x(2 sin x-√2)=0 T Answer: x==+2nk, 4 TT ak 3π x== +2 4

A: Given query is to find the solution of the expression.

Q: Which of the statements a through i about the function y = f(x) graphed here are true, and which are…

A:

Q: Obtain the general solution of the D.E. y - 4y + 4y=e²x O 1 + y=c₂e²+ = x²e² O 1 2x y=₁₁²³² +₂²² + =…

A:

Q: 32. The radius of a circle is increasing at a constant rate of meters per second. What is the rate…

A:

Q: Differentiate. f'(t) = f(t) = 8t t³t-1

A:

Q: 24. Below is the graph of f(x) lim f(x) = x-1 f(-1)=

A:

Q: Find a polar equation for the curve represented by the given Cartesian equation. x² + y² = 4cx k

A:

Q: Differentiate. y' = у 4x 3 - tan(x)

A:

Q: assume that Dr. Kim decides to purchase a car which is selling for $55,000 today. She needs to make…

A: Given query is to find monthly payment.