Find the maximum product of two positive numbers given that the sum of the firstnumber and twice the second number is 12.O 1) 122) 363) there is no such maximum4) 18 An open rectangular box has an area of 441 cm2. If its length must be 3 times itswidth, find its dimensions so that its volume is a maximum.O 1) 7.25 cm, 21.75 cm, 4 cmO 2) 7 cm, 21 cm, 5.25 cmO 3) 7 cm, 21 cm, 6.5 cmO 4) 6.5 cm, 19.5 cm, 6 cm

Answered: Image /qna-images/answer/284b62b8-5d2a-40c7-81a3-bea50c6ddb40.jpg

Answered: Find the maximum product of two…

Find the maximum product of two positive numbers given that the sum of the first number and twice the second number is 12. 1) 12 2) 36 3) there is no such maximum 4) 18

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 34E: The numerical value of the volume of a cube equals the numerical value of its total surface area....

See similar textbooks

Related questions

Q: Consider the series (z – 9)6, (z - 9)8 E4. = (2 - 0)2 + (- 9)“ E, = (z - 9) + +... 3- 2! 9.3! 27- 4!…

A: This question can be solved using the concept of general term of series.

Q: Find the surface area formed when the curve f(x)=x^3 between x=1 & x=3 is rotated around the x-axis

Q: Given the function, y = x' + 3x which of the choices is the correct second step based on the…

Q: Find the area of the parallelogram that has u = 2i – 2j +k and v = j+ 3k as adjacent sides. NOTE:…

Q: Use the formula k(t) = ||r' (t) × r"(t)|| to find k(t). 13 ||r(t)||* r(t) = t'i + t6j K(t) =

Q: Find the derivative of 1-3)* (t3 -8) ,t # 2 2-t

A: Explanation of the answer is as follows

Q: Compute the derivative, and simplify your answer. You must show your work. t3/2 +t1/2 dt d dx

Q: Let Ā = (1,3, –2) and B = (–1,-2,3,). Find the following. 1. The cosine of the angle between 3Ã + B…

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

Q: 993 + 5x + 0.16x2. Use e level of production is changed

A: We have to calculate level of production change .

Q: Evaluate. (Be sure to check by differentiating!) dx, x -2 4 + 2x dx 4 + 2x (Type an exact answer.…

A: To evaluate: ∫14+2xdx Let I= ∫14+2xdx

Q: Use an improper double integral to find the volume of the indicated solid. 2--(* + y)/9 Osy<co 8 6 4…

A: We need to find the volume of the given shape.

Q: The slopes of the lines tangent to the function y = 4x° – 4 T on the interval (-oo, 00) is a…

A: Given , The slopes of the lines tangent to the function y = 4x3 -4√x on the interval (-∞, ∞) is a…

Q: eight The height of a building is 170 feet. Find the angle of elevation (in degrees) to the top of…

A: Use trigonometric ratio to solve

Q: 2In(sin) de tan() 02

Q: From Rogawski ET 2e section 10.2, exercise 11. Calculate S3, S4, and S5 and then find the sum for…

A: Sum of First n terms: = (1/10 - 1/11) + (1/11 - 1/12) + (1/12 - 1/13) + (1/13 - 1/14) + (1/14 -…

Q: (a) x = 4t, y = – 3+ 3t O (x, y) = ( – 3, 0) + 1(3, 4) ai + bj = - 3i + t(3i + 4j) O (x, y) = (0, 4)…

Q: Y=x(root2-x) Can someone explain why the domain is x=

A: The domain of the function is set of all possible input values for which function is defined.

Q: Suppose F is an antiderivative of f(x) = VT. If F(0) 1 then F(1) 4 %3D %3D is 3 A. –1, B. -, C. 0,…

A: Let f be a function . Suppose F is a function such that F'(x) =f(x) then F is an antiderivative of…

Q: Find the general antiderivative F(x) + C for the function. 126+ 3x+ f(x) = x3 O 3x4 +x2 + C 3x* +x +…

Q: 3. Determine the exact value of x given the following information. a) a = 2,r = 3, t, = x b) a =…

Q: 5 In(3x) dx sln²(3x) + C

Q: Find all values of x where tangent lines to y = x° and y = x' are parallel. (Give your answer in the…

Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

Q: Determine the area outside the black graph given by r(0)=1+7cose and inside the red graph given by…

Q: Which of the following is an infinite limit? lim f(x) = o lim x→f(x)x=a g(x) = c0 lim f(x) = a %3D…

A: we have to check which of the following is an infinite limit. we say that a limit of a function…

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

A: We will find the unit vector satisfying the given conditions in the following step.

Q: Consider a triangle ABC like the one below. Suppose that a=31, b= 68, and c=51. (The figure is not…

A: To solve the following problem to find the angles

Q: y= V x

A: Here is the solution

Q: Preview Activity 1.3.1. Suppose that f is the function given by the graph below and that a and a + h…

A: Use slope formula for finding the value .

Q: Use the Product Rule to calculate the derivative for the function h(t) = (t² + 3) (t + 8) at t = 2.…

A: Product rule:d(uv) = u v' + v…

Q: Find the derivative of the function using the definition of derivative.

Q: 5g is moving horizontally with speed v o. Question 1: A bullet of mass m= hits a block of mass 100m…

Q: Given h(x)dx=- and G(x)dx =What is [8h(x)-3G(x) ]dr? 3. %3D O Cannnot be determined O 2 O none of…

Q: Find a parametric equation for the path of a particle that moves halfway around the circle…

A: We have to find the parametric equation for the path of a particle.

Q: Evaluate

Q: From Rogawski ET 2e section 10.2, exercise 25. Use the formula for the sum of a geometric series to…

Q: Find the Laplace transforms of the functions: (a) f(t) = t² (b) f(t) = t – 2e3t |

Q: Rewrite the Cartesian equation x = 7y as a polar equation. r(0) = Use the math palette or type theta…

Q: Use the shell method to set up and evaluate an integral that gives the volume of the solid generated…

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

Q: b) Find the exact area of the region enclosed by the curve y = x² – 3x, the x-axis and the vertical…

Q: (2) Find the full Fourier series for the periodic function ƒ : R → R defined by ƒ(x) = 1+ |æ| on the…

A: the fourier series expansion is as follow

Q: show

Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). 13 15. r(t) = t'i + t5j K(t) =

Q: Test the series below for convergence using the Ratio Test. n + 4 53п + 4 n=1 The limit of the ratio…

Q: 28 74.6°

A: Given query is to find the vector components.

Q: If the series 1(-1)" 2 were approximated using its first k terms, what would be the smallest number…

A: We have to find the smallest number of k such that the error bound would guarantee an error of not…

Q: Determine the number at which h(x) = V16 – x² is continuous. %3D | Vx²-1 Determine the largest…

A: Note that: A function is said to be a continuous function on some interval when the function is…

Q: Find all cube roots of the complex number 64(cos (219°) + i sin (219°). Leave answers in polar form…

Question

Find the maximum product of two positive numbers given that the sum of the first
number and twice the second number is 12.
O 1) 12
2) 36
3) there is no such maximum
4) 18

An open rectangular box has an area of 441 cm2. If its length must be 3 times its
width, find its dimensions so that its volume is a maximum.
O 1) 7.25 cm, 21.75 cm, 4 cm
O 2) 7 cm, 21 cm, 5.25 cm
O 3) 7 cm, 21 cm, 6.5 cm
O 4) 6.5 cm, 19.5 cm, 6 cm

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the volume and the surface area of a closed box that has dimensions of 9 in., 10 in., and 1 ft.
Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?
The numerical value of the volume of a cube equals the numerical value of its total surface area. What is the length of each edge of the cube?
As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in. are cut from the corners of a rectangular piece of poster board that is 20 in. wide by 30 in. long. Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?
Find the total area surface area of a regular dodecahedron 12 faces if the area of each face is 6.4cm2.