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3 years ago

Subtract six from a number cubed

Mathematics

1 answer:

Shkiper50 [21]3 years ago

4 0

Answer:

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The arithmetic sequence a_ia i a, start subscript, i, end subscript is defined by the formula: a_1 = 15a 1 =15a, start subsc

daser333 [38]

Answer:

-1,512,390

Step-by-step explanation:

Given

a1 = 15

$a_i = a_{i-1} -7$

Let us generate the first three terms of the sequence

$a_2 = a_{2-1}-7\\a_2 = a_1 - 7\\a_2 = 15-7\\a_2 = 8$

For $a_3$

$a_3 = a_{3-1}-7\\a_3 = a_2 - 7\\a_3 = 8-7\\a_3 = 1$

Hence the first three terms ae 15, 8, 1...

This sequence forms an arithmetic progression with;

first term a = 15

common difference d = 8 - 15 = - -8 = -7

n is the number of terms = 660 (since we are looking for the sum of the first 660 terms)

Using the formula;

$S_n = \frac{n}{2}[2a + (n-1)d]\\$

Substitute the given values;

$S_{660} = \frac{660}{2}[2(15) + (660-1)(-7)]\\S_{660} = 330[30 + (659)(-7)]\\S_{660} = 330[30 -4613]\\S_{660} = 330[-4583]\\S_{660} = -1,512,390$

Hence the sum of the first 660 terms of the sequence is -1,512,390

6 0

3 years ago

Can you give me an example of an equation with a variable on both sides of the = that has infinitely many solutions. Please help

Vesna [10]

The most basic example would be x = x, because x only has to equal itself, it could be anything, creating an infinite amount of solutions.

3 0

3 years ago

Peanuts are sold $1.67 for one pound. A bag of peanuts weights 2.5 pounds. How much will you pay for that one bag?

Gekata [30.6K]

Sym 10 times u bumbaclart idiaat

7 0

3 years ago

A sample of marble has a volume of 6 cm3 and a density of 2.76 g/cm3. What is its mass?

Alenkasestr [34]

To solve for the mass of a substance is to simply get the product of volume and density, that is:

mass = density * volume

So calculating for mass:

mass = (2.76 g / cm^3) * 6 cm^3

3 0

3 years ago

Read 2 more answers

14. A right cone has a height of 14 in and a base diameter of 17 in.

Mars2501 [29]

Given:

The height of a right cone = 14 in

Base diameter = 17 in

To find:

The diagram of the cone and its lateral surface area.

Solution:

(a)

The diagram of a right cone with height 14 in and base diameter of 17 in is shown below.

Diagram is not to scale.

(b)

We know that lateral surface of the cone is

$A=\pi rl$

$A=\pi r\sqrt{r^2+h^2}$ ...(i)

Where, r is the base radius, h is vertical height and l is the slant height of the cone.

Base radius of the cone = $\dfrac{\text{Base diameter}}{2}$

$r=\dfrac{17}{2}$

$r=8.5$

Now,

Putting r=8.5, h=14 and π=3.14 in (i), we get

$A=(3.14)(8.5)\sqrt{(8.5)^2+(14)^2}$

$A=26.69\sqrt{72.25+196}$

$A=26.69\sqrt{268.25}$

$A=437.1379$

$A\approx 437$

Therefore, the lateral surface area of the cone is 437 sq. inches.

5 0

3 years ago