Homework help: Question: A ball is thrown vertically upward from the ground at a velocity of 98 feet per second. Its distance from the ground after t seconds is given by s(t) = -16t^2 + 98t. How fast is the ball moving 4 seconds after being thrown?

Q: Find the tangent line and the normal line to the curve at the given point. x2y2=100, (2,5)

A: Differentiate both sides w.r.t. xUsed product rule and chain rule on the left side.

Q: 6x318x2 10x +30 f(x) x 3 -3 and by the formula when x f(x) 3x2 5x a when -3 x What value must be cho...

A: To determine the value of a.

Q: Mary, Goran, and Trey sent a total of 66 text messages over their cell phones during the weekend. Go...

A: There are three people in the question.Let Mary be denoted by m, Goran by g and Trey by t.As per the...

Q: Calculus Question

A: The given function is,

Q: Find the area between the curves. x= -5, X 3, y = 6x, y x-7 The area between the curves is (Type an ...

A: To determine the area of the region enclosed by the staight lines

Q: Determine if the series below converges or diverges using either the Test of Divergence or Intergral...

A: Given, series is

Q: Can you help me step by step?

A: f(x)= x^(2/7) is continuous in the interval [-5,8].Image of the graph attached. It shows f(x) is con...

Q: Find the critical points for the function: f(x,y)=x3+y3-9x2-48y-3 and use the Second Derivative Test...

A: To determine the critical points for the function and classify the critical points.

Q: Q 7. Is cos x| differentiable in (-oo, oo). If so find its derivative. If not, is it differentiable ...

A:  Let us begin with plotting the graph for |cos x|.

Q: If an object is thrown upward at 128 feet per second from a height of 36 feet, its height S after t ...

A:

Q: Consider the function f(x) = x3 + 4, and the point (1, 5). Write the equation of the line tangent to...

A: Compute the slope as follows.

Q: (a) what's the derivative of  f(x)= 1/((x-1)(x-3))2 (b) Find all (three) locations where the derivat...

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for ...

Q: A lamp has a lightbulb with an average lifetime of 4 hours. The probability density function for the...

A: Probability density function is 

Q: Let (xo, yo) (2, 6) and (x1, y1) = (2.4, 6.1). Use the following graph of the functionf to find the ...

A: According to the given two points that lie on tangent are:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. Give exact answers...

A: The given function is,

Q: Solve the indefinite integral:

A: Given:

Q: The half-life of iodine-123 is about 13 hours. You begin with 52 grams of iodine-123.   (a) Write an...

A: Consider the amount of iodine(I) as a function of time(t).

Q: step by step on how you would evaluate this function and rounding answer to four decimal places if n...

A: Consider the given function.

Q: One solution of the differential equation y" +y' = O is y = e. Use Reduction of Order to find a seco...

A:

Q: Use a linear approximation (or differentials) to estimate the given number. (Do not round your answe...

A: Given,

Q: Find the equation of a) parallel and b) perpendicular lines to the line 4? – 6? = 9.

A: Assuming the given line is 4x – 6y = 9

Q: Differentiate the function F(t) = (ln t)2 sin t

A: Given function is,       

Q: Find the derivative.

A: Given function is

Q: 2. For each of the following, sketch the parametrized curves. Be sure to indicate the direction of m...

A: Firstly for solving subpart (a), substitute the value of t = y in f(t) = t.And simplify to get the v...

Q: Suppose the derivative of a function f is f'(x) = (x + 2)°(x - 4)5(x - 7)8. On what interval is f in...

A: Given,

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

A: According to the given function:

Q: Find dy/dx

A: Given expression,

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x)=3-2lnx; x=...

A: To determine equation of tangent line at given point.

Q: Solve the given system of differential equations by systematic elimination. Select all solutions to ...

A: To determine the solution of given differential equation.

Q: Sketch the graph of a function that satisfies the following 3. conditions: (a) f'(0) f'(2) = f'(4) =...

A: There are many ways to draw the graph. From part (a), observed that the function has local minimum o...

Q: step by step please. was told this was using the compound interest formula

A: To calculate the value of the account after the given time period at the given rate of interest we u...

Q: see attachment

A: Given functions

Q: Can you help me with this problem step by step?

A: To determine:Part a) The intervals on which the function is increasing and decreasing.Part b) Points...

Q: Can you help me on #27

A: The series1/k2  converges. We compare given series to this series and use comparison test. 

Q: Calculus Question

A: Given information:

Q: Can you help me with this problem step by step?

A: Consider the function f(t) = 12t - t3 in the interval [-3, ∞).

Q: (x1) Solve the IVP: y/ , y (0) = 1 y2 O y22y( 1)3 9 O 3y2 6y 2 (x + 1)3 7 O y22y

A: It is given that,

Q: Can you show me the steps to solve the problem? 3.1 Directions: Find the critical numbers of the fun...

A: The given function is,

Q: see attachment

A: Given that the initial point and terminal point are (–3,5) and (1,6), respectively.

Q: Find an equation of the line tangent to the curve defined by x^3+6xy+y^5=21 at the point (2,1)

A:

Q: see attachment

A: Given:

Q: Find the derivative using the following information.

A: Given,

Q: 10(a +2)3 2. Expand. n 7ь

A: The expansion of the provided expression is given by,

Q: Find the equation of the tangent line to the curve y=8ln((x^3)-26) at the point (3,0)

A: Given,

Q: In the 2000 U.S.​ Census, a small city had a population of 45,000. By​ 2010, the population had reac...

A: Given,           In the 2000 U.S.​ Census, a small city had a population of 45,000. By​ 2010, the po...

Q: Given the following piecewise function, evaluate f(−3).f(x)={6x+5   x<−3       −5x+2   x≥−3

A: Consider the given function.

Q: Given that x and y are functions of time, find the indicated rate of change. dy when x 2 and dt dx F...

A: Compute the value of y as follows.Substitute x = 2 in x3 + y3 = 16.

Q: Determine if the series below converges or diverges. If it converges, determine what to do.

A: To discuss the convergence or divergence of the given series

Q: An open-top bin is to be made from a 15-centimeter by a 40-centimeter piece of plastic by removing a...

A: Assume that side of square which should be cut from each corner is a.Given the dimension of piece of...

Q: Calculus Question

A: Given,

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.