Which of the following formulas, when evaluated using rational values for the variables, will result in an irrational number?

the scale of a map is 0.5 inch : 40 miles. On the map, the distance between 2 cities is 5 inches. What is the actual distance be

kolbaska11 [484]

This is a proportion question.

0.5:40 miles :: 5:x

Translated into division you get 0.5/40 = 5/x Cross multiply

0.5 x = 40 * 5 combine the right

0.5x = 200 divide by 0.5

0.5x/0.5 = 200/0.5 Divide

x = 400

Answer: The two cities are 400 miles apart

8 0

2 years ago

Data obtained from a nominal scale: A. must be alphabetic B. can be either numeric or nonnumeric C. must be numeric D. must rank

cupoosta [38]

Answer:

Option B

Step-by-step explanation:

The data constitutes nominal scale of measurement when the observations can be classified into groups. For example, students are classified into groups on the basis of eye color. The numerical values can also be use in nominal scale for grouping. For example, the students can be categorize into 1,2 and 3 if they have brown, black and green eye color. But they have no numerical significance. Thus, data obtained from a nominal scale can be either numeric or non-numeric.

3 0

2 years ago

Choose the function whose graph is given by:

Leni [432]

Answer:

y = tan(x -π) -1

Step-by-step explanation:

It looks like a straight tangent function shifted down one unit. Since the tangent function has a period of π, ...

tan(x -π) = tan(x)

so you're only looking for the function that has a translation downward of 1 unit. Of course that translation is accomplished by adding -1 to the original function.

The appearance of the graph is of ...

y = tan(x) -1

The choice that is equivalent to this is ...

y = tan(x -π) -1

5 0

2 years ago

Read 2 more answers

Consider the function f(x) = x3 − 4x2 + 2. Calculate the limit of the difference quotient at x0 = 3 for f(x).

m_a_m_a [10]

Answer: $\boxed{f'(x)=3x^2-8x}$

The limit of the difference quotient is simply the derivative, so we can express this as follows:

$f'(x)=\underset{\Delta x\rightarrow0}{lim}\frac{\triangle y}{\Delta x}=\frac{f(x+\Delta x)-f(x)}{\Delta x}$

So our function is:

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

Taking the derivative, we have:

$f'(x)=3x^2-8x$

So the correct option is:

$\boxed{f'(x)=3x^2-8x}$

Answer: $\boxed{y=3x-16}$

The equation of the line that passes through the same point can be found as:

$y-y_{0}=m(x-x_{0})$

Where $x_{0}=3$ , so we need to find $y_{0}$ . Plug in that x-value in the function we have:

$y_{0}=f(3)=(3)^3-4(3)^2+2 \\ \\ y_{0}=-7 \\ \\ \\ So \ the \ point \ is: \\ \\ P(x_{0},y_{0})=(3,-7)$

And the slope is:

$m=f'(3)=3(3)^2-8(3) \\ \\ m=3$

Then, the equation of the line is:

$y-(-7)=3(x-3) \\ \\ \therefore y+7=3x-9 \\ \\ \boxed{y=3x-16}$

Answer: Shown below

As you can see below, the graph of the function of $f$ is continuous. This is so because we have plotted a polynomial function whose domain is the set of all real numbers. So the function is defined at the point $P(3,-7)$ , so the derivative exists at this point, hence we can calculate a tangent line there. In conclusion, we get the graph shown below. The blue line is the tangent line while the red curve is the graph of $f$