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3 years ago

Differentiate an arithmetic sequence from a geometric sequence?

Mathematics

1 answer:

lord [1]3 years ago

4 0

Answer: Arithmetic sequences follow terms by adding, while geometric sequences follow terms by multiplying.

Step-by-step explanation: Please mark Brainliest!

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Please help i will give brainliest to the first person that answers correctly

timurjin [86]

Answer:

From what i know your answer will be a.

6 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:

Optimizing With Derivatives

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

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

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago

You borrow $3750 to buy new fitness equipment.The simple interest rate is 2%. You pay the loan off after 4 years. What is the to

Alinara [238K]

Provided the 2% interest rate. The interest itself over a period of 4 years, compounds to $300. Thus, the total interest plus the cost of the fitness equipment would be a total of, $4,050.

6 0

3 years ago

Use addition to solve the linear system of equations.

Ipatiy [6.2K]

I'm not quite sure if this is what you need, but I am going to solve these equations by elimination. x= 8/17 and y = 11/17 (8/17, 11/17).

6 0

3 years ago

If x > 0 and y > 0, where is the point (x, y) located?

Scrat [10]

Given, x > 0, y > 0.
So, the values of x and y are less than 0, that means, they are negative integers.
If we divide a Cartesian plane with the x-axis and y-axis, we get four quadrants.
1st Quadrant : (+,+)
2nd Quadrant : (-,+)
3rd Quadrant : (-,-)
4th Quadrant : (+,-)
Since the values of x and y are both negative, so (x, y) is located in the 3rd Quadrant.

Hope you could get an idea from here.

Doubt clarification - use comment section

8 0

2 years ago