The height y (in feet) of a ball thrown by a child is 1 2 -x² + 6x +3 y = 12 where is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child's hand? (Hint: Find y when x = 0) Your answer is y (b) What is the maximum height of the ball? (c) How far from the child does the ball strike the ground?

Q: 5. Find the equation of the tangent line to the graph f(x)=(9-x²) at the point (1,4). Use a graphing…

A: Given: f(x)=(9-x2)23 at the point (1, 4)

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A: We need to find if series converges or not.

Q: For a sequence {a} satisfying п в U A U C F 4" an A) n=1 ∞ ΣΑ" an B) =1 O Σ6" an n=1 6⁰ an D) n=1…

A: Given that , an+1an→15

Q: Find dy du du dx dy du du'dx = y=u 52 51 = 52u , and dy dx and u = 5x3 + 2x2

A:

Q: A rectangular field is on Sides and throo side. Find the that area can dimensions by of be enclosed…

A:

Q: Find the points at which y=f(x)=4x−ln(6x) has a global maximum, a global minimum, and a local,…

A: we need to find out the global maximum, global minimum, and local maximum.

Q: . Find the maximum and minimum values of the function f(x, y, z) = x²y²z² subject to the constraint…

A: To find the maximum and minimum values by langrage multiplier

Q: -8 -7 -6 -5 -4 -3 -2 -1 8 7 6- 5 4 3 2 6 7 8 1 2 3 4 5 5 6 ind the area inside the circle x² + y² =…

A: We have to find the area according to the given information

Q: 3. Find the general solution of these five constant coefficient linear homo- geneous ODES: (a) y" +…

A: General solution

Q: Find the interval of convergence of Σ n=2 (x-7)" In (6n) (Use symbolic notation and fractions where…

A: Solution: ∑n=2∞(x-7)nln(6n) Use the ratio test to compute the convergence interval

Q: Find the derivative of the function below. Use lower case letters. (Remember to simplify the…

A:

Q: Given that is a random variable having a Poisson distribution, compute the following: (a) P(x = 1)…

A:

Q: If 2=3xy-y³+(y²-2x)*, .. हे है джду дудо verify друз

A: Given that z=3xy-y3+y2-2x32

Q: f(x)dx = F(b) - F(a) and ſf(x)dx = P(x)+C. Consider the two expressions A) a and b are called the…

A: Given expression ∫abf( x )dx = F( b ) - F( a ) ∫f( x )dx = F( x ) + C

Q: Find the Maclaurin Series for the function

A:

Q: 44 ♫f sin (y²) dydx 0 x

A:

Q: -4x+3y=8 x-5y =-19 To solve the given system by substitution, the first step could be to solve the…

A:

Q: 3. About the y-axis УА 1 y = 9 y=x³+1

A:

Q: Verify that the function is a solution of the initial value problem. (a) y = x²(1 + Inx): y" =…

A: Given:y=x23+x-1   We are required to find: If y is the solution of the initial value problem…

Q: 8. The half-life of caffeine (how long it takes for the amount of caffeine in your system to cut in…

A:

Q: Find the area between the curves y = interval -4 < x < 4. +2 and y = -x - 3 on the

A:

Q: Describe all of the transformations 5(x + 3)² - 2. Be sure to be specific in describing each…

A: Given parent function f( x ) = x2

Q: f 1 - 326² x²(x+1)(x² +21³ dre

A: We have to use the concept of integration.

Q: You are designing a fenced-in area in your yard. You have a maximum 50 meters north-south where you…

A: It is given that you have a total of 250 meters of fence and you have a maximum 50 meters…

Q: Consider the function f(x)= (x^7) (e^(5x)) with an interval [-4<x<1]. * The absolute maximum value…

A: We need to find out the absolute maximum, absolute minimum and the value of x at which these occurs.

Q: Consider the function f(x)= x - 4ln(x) with an interval [0.25<x<8]. * The global maximum value is?…

A: Here we have to find the global extrema.

Q: Write an equation of the form y = A· b + k for the graph sketched below: -5 -4 -3 -2 -1 f(x) = 8+ 7…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Suppose f is continuous on [0,13] and differentiable on (0,13). If f(0)=3 and f′(x)≥9 for all…

A:

Q: Use Newton's method with 3 iterations to estimate the solutions to arctan(x)=x^2 - 3 . Round your…

A:

Q: Find the value of c if C = 00 Σ(1 + c)-7 = 1 n = 2

A: We have to slove above geometry series

Q: Convert each exponential equation to the corresponding logarithmic equation.

A:

Q: t K Solve the exponential equation. cc=45c Select the correct choice below and fill in any answer…

A:

Q: A = 1 -5 1 -3

A: Given: Find the general solution to the system x'= Ax, where  A=1-51-3

Q: QUESTION 4 A kindergartener made the following pattern with color tiles. RBYRBY... This is an…

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

Q: When a particular amount of money P, called the principal, is invested at the interest rate r and is…

A:

Q: Use a tangent plane to approximate the value of the following function at the point (-4.9,-2.1).…

A:

Q: A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the…

A:

Q: Let P = f(t) represent the US population in millions in year t. (a) What does the statement f(2005)…

A:

Q: Factor out the negative greatest common factor, -5a-10. Drag pencil to correct answer.

A:

Q: Σ27(x – - 1)³n+2 n=0 (Use symbolic notation and fractions where needed. Give your answers as…

A:

Q: If you have 120 meters of fencing and want to enclose a rectangular area up against a long, straight…

A: Given f you have 120 meters of fencing and want to enclose a rectangular area up against a long,…

Q: Suppose you want to find an equation for a curve whose slope at any point (x,y) is 6² You'd need to…

A:

Q: A particle moves along a straight line so that its distance x, in metres, from a fixed point O is…

A: 1) When t = 0, x = 2(0) + 2cos(2(0))       = 2, so the particle is initially 2 metres away from the…

Q: Consider the function f(x) = x² + 2x - 8. (a) Find a simplify: f(C)-f(1) = (b) Find and simplify:…

A: The given function fx=x2+2x-8. We have to find and simplify the expression fC-f1C-1.

Q: Evaluate [²(x² + by the method of integration by parts. (x + 1)e dr

A:

Q: (a) Find the equation of the tangent line to y = In x at x = 1. (b) Use your answer to part (a) to…

A: a) The given data is: y=lnx  Find the equation of the tangent line at x=1 At x=1, y=ln1y=0 ∴point is…

Q: The function A = Aoe 0.18t models the amount an individual owes a credit company t years after some…

A:

Q: Producers' Surplus A certain manufacturer of Blu-ray players will make x thousand units available in…

A:

Q: (z + y) dA, where R is the region in the first quadrant that is bounded by the graph of R y = √4-1²…

A: Graph

Q: f 1-3₂² x²(x+1)(x²72)² dre

A: