A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 5. f(t) = 70t – 8² velocity m/s speed m/s

Q: Which of the following statement/s is/are true about the function whose graph is shown below? A. lim...

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Q: Consider f(x) = 1 – x for 0 1: an b) O an = c) O ao = 1/2, and for n > 1: a, = 4(1+ cos(nT/2))/n²n²...

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Q: 2. Summation of a constant: E,=c, +c, +c3 +...+ c, = nc %3D Example Evaluate the following summation...

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Q: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, ...

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Q: State the property presented 10 + (4 + 11) = 10 + (11 + 4) a. commutative property b. associative...

A: Here is given that  10+(4+11)=10+(11+4)

Q: 2. Find the cartesian equation of the following: а. r = 3-sin e b. r? cos(20) = 4 9. r2 C. 4 sin(26)

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Q: Vx+3 4. f(x) = **3 f'(1) x-4

A: Given:- f(x) = √(x+3)/(x-4)  To find:- f'(1) 

Q: a population of 7.2 million grows at a constant percentage rate.  1. what is the population 1 centu...

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Q: There is a relationship between perceived corruption and human development in a country that can be ...

A: Given  H(x)=0.3+0.28 In x                 where H(x) is Human development index                     ...

Q: Given: G(x) = [x] + [4 – x]. Determine lim G(x). x-3

A: We will find the limit of the given function.Below find the solution in the image.

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Q: C 1000 A В

A:  We know that law of sine is : SinA/a = SinB/b = SinC/c. Here A,B,C are angle of triangle and a,b,c ...

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Q: 47. For the equation: y= Vx? + 20x dy ay using the chain rule dx a. Find а. b. Find the slope of the...

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Q: Written Work Directions: Please write your solution on the space provided and boxed your final answe...

A: limit

Q: A series RLC circuit is shown in Figure Q4 (b) where R= 4Q, L = 0.5H, C= 0.1F,E(t)=10 V and i(0) = 0...

A: Given: R=4ΩL=0.5 HC=0.1  FE(t)=10 V

Q: For the function defined as follows, find all values of x and y such that both f, (x.y) = 0 and f, (...

A:   Differentiate partially with respect to x and y to get the solution

Q: Let X be the set {5, –6, 2}. For the first three parts of this problem you are asked to define a fun...

A: Consider the set 5,-6,2. The function is f:X→X and the relation is u~w⇔w=fu.   a) The relation is re...

Q: (a) Calculate the first-order differential equation below using transformation y = xv. dy +3у %3D 2х...

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Q: Determine the direction in which f has maximum rate of increase from P. S(x. y. 2) = x²y/z, P =(-1,2...

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Q: Use the graph to answer the question. Is f continuous at x = 0? %3D -4- -5- 2.

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Q: Find all local extrema for the function f(x,y) = - 6x - 9xy - 4y + 72x+54y+ 6.

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Q: Determine if the given function is a continuous on each of the given intervals. A. f(x) = 3x³ + 4x² ...

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Q: For f (x) = Vx – 3 +1 Find the derivative function of f' Evaluate the derivative at x = 4 Find the e...

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Q: Given the differential equation y" - 2y' - 15y = 3x + cos(5x) (1) Find the combined differential ope...

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Q: A ball is thrown straight up into the air off the top of a building so that is height in feet after ...

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Q: F(y) = In(1 – 5y² +y³)

A: Topic = Derivative

Q: Test the series below for convergence using the ratio test. 5n n! n=1 The limit of the ratio test si...

A: Given:     Equation is given

Q: Q2 Second-order non-homogeneous ordinary differential equation given as; y" + 3y' –10y = e2* Calcula...

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Q: if a 2 Compute the quantities below. Write "DNE" if the limit does not exist or the value is undefin...

A: Given that: f(x)=7x+7     if    x≤27x-8      if   x>2

Q: 3) The electrical power, p(), in kilowatts, being used by a household as a function of time t, in ho...

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Q: The temperatue of a town t months after January can be estimated by the function f(t) = – 28 cos( + ...

A: Given that: f(t)=-28cosπt6+41

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is approximat...

A: Revenue function is given R(x,y) = 19+162x+210y-3x2-5y2-6xy  , it is function of two variable  Findi...

Q: The given problem needs the fırst derivative. Find the first derivative. a² x Y= a2 + x

A: Here we have to find the first derivative of the function. dxndx= n xn-1

Q: 10z2 Evaluate the integral: -dr 100 (A) Which trig substitution is correct for this integral? Oz = 1...

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Q: Find the volume formed by rotating about the y-axis the region enclosed by: x = 11y and y = x with y...

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Q: A tree on a hillside casts a shadow c = 225 ft down the hill. If the angle of inclination of the hil...

A: Topic = Trigonometry Height of the tree is 130 ft.

Q: 1. A missile fired ground level rises x meters vertically upwards in t seconds and x = 50t – 6.2512....

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Q: If labor (x) costs $235 per unit, materials (y) cost $169 per unit, and capital (z) costs $60 per un...

A: Given that: Labour costs $235 per unitMaterials y cost $169 per unitCapital z costs $60 per unit.

Q: Find all the values of a such that the given series would converge. (- 1)"z" L 2"(n² + 7) n=1 The se...

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Q: Evaluate the integral. dx x In x6 O !In(lIn x) + C O In x6+ C O tin xé + C O In(In x) + C

A: Solve the integration by substitution method

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for th...

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Q: Evaluate the difference quotient and simplify the result. h(x) = x2 + x + 5     h(x + Δx) − h(x) Δx...

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Q: x+1 x-x-2

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Q: Q3 Given the following non-homogeneous system of first-order linear differential equation: yi' = 5y,...

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Q: 6. f(x) = V7x + 6; f'(3)

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Q: Identify the type of generalized integral +00 fx'e* dx- and in continuity (if converging) to be calc...

A: According to question,Given Integral,Let I= ∫0+∞ x2ex3 dx

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Q: (D² – 2D + 1) y = e*/x3

A: Given ,(D2-2D+1)y=exx3The A.E. is, m2-2m+1=0(m+1)(m+1)=0⇒m+1=0 or m-1=0⇒m=-1,-1Therefore C.F.=(C1+C2...