A semicircle of radius r = 5x is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure on the right. A. Express the area A of the rectangle as a function of x. B. Express the perimeter P of the rectangle as a function of x. A. A(x) = B. P(x)= G 5x

Q: Evaluate the following limit. lim x→0 3 (²2 x 3 sin(2))

A: L=limx→0(3x−3sin⁡(x))

Q: Find all the critical numbers of the function. 2 f(x) = x³ + x²-21x+2 OA. 3 OB. -3, -3, 7/2 OC. -…

A: In this question, we will find the critical point.

Q: 1. If y2 = 10x, then A. - 5 2xy 1 C. -2232 2x d² y dx2 = B. D. - 1 5x 2y 5xy 2

A: Given,

Q: 5. Find the outward flux of the field F = xzi+yzj+k across the surface of the portion of the sphere…

A:

Q: Determine the velocity of progress with the given equation: D = 20t + 5/t+1 when t = 4 seconds.

A: We have to determine the velocity of progress with the given equation:  when t = 4 seconds.

Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

A:

Q: The median home value in Texas and Missouri (adjusted for inflation) are shown below. Year Texas…

A:

Q: 1 Ifh (r) = e*, then h' (r) =? 04 x O(z) = _ r2

A:

Q: please show all steps what are 2 critical points of the function: f (x)  =  esin(πx/20) −…

A: Consider the function f (x)  =  esin(πx/20) − cos(πx/20)

Q: The odds on (i.e. odds against) TripleTreat winning the Kentucky Derby are 7 to 2. This means the…

A: The odds on (i.e. odds against) TripleTreat winning the Kentucky Derby are 7 to 2.

Q: 0 -3 5 1 0 1 0 6-58 0 -1 -1 3 4 -2 0

A: The given determinant is

Q: Show the limit x³ y lim (x,y) →(0,0) x6 + y²

A: L=lim(x,y)→(0,0)x3yx6+y2

Q: Evaluate the following limit. lim x³e -x² xxx = Note: Input DNE, infinity, and -infinity for does…

A:

Q: A golf ball manufacturer knows the cost associated with various hourly production levels, given…

A: Production cost for golf balls is given as,

Q: If y = cos² 3x, then =? dy dx dy dx O dy dx dy dx = 6 cos 3x = = -2 cos 3x -6 sin(3x) cos(3x)

A: Given,

Q: dy dx cos(x + y) = 3x Find dy dx dy dx dy dx dy dx = = -3 csc (x + y) - 1 = -3 cos(x + y) - 1 = −3…

A: we need to find out the derivative.

Q: H.W/ Maximize QuiZ 1/ 2= 80×1+ 60 X ₂ X₁ + X₂ 15 100. subj to: + X₂ 15 150 X₁ + 10X₂ If Boo الاحدا

A:

Q: the object. A person coughs when a foreign object is in the windpipe. The velocity of the cough…

A: Given that                                                            Where k = Some positive…

Q: 47. Determine whether these statements are true or false. a. b. C. dx O True O False dx True O False…

A:

Q: 18. Find dy/dx by implicit differentiation.

A:

Q: The number of books checked out from the library from 25 students are as follows: 0; 0; 0; 2; 2; 3;…

A: Consider the data 0,0,0,2,2,3,3,4,4,5,5,6,7,7,8,8,8,8,10,10,11,11,12,12

Q: Find the square root of 7225 with the modern method

A: A number's square root is a value that, when multiplied by itself, returns the original number.

Q: Indicate whether the graph specifies a function. 10 15 10 O The graph does specify a function. The…

A: to identify that the given graph shows a function or not.

Q: Consider the curve r(t) = (t² + 1)i + tj + (2t² + 3t)k. What is the velocity? What is the accelera…

A:

Q: The indicated function y₁(x) is a solution of the associated homogeneous equation. Use the method of…

A:

Q: 8. Consider the gradph of the function f(x, y) = x² - 5xy given by z = x² - 5xy (a) ( (1,2). Find an…

A:

Q: 7. Σ n=2W 3 2 n2 + I 00 8. Σ n?e=n n=1

A:

Q: Find the marginal cost function. C(x)=250 +3.5x-0.01x² c'(x) = [

A: we are given the cost function and we need to find out the marginal cost function.

Q: Find the derivative b. y= sec^-1(2x+1) c. y=x^e^x

A: I have appended the formula used in the solution procedure.

Q: 3) Prove the following statement using the Intermediate Value Theorem (IVT): 2+3* = 4* has a…

A: Question No. (3):To prove the following statement using the Intermediate Value Theorem (IVT):  has a…

Q: Find the general solution: y" + 5y' + 5y = 0

A:

Q: find derivative arcsin(2x) log5(3x2+4x)

A: (1) y=arcsin⁡(2x)

Q: Show algebraically that y = 4e + 5e can be written in the form y = A cosh(x - c). Calculate the…

A:

Q: A ball of radius 15 has a round hole of radius 8 drilled through its center. Find the volume of the…

A:

Q: Solve the following differential equations using HOMOGENEOUS DE. Show your complete 3. (x²y + 2xy² -…

A: The given differential equation

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A:

Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. (If the…

A: Consider the series Sum of a geometric series

Q: Given the vector = (2y, 5x, 0), the curl of = 7 Give your answer in terms of the unit vectors i, j…

A: Consider the vector v

Q: inld4u trated 1. T1: I can apply mathematical definitions. 8\II out frowemdit coin 11 auber a ora ea…

A: Limx-infinity (lnx+x)/(x+3)

Q: describe what you would have to do to your graph of f(x) to sketch g(x)= (x+1)^2-4(x+1)+3

A: The given function is .The aim is to describe how to sketch the graph of the function using the…

Q: HOMOGENEOUS DIFFERENTIAL EQUATION Solve the following differential equations using HOMOGENEOUS DE.…

A:

Q: Suppose that f(2)= -5, g(2) = 2, f '(2) = -4, and g'(2) = 1. Find h'(2). (a) h(x) = 5f(x) 3g(x)…

A:

Q: Find the area enclosed by the given parametric curve and the y-axis. sin²(t), y = 4 cos(t) X = y 4 2…

A:

Q: 2. Some psychologists have said that the hours is given by f(t)= (a) How many facts are remembered…

A: Consider the function

Q: Consider the function f(x) = 2x³ – 2x on the interval [-5, 5]. (a) The slope of the secant line…

A:

Q: The volume, V, of a sphere in terms of its radius, r, is given by V (r) = 77³. Express r as a…

A:

Q: Find the inflection points of thefunction f(x) = e(79-x²). INTERMEDIATE WORK f'(x) = f"(x) = On what…

A:

Q: Solve the following differential equations using HOMOGENEOUS DE. Show your complete solutions. 2.…

A: To solve the following differential equation by using Homogeneous DE.

Q: Let f (x) 8-x-x² if x ≤3 2x-7 if x>3 Calculate the following limits. Enter "DNE" if the limit does…

A:

Q: Find the marginal cost function. C(x) = 190 +5.7x-0.07x² c'(x) =

A: