A rectangular swimming pool is designed to be 7 times longer than it is wide. The total surface area of all 4 sides of the pool and the bottom is 90.0 m². What are the dimensions of the pool that will hold the MAXIMUM Volume of water?

Q: Find the length of the indicated portion of the curve.. r(t) = (7 cost) + (7 sin t) + (√51) k. Ostst…

A:

Q: etch the region enclosed by the given curves. y=16-x², y=x²-2 CHOICE A -6 CHOICE D -6 -2 y -10- 15…

A: First we find the point of intersection of the given curves.Then draw the graphs of the curves and…

Q: please answer the following for me

A: The objective of the question is to find the first five terms of the sequence defined by aₙ =…

Q: The graph of the derivative of a continuous function f is shown. (Assume continues to .) y 4 y-fix 2…

A: As per our guidelines we can answer only 3 subparts of a given question so kindly repost the…

Q: if f(x)=16x+3 find f prime of zero

A: The objective of the question is to find the derivative of the function f(x) = 16x + 3 at the point…

Q: f'(s) = 10s - 12s³, ƒ(3) = 2

A: Find the particular solution for :

Q: 2. Write an equation for sine and cosine for the graph below. 5. 0 5 10 15 20

A: We have given a graph of the function and we have to find the corresponding sine and cosine function…

Q: 1) Write an equation of a function that meets the given conditions (a) x-intercept: (1,0), (3,0);…

A: Given conditionsx-intercept  ,vertical asymptotes , horizontal asymptote x-intercept  ,vertical…

Q: Assume that y is differentiable at every x in (-00, 00) and that for every x in (-∞, ∞0), y'(x) =…

A:

Q: Find all the values of x such that the given series would converge. n=1 (x-6)" 6n The series is…

A:

Q: Use the Table of Integrals in the back of your textbook to evaluate the integral: sec sec³ (9x) dx

A: Given Indefinite integral as follows

Q: The base of a solid is the region in the xy-plane bounded by the curves y = 1- x² and y = 0. Every…

A: Given that the region is bounded by the curve

Q: Use Green's Theorem to evaluate the line integral of F = (x5,2x) around the boundary of the…

A:

Q: f(x) and (f'(x))² into the surface area equation above to find b Surface Area = Lº 2π. = a 5 5 2π…

A: To explain how was the 2 used from 2pie. How is it determined the 2 is needed, when in other cases…

Q: (a) Domain of f(x). (b) r-intercepts and y-intercepts. (c) Vertical asymptotes and holes. (d)…

A: Here we have given a function: .

Q: The function f(x)- is concave down on which interval?

A: The function f(x) is concave up on the interval I if f"(x) >0 for all x in I.The function f(x) is…

Q: -olve 2 cos² (w) - 3 cos(w) + 1 = 0 for all solutions ≤w<2π พ

A: Explanation of the answer is as follows

Q: Evaluate the integral 0 [(6te³¹²) i + (3e¯71) j + (1) k] dt.

A:

Q: Find the distance from the point (0,1,-1) to the line a(t) = (-2, 2, 4)t + (-6, - 1,5)

A:

Q: Find f'(x) and simplify. f(x)=2x5(x-9)

A: Given that the expression we have to find the derivative of the given expression

Q: a) Find an equation of the tangent line, at the designated point, to each of the following: i) f(x)…

A:

Q: I need help with this problem and an explanation for the solution described below (Discrete…

A: The objective of the question is to find the negation of the given statement. In logic, the negation…

Q: Find the critical numbers of the function f(x)=-12x to the fifth power  - 75x to the fourth power +…

A: The objective of this question is to find the critical numbers of the given function and classify…

Q: ← The position of a particle in space at time t is r(t) as shown below. Find the particle's velocity…

A:

Q: Exercise: Solve the equation d²y dx² + y = tan x

A: The given differential equation is

Q: Vector-valued functions (VVF) VVF Point P t value (for point A) r(t) = ½t²i + √4 − t j + √t + 1k (0,…

A: The objective of the question is to find the domain of the given vector-valued function, find the…

Q: solve using The Method of Partial Fractions

A: x−2−3​+x−35​Explanation:If you have any problem let me know here in comment box for this thankyou.

Q: Consider the logarithmic function: g(x) = 3 log2 (1-x) - 6 d) Sketch the function using the method…

A: Check explanation Explanation:Problem:Consider the logarithmic function:g(x) = 3log₂(1 - x) - 6d)…

Q: Find the exact length of the curve. y = ² ²x³/2, 3 0≤x≤6

A:

Q: Find f'(x) and find the values(s) of x where f'(x) = 0. f(x)=(2x-27)(x²+60)

A: given function

Q: Find the interest rate needed for an investment of $4000 to grow to an amount of $8500 in 4 years if…

A: To find the interest rate needed for an investment of $4000 to grow to anamount of $8500 in 4 years…

Q: Let s(t)=4t to the thrid power+30t squared+72t be the equation of motion for a particle. Find a…

A: Part(a) :  v(t) = 12t2+60t+72 Part(b) :  t = -3 and t = -2 Part(c) :  a(t) = 24t+ 60Explanation:

Q: Find the area of the region inside the blue circle r = 2 cos 0 but outside the red circle r = 1…

A: To find the area of the region inside the blue circle  butoutside the red circle  shown below.

Q: Question 6: Find the equations of the tangent and the normal line to the curve g(x) = the point…

A: As we knowThe equation of tangent line at the point with slope  is The equation of the normal line…

Q: An offshore oil well is 2 kilometers off the coast. The refinery is 5 kilometers down the coast.…

A:

Q: Find the length of the curve over the given interval. y = 10+10sinė, 0 ≤0≤2π Select one: ○ a. 20 O…

A: follow the solution part.Explanation:

Q: A state government is planning to construct a new bridge over a river to improve transportation…

A: Given: The bridge's design includes a main span of 300 meters and two approach spans of 100 meters…

Q: Please help me with this, Look at the image Question: what are the x-coordinates of all points of…

A: The objective of this question is to find the x-coordinates of all points of inflection of the…

Q: let f(x) = In (1+x). find second degree taylors polynomial centered at x=1 for f(x): f" T₂ (x) = f…

A:

Q: 1. f(x) = (4 — x²)5

A: Second derivative test for local maxima and minima :

Q: A long solenoid with 1.50 x 10³ turns per meter and radius 2.00 cm carries an oscillating current I…

A: a)E=0.01865cos(90πt)V/mb)clockwiseExplanation:Step 1:Step 2:Step 3:

Q: 5 A polar curve is given by r = (3-cos(0)) What is the rectangular equation of the tangent line at 0…

A:

Q: Use integral tables to evaluate the integral. Sx√29x-7dx Click here to view page 1 of the Table of…

A:

Q: The curve y=f(x) is shown below. In which region(s) of x is f(x) increasing? A. −1<x<1, x≠0…

A: given a function f(x)

Q: 1. f(x) = (4x2)5

A: As per company guidelines for a question posted we are allowed to solve only first three subparts…

Q: Website Profit You operate a gaming website, www.mudbeast.net, where users must pay a small fee to…

A: explained below Explanation:Step 1:(a) Construct a linear demand function for your website and hence…

Q: x(t) = 6-7t Find a plane containing the point (-6,-5,-3) and the line y(t) = -6-7t z(t) = 5 - 8t

A: Given that the plane containing the point (−6,−5,−3) and the line {x(t)=6−7ty(t)=−6−7tz(t)=5−8t

Q: Suppose you want to have $700,000 for retirement in 20 years. Your account earns 4% interest. a) How…

A:

Q: Complete the parametric equations of the line through the point (-6,1,-3) and perpendicular to the…

A: Point: (-6,1,-3)Plane: 6x-2y+2z=5

Q: 4) A company wishes to manufacture a box with volume 36 ft, has an open top, and is twice as long as…

A: Question No. (4): A company wishes to manufacture  a box with volume 36 ft3, has an open top, and is…