Every summer, Richard plants a garden on a rectangular plot of land. Last summer, Richard's garden measured 45 feet in length and 18 feet in width. This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction. The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced. What is the maximum potential area of this year's resized garden?Every summer, Richard plants a garden on a rectangular plot of land. Last summer, Richard's garden measured 45 feet in length and 18 feet in width. This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction. The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced. What is the maximum potential area of this year's resized garden?

Question

06-07-2022
Mathematics

Answered

IDNLearn.com offers a unique blend of expert answers and community-driven knowledge. Ask your questions and get detailed, reliable answers from our community of experienced experts.

Every summer, Richard plants a garden on a rectangular plot of land. Last summer, Richard's garden measured 45 feet in length and 18 feet in width. This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction. The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced. What is the maximum potential area of this year's resized garden?Every summer, Richard plants a garden on a rectangular plot of land. Last summer, Richard's garden measured 45 feet in length and 18 feet in width. This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction. The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced. What is the maximum potential area of this year's resized garden?

Sagot :

We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.

What Initiates T Cell Activation?A. When Its T Cell Receptor Binds To An Antigen Displayed On An MHC Of Another CellB. When The T Cell Displays The Antigen On I

Net To Seller Equals The ______ Multiplied By The Percent To Seller. A. Closing Costs B. Commission Rate C. Sales Price D. Tax Rate

What Value Of [tex][tex]$x$[/tex][/tex] Makes This Proportion True?[tex]\[ \frac{3}{x} = \frac{15}{40} \][/tex]A. 105 B. 5 C. 28 D. 8

The Supplies Account Had A $210 Debit Balance At The Beginning Of The Year, And $2,680 Of Supplies Were Purchased During The Year. The December 31 Physical Coun

Consider The Equations Below.[tex]\[ \begin{aligned} H_2 & \rightarrow 2H \\ C_2H_4 + H & \rightarrow C_2H_5 \\ C_2H_5 + H & \rightarrow C_2H_6 \end

Check All That Apply: Which Of The Following Contains Both [tex]$\alpha$[/tex]-1,4- And [tex]$\alpha$[/tex]-1,6-glycosidic Bonds?☐ Amylose ☐ Amylopectin ☐

\begin{tabular}{|l|l|}\hline \multicolumn{2}{|c|}{ Total War Spending (1920 Dollars) } \\\hline United Kingdom & [tex]$\$[/tex] 39.9[tex]$ Billion \\ \hline

Annie Is Planning A Business Meeting For Her Company. She Has A Budget Of [tex] \[tex]$1,325 [/tex] For Renting A Meeting Room At A Local Hotel And Providing Lu

A Security Administrator Is Running A Web Application Scanner And Notices That The Scanner Is Able To Identify The HTTP Server And Web Applications Running On A

Consider The Following Intermediate Chemical Equations:[tex]\[ \begin{array}{l} 2P(s) + 3Cl_2(g) \rightarrow 2PCl_3(l) \\ PCl_3(l) + Cl_2(g) \rightarrow PCl_5(s

Jainveenamrataidn Jainveenamrataidn · Answer 1 · 2022-07-08T02:09:59-04:00

The quadratic function is A(x) = 2(405 + 36x – x²). Then the maximum potential area of this year's resized garden will be 1458.

What is the maximum and minimum value of the function?

The condition for the maximum will be

f(x)'' < 0

The condition for the minimum will be

f(x)'' > 0

Every summer, Richard plants a garden on a rectangular plot of land.

Last summer, Richard's garden measured 45 feet in length and 18 feet in width.

This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction.

The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced.

Length = (45 – x)

Width = (18 + 2x)

Then the maximum potential area of this year's resized garden will be

A(x) = (45 – x)(18 + 2x)

A(x) = 810 + 72x – 2x²

A(x) = 2(405 + 36x – x²)

For maximum potential, A'(x) = 0

A'(x) = 0

36 - 2x = 0

2x = 36

x = 18

Then the maximum potential area will be

A(x) = 2(405 + 36 × 18 – 18²)

A(x) = 1458

More about the maximum and minimum value of the function link is given below.

https://brainly.com/question/13581879

#SPJ1

Sagot :

What is the maximum and minimum value of the function?

Other Questions