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Hyo-Jin makes bracelets and sells them on an online craft website. Last month, she sold 6 bracelets. After paying the website a

MissTica

The answer at the end of the day would be 4

3 0

3 years ago

I am having trouble with this relative minimum of this equation.<br>

Norma-Jean [14]

Answer:

So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach. You have to let me know if you want this done another way.

Here are some rules I'm going to use:

$(f+g)'=f'+g'$ (Sum rule)

$(cf)'=c(f)'$ (Constant multiple rule)

$(x^n)'=nx^{n-1}$ (Power rule)

$(c)'=0$ (Constant rule)

$(x)'=1$ (Slope of y=x is 1)

$y=4x^3+13x^2-12x-56$

$y'=(4x^3+13x^2-12x-56)'$

$y'=(4x^3)'+(13x^2)'-(12x)'-(56)'$

$y'=4(x^3)'+13(x^2)'-12(x)'-0$

$y'=4(3x^2)+13(2x^1)-12(1)$

$y'=12x^2+26x-12$

Now we set y' equal to 0 and solve for the critical numbers.

$12x^2+26x-12=0$

Divide both sides by 2:

$6x^2+13x-6=0$

Compaer $6x^2+13x-6=0$ to $ax^2+bx+c=0$ to determine the values for $a=6,b=13,c=-6$ .

$a=6$

$b=13$

$c=-6$

We are going to use the quadratic formula to solve for our critical numbers, x.

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}$

$x=\frac{-13 \pm \sqrt{169+144}}{12}$

$x=\frac{-13 \pm \sqrt{313}}{12}$

Let's separate the choices:

$x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}$

Let's approximate both of these:

$x=0.3909838 \text{ or } -2.5576505$ .

This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.

The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

$f(x)=4x^3+13x^2-12x-56$

$f'(x)=12x^2+26x-12$

$f''(x)=24x+26$

So if f''(a) is positive then we have a minimum at x=a.

If f''(a) is negative then we have a maximum at x=a.

Rounding to nearest tenths here: x=-2.6 and x=.4

Let's see what f'' gives us at both of these x's.

$24(-2.6)+25$

$-37.5$

So we have a maximum at x=-2.6.

$24(.4)+25$

$9.6+25$

$34.6$

So we have a minimum at x=.4.

Now let's find the corresponding y-value for our relative minimum point since that would complete your question.

We are going to use the equation that relates x and y.

I'm going to use 0.3909838 instead of .4 just so we can be closer to the correct y value.

$y=4(0.3909838)^3+13(0.3909838)^2-12(0.3909838)-56$

I'm shoving this into a calculator:

$y=-58.4654411$

So the approximate relative minimum is (0.4,-58.5).

If you graph $y=4x^3+13x^2-12x-56$ you should see the graph taking a dip at this point.

3 0

3 years ago

Please answer as soon as possible, im in a bit of a hurry.

12345 [234]

Easy bruh

Answer:

6w^3

Step-by-step explanation:

It can't be any answer with cubed in it because that would be volume. So, A and C magically vanish. If we know that the length of a cube is w that means that all sides are w. There are six faces on a cube. If we want to find surface area we will have to add up the area of all faces. the area of one face will be w^2. We multiply that number by six and we get 6w^3.

4 0

3 years ago

Read 2 more answers

—3x + 1/3y = 12<br> 2y = 18х + 72<br><br> I need the answer ASAP how many solutions and the answer

erica [24]

Answer:

Infinite solutions or all real numbers

Step-by-step explanation:

divide the bottom equation by 2 then....

-3x +1/3 (9x + 36) = 12

-3x + 3x + 12 = 12 (distribute the 1/3 to the terms in the parentheses)

12 = 12

Infinite solutions

8 0

3 years ago

Tracy wants to determine the coordinates of the minimum value of a quadratic function. She

OleMash [197]

The most helpful form to find the coordinates of the minimum is the vertex form.

<h3>Which form is better to find the minimum?</h3>

Remember that for a quadratic equation with a positive leading coefficient, the minimum is at the vertex.

So the better form to determinate the coordinates of the minimum value will be the vertex form, where if the vertex is (h, k), we get:

y = a*(x - h)^2 + k

In this case, the first option is in that form:

y = (x + 1)^2 - 25

so:

h = -1

k = -25

This means that the coordinates of the minimum are (-1, -25)

If you want to learn more about quadratic equations, you can read:

brainly.com/question/1214333

7 0

3 years ago