The slope and unit rate

A closed can, in a shape of a circular, is to contain 500cm^3 of liquid when full. The cylinder, radius r cm and height h cm, is

Gemiola [76]

To express the height as a function of the volume and the radius, we are going to use the volume formula for a cylinder: $V= \pi r^2h$
where
$V$ is the volume
$r$ is the radius
$h$ is the height

We know for our problem that the cylindrical can is to contain 500cm^3 when full, so the volume of our cylinder is 500cm^3. In other words: $V=500cm^3$ . We also know that the radius is r cm and height is h cm, so $r=rcm$ and $h=hcm$ . Lets replace the values in our formula:
$V= \pi r^2h$
$500cm^3= \pi (rcm^2)(hcm)$
$500cm^3=h \pi r^2cm^3$
$h= \frac{500cm^3}{ \pi r^2cm^3}$
$h= \frac{500}{ \pi r^2}$

Next, we are going to use the formula for the area of a cylinder: $A=2 \pi rh+2 \pi r^2$
where
$A$ is the area
$r$ is the radius
$h$ is the height

We know from our previous calculation that $h= \frac{500}{ \pi r^2}$ , so lets replace that value in our area formula:
$A=2 \pi rh+2 \pi r^2$
$A=2 \pi r(\frac{500}{ \pi r^2})+2 \pi r^2$
$A= \frac{1000}{r} +2 \pi r^2$
By the commutative property of addition, we can conclude that:
$A=2 \pi r^2+\frac{1000}{r}$

7 0

3 years ago

Southside is purchasing new materials for the school. The school has $1600 to spend on desks and a vending machine. The desks co

Mademuasel [1]

Answer:

$15d + 450 \leq 1600$

5 0

2 years ago

A ladder is leaning against a vertical wall. The distance from the top of the ladder to the base of the wall is 17 feet. The dis

Gennadij [26K]

Answer:

18.4 feet

Step-by-step explanation:

-use the formula C^2 = A^2 + B^2 for a right triangle, which is made by the ladder and the wall.

-let the ladder be C, the wall be a, the base to the bottom be b.

-substitude into the equation, which will leave us with:

C^2 = 17^2 + 7^2

C^2 = 289 + 49

C^2 = 338

C = square root of 338, which is 18.4 feet!

3 0

2 years ago

For the square find coordinates for B without using any new variables

damaskus [11]

The geometric term described as an infinite set of points that has length but not width is called a line. It has a negligible with and depth. In geometry, a line located in the plane is defined as the set of points whose coordinates satisfy a given linear equation. A line segment however is a line connected by two dots far apart from each other and then connected. For example is the equation y=mx+b. This is a slope intercept form which is a linear equation.

6 0

2 years ago

The temperature on June 23rd increased from<br> 67 degrees at 7:00 AM to 87 degrees at 2:00<br> PM.

Svetlanka [38]

Answer:

154

Step-by-step explanation:

7 0

2 years ago