1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lera25 [3.4K]
3 years ago
12

Evan wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence

on that side. The other three sides will be enclosed with wire fencing. If Evan has 1000 feet of fencing, you can find the dimensions that maximize the area of the enclosure. a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write an function for the area A of the enclosure in terms of w . (HINT first write two equations with w and l and A . Solve for l in one equation and substitute for l in the other). A(w) = ___________ b) What width would maximize the area? w = __________ c) What is the maximum area? A = _________ square feet
Mathematics
1 answer:
pentagon [3]3 years ago
3 0

Answer:  A.   A=(1000-2w)*w      B. 250 feet

C.  125 000 square feet

Step-by-step explanation:

The area of rectangular is A=l*w    (1)

From another hand the length of the fence is 2*w+l=1000        (2)

L is not multiplied by 2, because the opposite side of the l is the barn,- we don't need in fence on that side.

Express l from (2):

l=1000-2w

Substitude l in (1) by 1000-2w

A=(1000-2w)*w        (3)   ( Part A. is done !)

Part B.

To find the width w  (Wmax) that corresponds to max of area A   we have to dind the roots of equation (1000-2w)w=0  ( we get it from (3))

w1=0  1000-2*w2=0

w2=500

Wmax= (w1+w2)/2=(0+500)/2=250 feet

The width that maximize area A is Wmax=250 feet

Part C.   Using (3) and the value of Wmax=250 we can write the following:

A(Wmax)=250*(1000-2*250)=250*500=125 000 square feets

You might be interested in
The map shows a typical flight path between Seattle and London. Why does the path go over the Arctic? A) It is the shortest path
Triss [41]
The answer to the given question above would be option A. Based on the given map shown above which is a typical flight path between Seattle and London, the reason why the path goes over the Arctic is that, it is the shortest path. Hope this answers your question.
4 0
3 years ago
Read 2 more answers
What is the equation for the hyperbola shown?
amid [387]

Answer:

D. y²/5² - x²/8² = 1

Step-by-step explanation:

A and B are both incorrectly oriented, and D is the only hyperbola that contains the points (0,5) and (0,-5).

Verification (0,5) and (0,-5) are in the hyperbola:

First replace x and y with corresponding x and y values (We will start with x=0 and y=5)

\frac{5^{2}}{5^{2}}-\frac{0^{2}}{8^{2}}=1

Then simplify.

\frac{25}{25}-\frac{0}{16}=1

1-0=1

1=1

If the result is an equation (where both sides are equal to each other) then the original x and y values inputted are valid. The same is true with x and y inputs x=0 and y=-5, or any other point along   the hyperbola.

6 0
3 years ago
Read 2 more answers
The sum of a number and two more than twice the number is less than 50. Find the number
prisoha [69]

Answer:


Step-by-step explanation:19 and 31


7 0
2 years ago
A survey is made to determine the number of households having electric appliances in a certain city. It is found that 75% have r
Mashcka [7]

Answer:

The probability that a household has at least one of these appliances is 0.95

Step-by-step explanation:

Percentage of households having radios P(R) = 75% = 0.75

Percentage of households having electric irons P(I) = 65% = 0.65

Percentage of households having electric toasters P(T) = 55% = 0.55

Percentage of household having iron and radio P(I∩R) = 50% = 0.5

Percentage of household having radios and toasters P(R∩T) = 40% = 0.40

Percentage of household having iron and toasters P(I∩T) = 30% = 0.30

Percentage of household having all three P(I∩R∩T) = 20% = 0.20

Probability of households having at least one of the appliance can be calculated using the rule:

P(at least one of the three) = P(R) +P(I) + P(T) - P(I∩R) - P(R∩T) - P(I∩T) + P(I∩R∩T)

P(at least one of the three)=0.75 + 0.65 + 0.55 - 0.50 - 0.40 - 0.30 + 0.20  P(at least one of the three) = 0.95

The probability that a household has at least one of these appliances is 0.95

3 0
3 years ago
6. Select all values of x for which f(x) = g(x).<br> A.0<br> B. 1<br> C.-3<br> D.4
Sati [7]
The answer would be A
6 0
3 years ago
Other questions:
  • What polynomial has roots of -4,1,and 6
    11·1 answer
  • How much deeper is the deepest canyon on mars than the deepest canyon on venus
    12·2 answers
  • What are the year-2 CPI and the rate of inflation from year 1 to year 2 for a basket of goods that costs $25.00 in year 1 and $2
    14·2 answers
  • The mean sustained wind velocity, v, can be determined by the equation , where p is the air pressure, in millibars, at the cente
    15·2 answers
  • Marissa used the set of ordered pairs below to graph a relation.
    10·2 answers
  • Help me plss I’m lost ☺️❤️
    12·2 answers
  • △ABC is a right triangle with right angle C. Side AC¯¯¯¯¯¯¯¯ is 6 units longer than side BC¯¯¯¯¯¯¯¯. If the hypotenuse has lengt
    15·1 answer
  • The slope of the line that contains the points (4, 10) and (5, 13) is 3. Find the y-intercept.
    8·1 answer
  • Circumference of circle 132cm find the area of circle is​
    15·1 answer
  • Please help will give brainliest
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!