To solve this we are going to use the formula for the area of a circle:
![A= \pi r^2](https://tex.z-dn.net/?f=A%3D%20%5Cpi%20r%5E2)
where
![r](https://tex.z-dn.net/?f=r)
is tte radius of the circle
We can infer that the bases of our cylinder are circles with 2 in radius, so
![r=2in](https://tex.z-dn.net/?f=r%3D2in)
. Since we have tow circles, we are going to multiply the area by 2:
![A= \pi r^2](https://tex.z-dn.net/?f=A%3D%20%5Cpi%20r%5E2)
![A=2[ \pi (2in)^2]](https://tex.z-dn.net/?f=A%3D2%5B%20%5Cpi%20%282in%29%5E2%5D)
![A=2( \pi )(4in^2)](https://tex.z-dn.net/?f=A%3D2%28%20%5Cpi%20%29%284in%5E2%29)
![A=25.12in^2](https://tex.z-dn.net/?f=A%3D25.12in%5E2)
We can conclude that the <span>the combined area of the two bases of the cylinder is </span><span>
25.12 in.2</span>
Answer:
The equation of a line that is perpendicular to
and that passes through the point (2, −6) is
.
Step-by-step explanation:
If a linear equation is written in this form
, m represents the slope and b represents the y-intercept.
When one line has a slope of
, a perpendicular line has a slope of
.
We know the slope/intercept equation of the line
, the slope of this equation is
and the negative reciprocal of that slope is:
![m=\frac{-1}{\frac{7}{5} } \\m=-\frac{5}{7}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1%7D%7B%5Cfrac%7B7%7D%7B5%7D%20%7D%20%5C%5Cm%3D-%5Cfrac%7B5%7D%7B7%7D)
The perpendicular line will have a slope of:
![y-y_1=(-\frac{5}{7})(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%28-%5Cfrac%7B5%7D%7B7%7D%29%28x-x_1%29)
we use the point given (2, -6) to find the equation of the perpendicular line
and we solve for y
![y+6-6=\left(-\frac{5}{7}\right)\left(x-2\right)-6\\\\y=-\frac{5}{7}x+\frac{10}{7}-6\\\\y=-\frac{5}{7}x-\frac{32}{7}](https://tex.z-dn.net/?f=y%2B6-6%3D%5Cleft%28-%5Cfrac%7B5%7D%7B7%7D%5Cright%29%5Cleft%28x-2%5Cright%29-6%5C%5C%5C%5Cy%3D-%5Cfrac%7B5%7D%7B7%7Dx%2B%5Cfrac%7B10%7D%7B7%7D-6%5C%5C%5C%5Cy%3D-%5Cfrac%7B5%7D%7B7%7Dx-%5Cfrac%7B32%7D%7B7%7D)
The equation of a line that is perpendicular to
and that passes through the point (2, −6) is
.
We can check our work with the graph of the two lines.
Answer:
<h2>A. t ≥ 44</h2>
Step-by-step explanation:
Thomas earned $44 or more.
Thomas earned $44 → t = 44
Thomas earned more than $44 → t > 44
From both we have: t ≥ 44
Patty because she has the lowest time out of them all. From least to greatest Patty would be the least with her time being shorter than the rest
<h3>
Answer: Yes it is a rational number</h3>
All terminating decimals are rational numbers
In this case,
3.12311 = 312311/100000
which shows that 3.12311 can be written as a ratio of two integers, therefore making it a rational number.