I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. I have a budget of $176 for the project. What are the dimensions of the vegetable patch with the largest area I can enclose?

Answers

Answer 1

Answer: x = E/W dimension
y = N/S dimension

4x + 4x + 2y + 2y = 64
8x + 4y = 64
4y = 64 - 8x
y = 16 - 2x

Area = xy = x(16 - 2x) = 16x - 2x^2

Maximum of y = ax^2 + bx + c is when x = -b / 2a

so x = -16 / -4 = 4

(f - g)(x) = - x² + 2x + 3

Step-by-step explanation:

f(x) = 2x + 2

g(x) = x² - 1

To find (f - g)(x) subtract g(x) from f(x)

That's

(f - g)(x) = 2x + 2 - [ x² - 1]

(f - g)(x) = 2x + 2 - x² + 1

Group like terms

That's

(f - g)(x) = - x² + 2x + 2 + 1

We have the final answer as

(f - g)(x) = - x² + 2x + 3

Hope this helps you

Answer:

-x2+2x+3

Step-by-step explanation:

(2x+2)- (x2-1)

2x+2-x2+1

-x2+2x+3

Plz i need help on this

Answers

Answer:

nahnahnahnahnahnahnah

Find parametric equations for the line. (Enter your answers as a comma-separated list of equations. Let x, y, and z be functions of t.) The line in the direction of the vector 5 i + 5 j − 6k and through the point (−4, 4, −2).

Answers

The parametric equations are:

x = -4 + 5t

y = 4 + 5t

z = -2 - 6t

The given direction vector is:

$\bar{V} = 5i + 5j - 6k$

The direction vector can also be written as:

$\bar{V} = <a, b, c> = <5, 5, -6>$

The point X₀ = (x₀, y₀, z₀) = (-4, 4, -2)

The parametric equation is of the form:

$X = X_(0) + \bar{V}t$

This is:

$\left[\begin{array}{ccc}x\ny\nz\end{array}\right] = \left[\begin{array}{ccc}x_0\ny_0\nz_0\end{array}\right] + \left[\begin{array}{ccc}a\nb\nc\end{array}\right]t$

$\left[\begin{array}{ccc}x\ny\nz\end{array}\right] = \left[\begin{array}{ccc}-4\n4\n-2\end{array}\right] + \left[\begin{array}{ccc}5\n5\n-6\end{array}\right]t$

The parametric equations are therefore:

x = -4 + 5t

y = 4 + 5t

z = -2 - 6t

Learn more here: brainly.com/question/13072659

Answer:

x=5t-4 , y=5t+4 , z=-6t-2

Step-by-step explanation:

So we are going to use (-4,4,-2) as an initial point, p.

The direction vector is v=5i+5j-6k or <5,5,-6>.

The vector equation is r=vt+p.

That means we have r=<5,5,-6>t + <-4,4,-2>.

So the parametric equations are

x=5t-4

y=5t+4

z=-6t-2

For his long distance phone service, Bill pays a $3 monthly fee plus 11 cents per minute. Last month, Bill's long distance bill was $16.09. For how many minutes was Bill billed?

Answers

Answer:

1.19 minutes

Step-by-step explanation:

First, subtract the $3 monthly fee:

16.09 - 3

= 13.09

Then, divide this by 11:

13.09/11

= 1.19

So, he was billed for 1.19 minutes

Can you help me find abcd please

Answers

Answer:

A.2 B.4 C.3 D.4 E.6

Step-by-step explanation:

1/2 ÷ 3/4 = 1/2 x 4/3 (flip 3/4 and keep 1/2)

If you multiply 1/2 x 4/3 you will get 4/6.

Use the technique developed in this section to solve the minimization problem. Minimize C = −3x − 2y − z subject to −x + 2y − z ≤ 20 x − 2y + 2z ≤ 25 2x + 4y − 3z ≤ 30 x ≥ 0, y ≥ 0, z ≥ 0 The minimum is C = at (x, y, z) = .

Answers

Answer:

C= -145, (35/4, 295/8, 45)

Step-by-step explanation:

Use Gaussian elimination to find the values of x, y and z

Eq 1: -x+2y-z=20

Eq 2: x-2y+2z=25

Eq 3: 2x+4y-3z=30

Multily Eq1 by 1 and add to Eq 2

Eq 1: (-x+2y-z=20 ) × 1

Eq 2: x-2y+2z=25

Eq 3: 2x+4y-3z=30

⇒ Eq1: -x+2y-z=20

Eq2: z= 45

Eq 3: 2x+4y-3z=30

Multiply Eq 1 by 2 and then add to Eq 3

Eq1: (-x+2y-z=20 ) × 2

Eq2: z= 45

Eq3: 2x+4y-3z=30

⇒ Eq1: -x+2y-z=20

Eq2: z= 45

Eq3: 8y-5z= 70

swap Eq 2 and Eq 3

Eq 1: -x+2y-z=20

Eq 3: 8y-5z= 70

Eq 2: z= 45

Solve Eq 2 for z

Z=45

solve Eq Eq 3 for y.

y= 295/8

Using the value z=45 and y= 295/8, substitue in Eq 1 to get value of x

x= 35/4

Substitue values of x,y and z in C= -3x-2y-z to get minimum value of C

C= -145

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