Kris is performing an experiment in math class using a bag of colored

QveST [7]

If you're saying the circumference is 40 and we need the radius, then:
$\frac{40}{ \pi } =12.73$
If you're saying the radius is 40 and we need the circumference, then:
$2 \pi 40=251.33$

8 0

4 years ago

Which answer is it A B C or D

Tamiku [17]

The answer to this question is c

6 0

3 years ago

The absolute value function can be defined using piecewise notation.

den301095 [7]

<h3>Answers:</h3>

A(10) = 10
A(0) = 0
A(-3) = 3
A(3.14159) = 3.14159
A(x) = 7 leads to either x = 7 or x = -7
A(x) = -5 has no solutions

=============================================

Explanations:

The piecewise function has two identities based on what the x input is.

If x = 0 or larger, then A(x) = x based on the top row.

Or, if x < 0, then A(x) = -x based on the second row.

So for an input like x = 10, we have A(10) = 10. The input is identical to the output. The same goes for x = 0 and x = 3.14159

Each output tells us how far away the input is from zero on the number line.

----------------

For a negative input, we'll use the second row

A(x) = -x

A(x) = -(x)

A(-3) = -(-3)

A(-3) = 3

Showing that the number -3 is exactly 3 units away from zero on the number line. In other words, |-3| = 3.

----------------

To solve A(x) = 7, we have to think what input(s) will lead to an output of 7.

What two numbers are 7 units away from zero on the number line? That would be -7 and 7.

If you plugged x = 7 into the piecewise function, you'll use the top row to get A(7) = 7. The bottom row will have A(-7) = 7.

-----------------

There are no solutions to A(x) = -5 because the result of an absolute value is never negative. Negative distances do not make sense, so that's why absolute value is defined this way.

If you tried x = 5 then A(5) = 5

Trying x = -5 leads to A(-5) = 5

There's no way to get a negative output.

8 0

2 years ago

Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. (If a

kipiarov [429]

Answer:

Horizontal tangent

(x, y) = (1, 0)

Vertical tangent

(x, y) = DNE

Step-by-step explanation:

The equation for the slope (m) of the tangent line at any point of a parametric curve is:

$m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

Where $\frac{dx}{dt}$ and $\frac{dy}{dt}$ are the first derivatives of the horizontal and vertical components of the parametric curves. Now, the first derivatives are now obtained:

$\frac{dx}{dt} = -1$ and $\frac{dy}{dt} = 2\cdot t$

The equation of the slope is:

$m = -2\cdot t$

As resulting expression is a linear function, there are no discontinuities and for that reason there are no vertical tangents. However, there is one horizontal tangent, which is:

$-2\cdot t = 0$