The complete formula for circumference is:

Since we know the circumference of the circle is 314 inches, we can then solve for d, the diameter:

Using 3.14 for pi, we get:

Then solve for d:

And now we know the diameter of the circle is 100 inches.
Answer:
they are corresponding angles
Answers:
- Exponential and increasing
- Exponential and decreasing
- Linear and decreasing
- Linear and increasing
- Exponential and increasing
=========================================================
Explanation:
Problems 1, 2, and 5 are exponential functions of the form
where b is the base of the exponent and 'a' is the starting term (when x=0).
If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.
If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.
In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.
Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.
---------------------
Problems 3 and 4 are linear functions of the form y = mx+b
m = slope
b = y intercept
This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.
If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.
On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.
Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.
A parallelogram is a four-sided shape where the opposite sides are parallel to each other.
A rhombus is a parallelogram with the four sides equal.
Some of the properties of a rhombus are:
<span>1.) All sides are parallel and equal.
2.) Opposite angles are equal
3.) Consecutive angles add up to 180 degrees.
4.) <span>The diagonals bisect the angles.</span></span>
<span>Generate a function for the height of the cyliner as a function of radius. Use this function to generate a function of r for the material used. Take the derivative of that function, set it to zero, and solve for r.
</span><span>V=πr2h</span>h=d h=d=2r h=2r <span>V=πr22r
</span><span>V(r,h)=180.5=πr2h⟹h=<span>180.5/<span>πr2</span></span></span><span>⟹A(r)=r(r+h)=r2+<span>180.5/<span>πr
</span></span></span><span>A(r)=2r(2r+h)=4r2+<span>361/<span>πr
</span></span></span>
<span>A′(r)=8r−<span>361/<span>π<span>r2</span></span></span></span>