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BartSMP [9]
3 years ago
11

If the farmer has 250 feet of fencing to create a rectangular pen, define a function f that expresses the area of the field (mea

sured in square feet) as a function of the width of the side of the field w (measured in feet). What is the maximum area possible?
Mathematics
1 answer:
hoa [83]3 years ago
8 0

Answer:

Maximum area possible

f(max)  = 3906,25 ft²

Dimensions:

a  = 62,5  ft

w  = 62,5 ft

Step-by-step explanation:

Perimeter of the rectangular fencing    P  =  250 feet

And sides of the rectangle  a  and  w (width of rectangle)

Then

A =  a*w

2a  + 2w  = 250       ⇒  a  =  (250 -2w)/ 2    ⇒  a = 125 - w

f(w)  =  (125  - w ) *w        f(w)  = 125w - w²  

Taking derivatives both sides of the equation

f´(w)   =  125  - 2w              f´(w)   = 0           125  - 2w = 0

w = 125/2

w = 62,5 ft            ⇒  a = 125 - 62,5

a = 62,5 ft

f(max)  = ( 62,5)²

f(max)  = 3906,25 ft²

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Answer:

see explanation

Step-by-step explanation:

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Where sin and tan are < 0 , cos > 0

The related acute angle is 2π - \frac{7\pi }{4} = \frac{\pi }{4}

Hence

sin([\frac{7\pi }{4} ) = - sin(\frac{\pi }{4}) = - \frac{1}{\sqrt{2} } = - \frac{\sqrt{2} }{2}

cos(\frac{7\pi }{4}) = cos(\frac{\pi }{4}) =  \frac{\sqrt{2} }{2}

tan(\frac{7\pi }{4}= - tan(\frac{\pi }{4} = - 1

6 0
3 years ago
Read 2 more answers
In the adjoining figure, XY = XZ . YQ and ZP are the bisectors of <img src="https://tex.z-dn.net/?f=%20%5Cangle" id="TexFormula1
svetlana [45]

Answer:

See Below.

Step-by-step explanation:

Statements:                                              Reasons:

1)\, XY=XZ                                              Given

2) \text{ $ m\angle Y= m\angle Z$}                                        Isosceles Triangle Theorem

\displaystyle 3) \text{ $m\angle Y=m\angle XYQ + \angle QYZ$}                  Angle Addition

\displaystyle 4)\text{ $YQ$ bisects $\angle XYZ$}                               Given

5) \text{ $m\angle XYQ=m\angle QYZ$}                           Definition of Bisector

\displaystyle 6)\text{ $m\angle Y=2m\angle QYZ$}                               Substitution

7)\text{ $m\angle Z=m\angle XZP+m\angle PZY$}              Angle Addition

8)\text{ $ZP$ bisects $\angle XZY$}                              Given

\displaystyle 9) \text{ $m\angle XZP=m\angle PZY$ }                          Definition of Bisector

\displaystyle 10) \text{ $ m\angle Z = 2m\angle PZY $}                            Substitution

11)\text{ } 2m\angle QYZ=2m\angle PZY                    Substitution

12)\text{ }m\angle QYZ=m\angle PZY                        Division Property of Equality

13)\text{ } YZ=YZ                                         Reflexive Property

14)\text{ } \Delta YZP\cong\Delta ZYQ                             Angle-Side-Angle Congruence*

15)\text{ } YQ=ZP                                         CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

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So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ

5 0
3 years ago
Read 2 more answers
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cricket20 [7]
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4 0
3 years ago
A chemistry teacher needs to mix a 20% salt solution with an 80% salt solution to make 20 qt of a 40% salt solution. How many qu
Svetlanka [38]

Answer:

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Step-by-step explanation:

It is often convenient to solve a mixture problem by letting a variable represent the quantity of the higher-concentration contributor to the mix.

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We can let x represent the number of quarts of 80% solution needed. Then (20-x) is the number of quarts of 20% solution needed. The amount of salt in the final mix is ...

  0.80x +0.20(20-x) = 0.40(20)

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The teacher should mix 6 2/3 quarts of 80% solution with 13 1/3 quarts of 20% solution.

3 0
2 years ago
PLEASE ANSWER ASAP CORRECT ANSWER GETS BRAINLIST
geniusboy [140]

I guess the number 2 is to indicate the question...

Then the equation would be 1/3 - 1/2x = -2/3

1/3 - 1/2x - 1/3 = -2/3 - 1/3

-1/2x = -3/3

-1/2x = -1

-1/2x *2 = - 1*2

-x = -2

-x * -1 = -2 * -1

x = 2

Good luck

5 0
3 years ago
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