Answer: ![\pi =\frac{47.1}{15}](https://tex.z-dn.net/?f=%5Cpi%20%3D%5Cfrac%7B47.1%7D%7B15%7D)
Step-by-step explanation:
The complete exercise is: "The circumference of a circle is 47.1 and the diameter of the circle is 15. Which best represents the value of π? "
In order to solve this exercise, it is important to remember that the circle can be calculated with the following formulas:
1. ![C=\pi D](https://tex.z-dn.net/?f=C%3D%5Cpi%20D)
Where "C" is the circumference of the circle and "D" is the diameter of the circle.
2. ![C=2\pi r](https://tex.z-dn.net/?f=C%3D2%5Cpi%20r)
Where "C" is the circumference of the circle and "r" is the radius of the circle (Remeber that the diameter is twice the radius).
In this case, the exercise gives you the circumference of the circle and its diameter. These are:
![C=47.1\\\\d=15](https://tex.z-dn.net/?f=C%3D47.1%5C%5C%5C%5Cd%3D15)
Then, knowing those values, you can substitute them s into the first equation
, as following:
![47.1=\pi (15)](https://tex.z-dn.net/?f=47.1%3D%5Cpi%20%2815%29)
The final step is to solve for
:
![\pi =\frac{47.1}{15}](https://tex.z-dn.net/?f=%5Cpi%20%3D%5Cfrac%7B47.1%7D%7B15%7D)
Answer:
m = -32.10
Step-by-step explanation:
You solve this the same way you do any two-step linear equation.
1. Subtract the constant that is on the side of the equal sign with the variable term:
m/5 = -6.42
2. Multiply by the inverse of the coefficient of the variable. That means multiply by 5 in this case.
m = 5·(-6.42) = -32.10
_____
Of course, the rules of equality tell you whatever you do to one side of the equation must also be done to the other side. So, when we say subtract 0.12, we mean subtract 0.12 from both sides of the equation. The same for multiplication or division.
Answer:
is the question want to ans to be in the form of x
Any tangent line to the curve has a slope given by
.
![\cos y=x-4y\implies-\sin y\,\dfrac{\mathrm dy}{\mathrm dx}=1-4\,\dfrac{\mathrm dy}{\mathrm dx}](https://tex.z-dn.net/?f=%5Ccos%20y%3Dx-4y%5Cimplies-%5Csin%20y%5C%2C%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D1-4%5C%2C%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D)
![\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1{4-\sin y}](https://tex.z-dn.net/?f=%5Cimplies%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D%5Cdfrac1%7B4-%5Csin%20y%7D)
Since
, the denominator ranges from 3 to 5, so the range of slopes is
.
Answer:
-30/5
Step-by-step explanation: