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3 years ago

6

4x+5y=3x+19 help please :(((

1 answer:

kiruha [24]3 years ago

8 0

16+15

combine like terms

the simplified answer is 31

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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

3 years ago

Which shows the first step in the solution to the<br> equation log₂x + log₂(x - 6) = 4?

iren [92.7K]

log was used calculate big numbers before calculators

log is a re-arranged way to show a number with an exponent

example

log₂ 16 = 4 means 2^4 = 16

logx(Z) = y means x^y=Z

log(x-6)/log(2) + log(x)/log(2) = 4

(log(x-6)+ log(x))/log(2) = 4

(log(x-6)+ log(x)) = 4log(2)

(log(x-6)x) = log(16)

x=8

6 0

1 year ago

Karl drove 619.5 miles. For each gallon of gas, the car can travel 41 miles. What is a reasonable estimate of the number of gall

dusya [7]

Answer:

15

Step-by-step explanation:

Calculation for What is a reasonable estimate of the number of gallons of gas Karl used

Estimated number of gallons used=619.5 miles/41 miles

Estimated number of gallons used=15

Therefore the reasonable estimate of the number of gallons of gas Karl used is 15

6 0

2 years ago

Which polynomial is prime

Vikentia [17]

We need more information. You don't give us enough information....? Provide an image please. Or at least name the polynomials...

7 0

3 years ago

The table above shows a number of each type of item in Harry’s liquor what’s the ratio of paper clips to the total number of ite

SVETLANKA909090 [29]

Answer:

its 3:5

Step-by-step explanation: if you don't see the answer talk with your teacher because I did it and I got 3:5

6 0

3 years ago