I need a lot of help

Simplify this expression 8n/17n

docker41 [41]

You can reduce the expression by cancelling out common factor $n$ :

$\frac{8n}{17n} = \frac{8}{17}$

4 0

3 years ago

Select all the shapes below that have a constant cross-section between a

meriva

The shapes below that have a constant cross-section between a pair of faces are cylinder, cube, sphere, hexagonal, and prism.

<h3>What is the definition of geometry?</h3>

It is concerned with the geometry, region, and density of various 2D and 3D shapes.

A cylinder is a closed solid with two parallel circular bases and a curving surface connecting them.

The shapes have a constant cross-section between a pair of faces like a cylinder.

Hence,cylinder, cube, sphere, hexagonal, and prism are the forms below that have a constant cross-section between a pair of faces.

To learn more about geometry, refer to brainly.com/question/7558603.

#SPJ1

5 0

2 years ago

In the scale used on a blueprint, 34

nydimaria [60]

Answer:

67

Step-by-step explanation:

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5 0

3 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$