16t – 0.8t meters in t sec. A rock thrown vertically upward from the surface of the moon at a velocity of 16 m/sec reaches a height of s = a. Find the rock's velocity and acceleration at time t. b. How long does it take the rock to reach its highest point? c. How high does the rock go? d. How long does it take the rock to reach half its maximum height? e. How long is the rock aloft?

Q: evaluate the integral by completing the square and using trigonometric substitution.

A:

Q: If y = xsin then y is equal to = X" at x =

A:

Q: What does the following table suggest about lim f (x) and lim f (x )? x ➔1-          x ➔1+   x 0....

A:

Q: Suppose that the range of g lies in the domain of ƒ so that the composition ƒ  g is defined. If ƒ a...

A: Given that ƒ and g are one-to-one Let, x1 ≠ x2 in the domain of g(x) Then g(x1) ≠ g(x2) because g is...

Q: Calculus Question

A: For a sequence to be arithmetic, the difference between the successive terms should be a constant.

Q: Brain weight B  as a function of body weight W in fish hasbeen modeled by the power function B= 0.00...

A: Given Substitute for W in first equation, we get Let t be time in millions of years. Differentiati...

Q: On a circle of radius 10 m, how long is an arc that subtends a central angle of (a) 4p>5 radians?...

A:

Q: Explain why the following integral is improper then evaluate it or show that it diverges: 1 dr

A: As the upper and lower limits of this integral are real numbers, that's why it is an improper integr...

Q: Gravel is being dumped from a conveyor belt at a rate of30 ft3/min , and its coarseness is such that...

A:

Q: Find the limits. Write ∞ or -∞ where appropriate.

A:

Q: Refer to the given figure. Write the radius r of the circle in terms of a and 0.

A:

Q: Suppose if we use a linear Lagrange polynomial, differentiate and evaluate at x = x0 what formula wi...

A: Consider the general equation for the linear Lagrange polynomial function and two points. Differenti...

Q: Find the moment of inertia of a solid sphere of radius a about a diameter. (Take d = 1.)

A:

Q: Let _f(x) = (x – 2)? Find a domain on which f is one-to-one and non-decreasing. Find the inverse of ...

A: We graph f(x)=(x-2)2 using a graphing calculator The function is nondecreasing in [2,infinity)  

Q: 3z2 – 7z – 20 f(x) = I# 4 - 20 -4z2 + 21z C, I = 4 What value of C would make f(x) continuous at z =...

A: If the function is continuous then the limit x-> 4 and f(4) must be equal   

Q: Define Row addition ?

A:

Q: Solve this please using first derivative.

A:

Q: 11. A string lies along the circle x² + y² = 4 from (2, 0) to (0, 2) in the first quadrant. The dens...

A:

Q: Find the Derivative of the Function: 2x2 3 | f (x) 5x? 6

A:

Q: 66. Determine whether the function is even, odd, or neither. (a) f(x)= 2x –x* .2 (b) k(w) = (1 – w)³...

A: We know that a function f(x)  is odd if f(-x)=-f(x) , for every x  and f(x) is even if f(-x)=f(x) fo...

Q: (2) A particle is moving along the path given by ~c(t) = (t^4 − 4t, t^3 + t). (a) Compute the veloci...

A:

Q: y(x)=(x+1)2(x+2)3(x+3)4,x>−1.

A:

Q: The derivative of the function y = cos VI at z = is equal to 4

A:  

Q: 6- Please I want answer of this question. Thanks Fill in the blanks (show all steps)

A:

Q: Evaluate the integral

A: To find the given integral.  

Q: For what values of a and b is -2, xS-1 f(x) = ax - b, -1 <x<1 3, continuous at every x?

A:

Q: sketch the graph and find the area of the region bounded by the graph of the function f and lines y=...

A: f(x) cuts the x axis at x=1  

Q: Which 4 statements are true?m. Profit equals Revenue plus Costn. In U-Substitution if u = g(x) then ...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Minimize the function f(x,y, z) = x² + 2y² + z² subject to the constraints x+y+z =0 and r – z = 1 by...

A:

Q: 2. The deltoid x = 2 cos t + cos 2t, find area y = 2 sin t – sin 2t, 0 <t< 27 y 3

A:

Q: Complete the square and find the maximum value of f(x) = -x 2 + 4x + 1.

A: To complete the square and find the maximum values of the given function.  

Q: Find the power series expansion for the following functions using the appropriate series, f(x)=sin2(...

A:

Q: Which of the following statements about the function y = ƒ(x)graphed here are true, and which are fa...

A:

Q: How is the graph of loga x related to the graph of ln x? What truth is in the statement that there i...

A:

Q: dx 1. Evaluate e x(In x)3

A: We’ll answer the first question that is question (1) since the exact one wasn’t specified. Please su...

Q: Consider the function. f(x) = x7 − 1 (a) Find the inverse function of f. f −1(x) = (b) describe the ...

A: Given function

Q: Find any intercepts and test for symmetry. Then sketch the graph of the equation 3y2 − x = 9

A:

Q: A balloon is inflating at a constant rate of 9 cubic centimeters per second. When the volume of the ...

A: We have,

Q: At what points are the functions continuous? y = x tan x/x2 + 1

A:

Q: 1. Evaluate the following integrals using u-substitution. Check your answer using differentiation. (...

A:

Q: Find the arc length of cardioid r=1+cos(t)

A:

Q: Determine the point(s), if any, at which the graph of the function has a horizontal tangent line. (I...

A:

Q: Find the limit

A: Here the given limit  

Q: Consider the following ODE y" = 4y What is a possible solution (select all) Select one or more: O a....

A: Consider the following ODE  

Q: The derivative of the function is equal to :Select one e7² +¤ (7ª In 7 + 1) .a x(7® In 7 + 1) .b e" ...

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?...

A:

Q: Let P(3, 4) be a point on the circle x2 + y2 = 25. (a) What is the slope of the line joining P and O...

A:

Q: if you could please show your work for this section so i know how to sole it going forward

A: Given, Height of water tank = 16 ft Radius of water tank = 8 ft Rate = 5 ft3 per second  

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.