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2 years ago

Find the vertex of f(x) = |x – 5| + 10

Mathematics

1 answer:

Novay_Z [31]2 years ago

6 0

The vertex will end up landing on (5,10)

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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

A carrot has 55 grams of sugar per serving. A banana has 15 grams of sugar per serving. Which statement is true?

GREYUIT [131]

For an equal number of servings, the bananas will have three times as much sugar.

To put it in perspective:
When we have one serving of each fruit, the carrot will give you 5 grams of sugar whereas banana will give you 15 grams.

Hope this helps!

7 0

3 years ago

Can someone please please help with these questions?

wolverine [178]

The answer to number seven is EDF!

5 0

3 years ago

Amy and Jade bought packages of gum. Amy bought a total of 48 pieces. Jade bought a total of 32 pieces. If each package had the

dolphi86 [110]

Answer:

16 pieces were in each pack of gum

7 0

3 years ago

4. Steve has a card collection. He keeps 12 of the cards in a pocket, which

BabaBlast [244]

Answer:

I think 80

Step-by-step explanation:

100/15=6.66666667

12x6.67=80.4

4 0

2 years ago