![kaylyns134](/avatars/32996.jpg)
kaylyns134
31.03.2020 •
Mathematics
A store sells rwo different types of coffee. Coffee a costs $7 per pound and coffee b costs $5 per pound. Amy bought 7 pounds of coffee and spent a total of $41. How many pounds of each type of coffee did she buy?
Solved
Show answers
More tips
- F Food and Cooking Why Doesn t the Confirmation Link Come to Email?...
- L Leisure and Entertainment What Movies You Should Watch: A Guideline to Make the Right Decision...
- F Family and Home How to Choose a Baby Stroller: Tips from Experienced Parents...
- H Health and Medicine 5 Simple Steps to Quit Smoking for Good...
- H Health and Medicine Coughing: Causes, Types, and Treatment Methods...
- H Health and Medicine How to Treat the Flu: A Comprehensive Guide...
- O Other What is a Disk Emulsifier and How Does it Work?...
- F Family and Home What does a newborn need?...
- F Family and Home Choosing the Right Car Seat for Your Child: Tips and Recommendations...
Answers on questions: Mathematics
- M Mathematics How do u solve for y and x 4x+9y=16 6x-9y=8 me....
- M Mathematics What is the solution to 4/9*-10 */3-12?...
- M Mathematics Select the expression that represents the multiplicative inverse of -1. a. b. 1 c. -1 d. )...
- M Mathematics Which statement is true regarding the functions on thegraph?...
- M Mathematics The linear function f(x) = 0.5x + 80 represents the average test score in your math class, where x is the number of the test taken. the linear function g(x) represents...
- M Mathematics Write each rate 26 cups for 8 people as a fraction in simplest form. then give the unit rate. solution : 26/8 = 13/4...
- M Mathematics Complete the recursive formula of f(n)....
- M Mathematics Whats the domain and range of the relation...
- M Mathematics The area of a rectangle is 36m. the length of the rectangle is 9m. what is the width?...
- M Mathematics Whats the domain and range of the relation...
Ответ:
The dimensions of the mural that maximize the total paintable area inside the border = 4 ft × 6 ft
Making the dimensions of the maximum paintable area to be 2 ft × 3 ft.
Step-by-step explanation:
Let the dimensions of the rectangular mural be x and y respectively.
The total area of the mural = 24 ft²
xy = 24
Then there's a 1 ft border on the left, right and bottom.
A 2 ft border at the top.
The dimensions of the printable area will be (x-2) ft and (y-3) ft
The area of the printable area will then be
(x-2)(y-3) = A(x,y) = (xy - 3x - 2y + 6)
This is the area to be maximized
Recall xy = 24; y = (24/x)
We can substitute for y in the area to be maximized
A(x,y) = (x-2)(y-3) = (xy - 3x - 2y + 6)
A(x) = x(24/x) - 3x - 2(24/x) + 6
A(x) = 24 - 3x - (48/x) + 6 = 30 - 3x - (48/x)
We then have to maximize
A(x) = 30 - 3x - (48/x)
First of, we obtain (dA/dx)
(dA/dx) = -3 + (48/x²)
At maximum point, (dA/dx) = 0
-3 + (48/x²) = 0
3x² = 48
x² = 16
x = 4 or -4
For the maximum of the function of the area, x = 4, y = (24/4) = 6
The area of the paintable part of the mural
A(x,y) = (x-2)(y-3)
At maximum area, x = 4 ft, y = 6 ft
Maximum paintable area = (4-2)(6-3) = (2)(3) = 6 ft²
The dimensions maximize the total paintable area inside the border = 4 ft × 6 ft
Hope this Helps!!!