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3 years ago

How do you solve this problem?

Mathematics

2 answers:

SpyIntel [72]3 years ago

5 0

I agree with her by adding 24y +18 and then the answer u get u add it with 36

lina2011 [118]3 years ago

4 0

You solve that problem by adding 24y +18 then that answer you will add it with 36

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Suppose a rectangular pasture is to be constructed using 1 2 linear mile of fencing. The pasture will have one divider parallel

timama [110]

Answer:

$\displaystyle A=\frac{1}{192}$

Step-by-step explanation:

<u>Maximization With Derivatives</u>

Given a function of one variable A(x), we can find the maximum or minimum value of A by using the derivatives criterion. If A'(x)=0, then A has a probable maximum or minimum value.

We need to find a function for the area of the pasture. Let's assume the dimensions of the pasture are x and y, and one divider goes parallel to the sides named y, and two dividers go parallel to x.

The two divisions parallel to x have lengths y, thus the fencing will take 4x. The three dividers parallel to y have lengths x, thus the fencing will take 3y.

The amount of fence needed to enclose the external and the internal divisions is

$P=4x+3y$

We know the total fencing is 1/2 miles long, thus

$\displaystyle 4x+3y=\frac{1}{2}$

Solving for x

$\displaystyle x=\frac{\frac{1}{2}-3y}{4}$

The total area of the pasture is

$A=x.y$

Substituting x

$\displaystyle A=\frac{\frac{1}{2}-3y}{4}.y$

$\displaystyle A=\frac{\frac{1}{2}y-3y^2}{4}$

Differentiating with respect to y

$\displaystyle A'=\frac{\frac{1}{2}-6y}{4}$

Equate to 0

$\displaystyle \frac{\frac{1}{2}-6y}{4}=0$

Solving for y

$\displaystyle y=\frac{1}{12}$

And also

$\displaystyle x=\frac{\frac{1}{2}-3\cdot \frac{1}{12}}{4}=\frac{1}{16}$

Compute the second derivative

$\displaystyle A''=-\frac{3}{2}.$

Since it's always negative, the point is a maximum

Thus, the maximum area is

$\displaystyle A=\frac{1}{12}\cdot \frac{1}{16}=\frac{1}{192}$

6 0

2 years ago

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes.

mote1985 [20]

Answer:

5 large boxes

3 small boxes

Step-by-step explanation:

Create two equations to represent the problem.

let "a" be the number of small boxes

let "b" be the number of large boxes

20a + 40b = 260 This equation shows the numbers of books

a + b = 8 This equations shows the number of boxes

Solve the system of equations (solve for a and b). We can solve using the substitution method.

Rearrange a + b = 8 to isolate one of the variables.

a = 8 - b New equation that represents "a"

Since we know an equation for "a", we can substitute what "a" equals into the other equation. There will only be one variable in the equation, so we can solve by isolating. Isolate by doing reverse operations.

Substitute "a" for 8 - b

20a + 40b = 260

20(8 - b) + 40b = 260 Distribute 20 over the brackets by multiplying

160 - 20b + 40b = 260 Collect like terms (numbers with same variables)

160 + 20b = 260 Start isolating "b". Subtract 160 from both sides

20b = 260 - 160

20b = 100 Divide both sides by 20

b = 5 Number of large boxes

Substitute "b" for 5 in the simplest equation

a + b = 8

a + 5 = 8 Subtract 5 from both sides to isolate "a"

a = 8 - 5

a = 3 Number of small boxes

Therefore there were 5 large boxes and 3 small boxes sent.

3 0

2 years ago

In which quadrant will the following points be plotted (-4;-4) (5;2) (-6;11)

AVprozaik [17]

(-4,-4) is quadrant 3
(5,2) is quadrant 1
(-6,11) is quadrant 2

3 0

3 years ago

Travis bought two plots of land at the beginning of 2000. When purchased, the smaller plot of land was valued at $20,000.00 and

stepan [7]

HAT MATH ARE U IN
i got part of it but it lost me the
<span>differ part of land is 49,500 but it lost meh hope it helps gl</span>

3 0

2 years ago

Read 2 more answers

How many gallons of gas are left after driving 200 miles

BaLLatris [955]

The equation y = -0.04x + 12 gives the number of gallons of gas in your car where x is the number of miles drivene

easy

y=gas left
x=miles

sub 200 for x
y=-0.04(200)+12
y=-8+12
y=4

4 gallons left

8 0

2 years ago