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emmainna [20.7K]
3 years ago
13

a rectangle of perimeter 100 units has the dimensions shown. Its area is given by the function A = w(50 - w). What is the GREATE

ST area such a rectangle can have? Please explain all steps written, there are parts such as 50W -W^2 and it ends up turning into the next part how?
Mathematics
1 answer:
Anna [14]3 years ago
7 0
If A=w(50-w)

A=50w-w^2

dA/dw=50-2w

d2A/dw2=-2

Since the acceleration is a constant negative, that means that when velocity, dA/dw=0, it is at an absolute maximum for A(w)...

dA/d2=0 only when 50=2w, w=25

So as the case with any rectangle, the perfect square will enclose the greatest area possible with respect to a given amount of material to enclose that area...

So the greatest area occurs when W=L=25 in this case:

A(25)=50w-w^2

Area maximum is thus:

Amax=50(25)-(25)^2=625 u^2
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F(x) = 3x + 6 please help quickly!!!!!!!
Georgia [21]

Given the function, <em>f(x) = 3x + 6,</em> we can solve for f(a), f(a + h) and \frac{(f(a + h) - f(a)) }{h} by substituting their values into f(x) = 3x + 6. We will have the following:

\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}

<em><u>Given:</u></em>

  • f(x) = 3x + 6

<em>We are told to find:</em>

  1. f(a)
  2. f(a + h), and
  3. \frac{(f(a + h) - f(a)) }{h}

1. <em><u>Find f(a):</u></em>

  • Substitute x = a into f(x) = 3x + 6

f(a) = 3(a) + 6

f(a) = 3a + 6

<em>2. Find f(a + h):</em>

  • Substitute x = a + h into f(x) = 3x + 6

f(a + h) = 3(a + h) + 6

f(a + h) = 3a + 3h + 6

<em>3. Find </em>\frac{(f(a + h) - f(a)) }{h}<em>:</em>

  • Plug in the values of f(a + h) and f(a) into \frac{(f(a + h) - f(a)) }{h}

Thus:

\frac{((3a + 3h + 6) - (3a + 6)) }{h}\\\\\frac{(3a + 3h + 6 - 3a - 6) }{h}\\\\

  • Add like terms

\frac{(3a - 3a + 3h + 6 - 6) }{h}\\\\= \frac{3h }{h}\\\\\mathbf{= 3}

Therefore, given the function, <em>f(x) = 3x + 6,</em> we can solve for f(a), f(a + h) and \frac{(f(a + h) - f(a)) }{h} by substituting their values into f(x) = 3x + 6. We will have the following:

\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}

Learn more here:

brainly.com/question/8161429

6 0
2 years ago
Ali is making brownies. She has 2/5 of a cup of flour the recipe asks for 3/4. How much of the recipe can Ali make?
Ostrovityanka [42]
To make Ali brownies she will only be able to make 1/3
4 0
3 years ago
Read 2 more answers
There are 3 people pulling on an object, the first person pulls with a force of 226 newtons at a direction of 145 degrees the se
Alona [7]

Answer:

R=883.74N

Step-by-step explanation:

From the question we are told that:

Force 1 F_1=226N

Force 2 F_2=331N

Force 3 F_3=377N

Direction 1  \theta_1=145 degrees \approx 35 \textdegree (2nd qudrant)

Direction 2 \theta_2=303 degrees \approx 57 \textdegree (3rd qudrant)

Direction 3 \theta_3=77 degrees

Generally Resolving forces to X axis is mathematically given by

 \sum f_x=337cos77+331cos57+226sin35

 \sum f_x=351.596N

Generally Resolving forces to Y axis is mathematically given by

 \sum f_y=337sin77+331sin57+226cos35

 \sum f_x=810.788N

Generally the equation for Resultant force R is mathematically given by

 R=\sqrt{\sum f_x^2+\sum f_x^2}

 R=\sqrt{351.596^2+810.788^2}

 R=883.74N

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3 years ago
Tyrone is buying candy by the pound to stuff into a piñata. Her purchased 14 pounds of candy for $12. How much is the cost of on
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I believe the answer is


26

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A rental car company charges $22.15 per day to rent a car and $0.07 for every mile driven. Aubrey wants to rent a car, knowing t
Luda [366]

The number of days that Aubrey can drive to stay in her budget is 5 days.

<h3>Inequality signs and their meanings</h3>

> means greater than

< means less than

≥ means greater than or equal to  

≤ less than or equal to  

<h3>Equation that represents the question</h3>

Total amount that can be spent ≤ (cost to rent a car per day x number of days) + (cost per mile x total miles driven)

$130 ≤ ($22.15 x dd) + ($0.07 x 275)

<h3>Determination of the number of days that Aubrey can drive</h3>

130 ≤ ($22.15dd) + ($0.07 x 275)

130  ≤  $22.15dd + 19.25

130 - 19.25  ≤ $22.15dd

110.75  ≤ 22.15d

d  ≤ 110.75 / 22.15

d  ≤ 5

To learn more about inequality, please check: brainly.com/question/5031619

8 0
3 years ago
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