Answer:
Part a) ![V(h)=6.25\pi h\ in^3](https://tex.z-dn.net/?f=V%28h%29%3D6.25%5Cpi%20h%5C%20in%5E3)
Part b)
(see the explanation)
Step-by-step explanation:
we know that
The volume of a cylinder is equal to
![V=Bh](https://tex.z-dn.net/?f=V%3DBh)
where
B is the area of the base of cylinder
h is the height of the cylinder
we have that
![B=\pi r^{2}](https://tex.z-dn.net/?f=B%3D%5Cpi%20r%5E%7B2%7D)
Part a) Write the function, V(h), that represents the volume of the cylinder
we have
----> the radius is half the diameter
substitute
![B=\pi (2.5)^{2}](https://tex.z-dn.net/?f=B%3D%5Cpi%20%282.5%29%5E%7B2%7D)
![B=6.25\pi\ in^2](https://tex.z-dn.net/?f=B%3D6.25%5Cpi%5C%20in%5E2)
The volume is
![V(h)=6.25\pi h\ in^3](https://tex.z-dn.net/?f=V%28h%29%3D6.25%5Cpi%20h%5C%20in%5E3)
Part b) Find V(3) and tell what it represents
V(3) represent the volume of the cylinder with a height of 3 inches
so
For h=3 in
substitute
![V(3)=6.25\pi(3)\ in^3](https://tex.z-dn.net/?f=V%283%29%3D6.25%5Cpi%283%29%5C%20in%5E3)
![V(3)=18.75\pi\ in^3](https://tex.z-dn.net/?f=V%283%29%3D18.75%5Cpi%5C%20in%5E3)
Answer:
C. y = -2x + 3
Step-by-step explanation:
The equation of a line in slope-intercept form is given as y = mx + b.
m = slope, while b = y-intercept.
We already know that the slope, m, = -2.
We are given a point also as (0, 3). This means, at x = 0, y = 3.
Therefore, the y-intercept, b, = 3, because, the line would intercept the y-axis of the graph at y = 3, and at that point, x = 0.
Thus,
Slope (m) = -2,
y-intercept (b) = 3
Plug these values into y = mx + b
✅The equation of the line in slope-intercept form would be:
y = -2x + 3
Answer:
All angles are 90.all rectangles have angle measures of 90* and a dilation just decreases the size and does not change its shape or angles.
Step-by-step explanation:
All rectangles have angle measures of 90* and a dilation just decreases the size and does not change its shape or angles.
The radical expressions and their corresponding expression in rational exponent form are
,
,
and ![4050^\frac 14 = 3\sqrt[4]{50}](https://tex.z-dn.net/?f=4050%5E%5Cfrac%2014%20%3D%203%5Csqrt%5B4%5D%7B50%7D)
<h3>How to match the tiles?</h3>
We start by evaluating each expression as follows:
![972^\frac 15](https://tex.z-dn.net/?f=972%5E%5Cfrac%2015)
Expand 972
![972^\frac 15 = (243 * 3)^\frac 15](https://tex.z-dn.net/?f=972%5E%5Cfrac%2015%20%3D%20%28243%20%2A%203%29%5E%5Cfrac%2015)
Take the 5th root of 243
![972^\frac 15 = 3* (4)^\frac 15](https://tex.z-dn.net/?f=972%5E%5Cfrac%2015%20%3D%203%2A%20%284%29%5E%5Cfrac%2015)
Rewrite as:
![972^\frac 15 = 3\sqrt[5]{4}](https://tex.z-dn.net/?f=972%5E%5Cfrac%2015%20%3D%203%5Csqrt%5B5%5D%7B4%7D)
Next, we have:
![448^\frac 13](https://tex.z-dn.net/?f=448%5E%5Cfrac%2013)
Expand 448
![448^\frac 13 = (64 * 7)^\frac 13](https://tex.z-dn.net/?f=448%5E%5Cfrac%2013%20%3D%20%2864%20%2A%207%29%5E%5Cfrac%2013)
Take the 3rd root of 64
![448^\frac 13 = 4 * (7)^\frac 13](https://tex.z-dn.net/?f=448%5E%5Cfrac%2013%20%3D%204%20%2A%20%287%29%5E%5Cfrac%2013)
Rewrite as:
![448^\frac 13 = 4\sqrt[3]{7}](https://tex.z-dn.net/?f=448%5E%5Cfrac%2013%20%3D%204%5Csqrt%5B3%5D%7B7%7D)
Next, we have:
![3528^\frac 12](https://tex.z-dn.net/?f=3528%5E%5Cfrac%2012)
Expand 3528
![3528^\frac 12 = (1764 * 2)^\frac 12](https://tex.z-dn.net/?f=3528%5E%5Cfrac%2012%20%3D%20%281764%20%2A%202%29%5E%5Cfrac%2012)
Take the square root of 1764
![3528^\frac 12 = 42 * (2)^\frac 12](https://tex.z-dn.net/?f=3528%5E%5Cfrac%2012%20%3D%2042%20%2A%20%282%29%5E%5Cfrac%2012)
Rewrite as:
![3528^\frac 12 = 42 \sqrt 2](https://tex.z-dn.net/?f=3528%5E%5Cfrac%2012%20%3D%2042%20%5Csqrt%202)
Lastly, we have:
![4050^\frac 14](https://tex.z-dn.net/?f=4050%5E%5Cfrac%2014)
Expand 4050
![4050^\frac 14 = (81 * 50)^\frac 14](https://tex.z-dn.net/?f=4050%5E%5Cfrac%2014%20%3D%20%2881%20%2A%2050%29%5E%5Cfrac%2014)
Take the 4th root of 81
![4050^\frac 14 = 3 (50)^\frac 14](https://tex.z-dn.net/?f=4050%5E%5Cfrac%2014%20%3D%203%20%2850%29%5E%5Cfrac%2014)
Rewrite as:
![4050^\frac 14 = 3\sqrt[4]{50}](https://tex.z-dn.net/?f=4050%5E%5Cfrac%2014%20%3D%203%5Csqrt%5B4%5D%7B50%7D)
Read more about radical expressions at:
brainly.com/question/8952483
#SPJ1
Answer:
28/3
Step-by-step explanation: