dy 2v= cos2y = cos2y

Q: Suppose thatf is a function defined as f(T) = – 3x* r° + 2x – 5. Find an equation for the tangent li...

A: Given fx=-3x4-x3+2x-5. Find the derivative as shown below: f'x=-12x3-3x2+2. Obtain the value of the ...

Q: The area of a square classroom is 169, what is the side length of the classroom?

A: Given,  Area of a square classroom is 169. We have to find side length of the classroom.

Q: 1- Find the average rate of change for y = xo = 1 X, = 2

A:

Q: Fernando invested money in a 3-yr CD (certificate of deposit) that returned the equivalent of 4.4% s...

A: let x be the amount invested with a 4.400 interest in 3 years and the amount invested with a 300 int...

Q: Two planes leave from Atlanta, Georgia. One makes a 5.2-hr flight to Seattle, Washington, and the ot...

A:

Q: dy 3. dx cosx – ysinx = sin2x

A:

Q: Work though all integrals. Determind the area of the bounded region the region is bounded by y = x, ...

A: Consider the curves, y=x,   y=3-2x,    x=0 To sketch the region,

Q: x2 -9 + т, х# 3 Let f(x) = x-3 тx + 3k, x = 3 Is cont. at x = 3, find the value m&k if f(-1) = 8. %3...

A: Givenf(x)=x2-9x-3+m, x≠3           mx+3k ,    x=3To check f is continuous at x=3.

Q: Find an equation of the tangent line to the following curve at the given point. y = e cos TX, (0, 1)

A:

Q: p2 (x³ – 1)(x² + 1) What is the value of F(a) in the evaluation of the definite integral xp- -1 X-1

A: Perform integration

Q: Is R, equipped with the finite-closed topology, Hausdorff? Provide a proof supporting your answer.

A: Given: ℝ is equipped with the finite-closed topology. Let, ℝ with this topology be Hausdorff and x, ...

Q: How many square units is the total area bounded by y=x° +1 and by the x-axis from x = -2 to x = 2?

A:

Q: 4x2 . Find the open intervals on which Let f(x) %3D X – 4 f is increasing (decreasing). Then determi...

A: fx=4x2x-4 Differentiating with respect to x, we get f'x=d4x2dx·x-4-dx-4dx·4x2x-42=8x·x-4-1-0·4x2x-42...

Q: Let p,q and r are three propositions. Using the truth table, show that: 1. pv q=q v p(J la) (H. W) 2...

A:

Q: z + 14z + 49 f(z) = f(7) =| lim f(z) = 1. %3D z2 - 14z + 49

A: Since you have asked multiple question, we will solve the first question for you. If youwant any spe...

Q: Differentiate: y = 6ª · log6 x (Hint: simplify your answer as much as possible. Use logy M = N, if n...

A: Given: The function is  y=6x·log6x   To determine: The derivative of y=6x·log6x   Formula used: Log ...

Q: The ____ term of a polynomial is the term of highest degree

A: Given: The _____ term of a polynomial is the term of highest degree

Q: What is the maximum volume of an open box that can be made from a square piece of cardboard, 10in on...

A:

Q: dy Q2) Find by using Chain Rule for y = sin34t dt

A: dy/dt for y= sin34t

Q: Write an inequality to represent the following statement. A pilot is instructed to keep a plane at a...

A: Let the attitude of plane is a.From the given information, a has to be greater than 29,000 feet and ...

Q: Evaluate the following integrals dr 9-x2

A:                                     Given: ∫x29-x2 dxFormula: ∫cos at dt=sin ata+CSubstitutions: x=3...

Q: The ratio of a polynomial and its opposite equals _____.

A:

Q: Can I have  a detailed step by step explanation for the following question? Thank you!

A:

Q: Integral Calculus: Integration by Substitution. Final answers should be in its simplest form.

A: To determine the indefinite integral.

Q: The marginal cost (dollars per item) of producing x items is 1.35 – 0.003x. What is the cost of prod...

A: Given that, the marginal cost for producing x items is 1.35-0.003x and cost of one item is $270, tha...

Q: A ____ is a polynomial that has two terms, and a _____is a polynomial with three terms.

A: We have to fill in the blanks: A ____ is a polynomial that has two terms, and a ____ is a polynomial...

Q: あ。(12イ45 bt-ef e

A: 2x+53ax-53

Q: Find the point(s) on the graph of f(x) where the tangent line is horizontal. f(x)= 2x/x sqaured+1

A: Given that  f(x)=(2x)/(x^2+1) To find the points on the graph f(x) where the tangent line is horizon...

Q: The height of a sunflower plant can be determined by the time t in weeks after the seed has germinat...

A: To: Write a model to represent the height h when the height is given by the product of 8 and the squ...

Q: If f(0) = 1, ƒ'(0) = -1. g(0) = –1, g (0) = –3, and h(x) = (x² + f(x))g(x) then h' (0) =... O -2 O 2...

A: Given: f0=1, f'0=-1, g0=-1, g'0=-3 and hx=x2+fxgx. To find: h'0 Solution: Product rule of differenti...

Q: Brad and Angelina can mow their yard together with two lawn mowers in 30 min. When Brad works alone,...

A: Brad and Angelina can mow their yard together with two lawn mowers in 30 mins                       ...

Q: 4) x²y'= y² +5xy+ 4x?

A: Explanation of the solution is given below...

Q: Integral Calculus: Integration by Substitution. Final answers should be in its simplest form.

A: The given integral is ∫12x+14x-3dx. ∫12x+14x-3dx=∫12x4x-3dx+∫14x-3dx Assume u=4x-3. Differentiate u ...

Q: Find the solution of the following Differential Equations by Homogeneous Equation ソ+x 6) y'= ソーx %3D

A:

Q: Planck’s Law says that the energy emitted by a black body is given by ((1/x5)/ (e(1/x) − 1)) where x...

A:

Q: 1-2y-4x 1+ y+2x 10) y'=

A:

Q: Find the 3rd derivative of the functions: y = 12(5x2 –1)(x2 –1)

A: Find the 3rd derivative of the functions: Given y=12(5x2-1)(x2-1) To find dydx, d2ydx2, d3ydx3

Q: What is the value of * cosx + sin2x + 1 lim x² – 7²

A: what is the value oflimx→π cosx+sin2x+1x2-π2

Q: A square garden has an area of 81, how many much fencing is needed to surround the square garden?

A:

Q: determine if the statement is true or false. If a statement is false, explain whyThe product of two ...

A: Statement: The product of two polynomials each of degree 4 will be less than degree 8.

Q: For the pair of functions, find the derivative of the composite function k(t(x)) in terms of one inp...

A: The derivative of the function is the rate of change of the function. A composite function is genera...

Q: Find the solution of the following Differential Equations by Homogenous Equation 8) y' = tan(x+ y)–1

A: Given : The differential equation is : y'=tan(x+y)-1 We have to find the solution of the given diffe...

Q: Integrate each of the following without using trigonometric substitutions. T/2 V1 - sin²(x) dx

A: Given that, the integral      I = ∫0π2 1 - sin2x dx To find the value of integral without using trig...

Q: If L{cos(ax)} then find L{x³ cos(ax)}. %3D p2+a²

A:

Q: Find the natural domain and graph the functions for the following: 1) y = Va? – 36 2) y = -t2

A:

Q: Q4) Find the natural domain and graph the functions for the following: 1) y = Va? – 36 2) y = -t/½

A: Part 1). It is given that,                                        y=a2-36  =a2-62 Therefore to get t...

Q: M Find dedz 2 -2 (z*_sh az) 3. y =

A: 1)Find  ∂2y∂x∂z =? given that y=z14-3 ln ax2-2 2) find ∫01∫01∫01 z3y3x3 dx dy dz

Q: A police officer uses a radar detector to determine that a motorist is traveling 34 mph in a 25-mph ...

A: Given: x represents the motorist’s actual speed The school zone have a limit of speed 25 mph

Q: (2x–1)(cos(/3(2x–1)3+6)dx V3(2x-1)3+6

A:

Q: Let f(x) = 2r - 6z + 4 The slope of the tangent line to the graph of f(x) at the point (4, 12) is Th...

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.