1) Identify the end behavior of the function ƒ(x) = −7x3 + 7x2 + 5x − 2.

What is the value of x?<br><br> Enter your answer in the box.<br><br> x = __ cm

BartSMP [9]

This is a proportionality question. We have two transversals meeting at a point; the indicated congruent angles indicates the traversals intersecting parallel lines. Usually in these sorts of questions the parallel lines are on the same side of the common vertex, but here the vertex is in between, so the x is proportional to the 42.

x/6 =42/36

x = 6(42/36) = 42/6 = 7

Answer: 7

6 0

4 years ago

Gage's math teacher entered the seventh-grade student in a math competition. There was an enrollment fee of $30 and also $11 cha

Amanda [17]

Answer:

110 test

Step-by-step explanation:

Let

x ----> the number of packet of 10 test

y ----> the total cost

we know that

The number of packet of 10 test purchase multiplied by $11 plus the enrollment fee of $30 must be equal to $151

so

The linear equation that represent this scenario is

$y=11x+30$

we have

$y=\$151$

substitute

$151=11x+30$

Solve for x

subtract 30 both sides

$11x=151-30$

$11x=121$

Divide by 11 both sides

$x=11$

The number of packets purchase was 11

To find out the number of test, multiply the number of packets by 10

$11(10)=110\ test$

4 0

3 years ago

The total cost (in dollars) of producing x food processors is C(x) = 2500 + 50x -0.28.

Darya [45]

Answer:

The exact cost of producing the 21st food processor is $38.52.

The marginal cost to approximate the cost of producing the 21st food processor is $38.24

Step-by-step explanation:

Consider the provided function.

$C(x) = 2500 + 50x -0.28x^2$

(A) Find the exact cost of producing the 21st food processor

The exact cost producing 21st food processor is C(21)-C(20)

Substitute x=21 in above function.

$C(x) = 2500 + 50(21) -0.28(21)^2$

$C(x) = 2500 +1050 -123.48$

$C(x) = 3426.52$

Substitute x=20 in above function.

$C(x) = 2500 + 50(20) -0.28(20)^2$

$C(x) = 2500 +1000-112$

$C(x) = 3388$

The exact cost producing is:

$C(21)-C(20)=3426.52-3388=38.52$

Hence, the exact cost of producing the 21st food processor is $38.52.

Part (B) Use the marginal cost to approximate the cost of producing the 21st food processor,

To find the marginal cost first differentiate the function with respect to x.

$C(x) = 2500 + 50x -0.28x^2$

$C'(x) =50-0.56x$

Now substitute x=21 in above function.

$C'(x) =50-0.56(21)$

$C'(x) =50-11.76$

$C'(x) =38.24$

The marginal cost to approximate the cost of producing the 21st food processor is $38.24

5 0

3 years ago

How do i use exponential decay models with radioactive isotopes and their life spans?

Dimas [21]

What are Half Lives and Mean Lives?

Specifying the half life or mean life of a process is a way of quantifying how fast it is occurring, when the whole process would in principle take forever to complete. The example we will talk about here is radioactive growth and decay, but examples from other fields include the recovery of a muscle after some exertion, and the filling of a cistern.

In particular then, the half life of a radioactive element is the time required for half of it to decay (i.e. change into another element, called the "daughter" element).

So if a radioactive element has a half life of one hour, this means that half of it will decay in one hour. After another hour, half of the remaining material will decay. But why didn't all of that remaining material decay in that second hour? Does the element somehow know that it's decaying, and alter its decay speed to suit?

Textbooks are usually content with deriving of the law of decay, and don't tend to address this question. And yet it forms a classic example of the way in which research in physics (and science in general) is carried out. Regardless of how we might expect an element to behave—where perhaps the second half might be expected to decay in the same amount of time as the first half—this simply does not happen. We must search for a theory that predicts this.

Science is often thought to proceed by our logically deducing the laws that govern the world. But it's not that simple; there are limits to what we can deduce, especially about things in which we cannot directly participate. Radioactive decay is a good example of this. We can't use a microscope to watch the events that make an element decay. The process is quite mysterious. But what we can do is make a simple theory of how decay might work, and then use that theory to make a prediction of what measurements we can expect. That's the way science proceeds: by making theories that lead to predictions. Sometimes these predictions turn out to be wrong. That's fine: it means we must tinker with the theory, perhaps discard it outright, or maybe realise that it's completely okay under certain limited circumstances. The hallmark of a good scientific theory is not what it seems to explain, but rather what it predicts. After all, a theory that says the universe just appeared yesterday, complete with life on earth, fossils and so on, in a sense "explains" everything beautifully by simply defining it to be so; but it predicts absolutely nothing. So from a scientific point of view it is not a very useful theory, because it contains nothing that allows its truth to be tested. On the other hand, while it's arguable that the theory of quantum mechanics explains anything at all, it certainly does predict a huge number of different phenomena that have been observed; and that's what makes it a very useful theory.

8 0

4 years ago

A line is perpendicular to y = -1/5x+1

natta225 [31]

Answer:

$y = 5\, x + 26$ .

Step-by-step explanation:

Start by finding the slope of the line perpendicular to $y = (-1/5)\, x + 1$ .

The slope of $y = (-1/5)\, x + 1$ is $(-1/5)$ .

In a plane, if two lines are perpendicular to one another, the product of their slopes would be $(-1)$ .

Let $m$ denote the slope of the line perpendicular to $y = (-1/5)\, x + 1$ . The expression $(-1/5)\, m$ would denote the product of the slopes of these two lines.

Since these two lines are perpendicular to one another, $(-1/5)\, m = -1$ . Solve for $m$ : $m = 5$ .

The $(-5,\, 1)$ is a point on the requested line. (That is, $x_{1} = -5$ and $y_{1} = 1$ .) The slope of that line is found to be $m = 5$ . The equation of that line in the point-slope form would be:

$y - 1 = 5\, (x - (-5))$ .

Rewrite this point-slope form equation into the slope-intercept form:

$y = 5\, x + 26$ .

5 0

3 years ago