Which number sentence is true?

liberstina [14]

A triangular prisms' formula is: lwh = Length * Width * Height
substitute the variables
L = 21in
W = 15in
H = 17in
21*15*17
= 5,355in

The volume of the figure is: 5,355in^3

7 0

3 years ago

We have N cars on a circular one-way road; they have the same make, same model, same year and the same fuel economy. The total a

Natasha2012 [34]

Answer: Satisfied for n=1, n=k and n=k+1

Step-by-step explanation:

The induction procedure involves two steps

First is

Basic Step

Here we consider that for the value n=1, there is one car and it will always make the full circle.

Induction Step

Since basic step is satisfied for n=1

Now we do it for n=k+1

Now according to the statement a car makes full circle by taking gas from other cars as it passes them. This means there are cars that are there to provide fuel to the car. So we have a car that can be eliminated i.e. it gives it fuels to other car to make full circle so it is always there.

Now ,go through the statement again that the original car gets past the other car and take the gas from it to eliminate it. So now cars remain k instead of k+1 as it's fuel has been taken. Now the car that has taken the fuel can make the full circle. The gas is enough to make a circle now.

So by induction we can find a car that satisfies k+1 induction so for k number of cars, we can also find a car that makes a full circle.

8 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each verbal description of a sequen

galben [10]

Answer:

I think the question is wrong so, I will try and explain with some right questions

Step-by-step explanation:

We are give 6 sequences to analyse

1. an = 3 · (4)n - 1

2. an = 4 · (2)n - 1

3. an = 2 · (3)n - 1

4. an = 4 + 2(n - 1)

5. an = 2 + 3(n - 1)

6. an = 3 + 4(n - 1)

1. This is the correct sequence

an=3•(4)^(n-1)

If this is an

Let know an+1, the next term

an+1=3•(4)^(n+1-1)

an+1=3•(4)^n

There fore

Common ratio an+1/an

r= 3•(4)^n/3•(4)^n-1

r= (4)^(n-n+1)

r=4^1

r= 4, then the common ratio is 4

Then

First term is when n=1

an=3•(4)^(n-1)

a1=3•(4)^(1-1)

a1=3•(4)^0=3.4^0

a1=3

The first term is 3 and the common ratio is 4, it is a G.P

2. This is the correct sequence

an=4•(2)^(n-1)

Therefore, let find an+1

an+1=4•(2)^(n+1-1)

an+1= 4•2ⁿ

Common ratio=an+1/an

r=4•2ⁿ/4•(2)^(n-1)

r=2^(n-n+1)

r=2¹=2

Then the common ratio is 2,

The first term is when n =1

an=4•(2)^(n-1)

a1=4•(2)^(1-1)

a1=4•(2)^0

a1=4

It is geometric progression with first term 4 and common ratio 2.

3. This is the correct sequence

an=2•(3)^(n-1)

Therefore, let find an+1

an+1=2•(3)^(n+1-1)

an+1= 2•3ⁿ

Common ratio=an+1/an

r=2•3ⁿ/2•(3)^(n-1)

r=3^(n-n+1)

r=3¹=3

Then the common ratio is 3,

The first term is when n =1

an=2•(3)^(n-1)

a1=2•(3)^(1-1)

a1=2•(3)^0

a1=2

It is geometric progression with first term 2 and common ratio 3.

4. I think this correct sequence so we will use it.

an = 4 + 2(n - 1)

Let find an+1

an+1= 4+2(n+1-1)

an+1= 4+2n

This is not GP

Let find common difference(d) which is an+1 - an

d=an+1-an

d=4+2n-(4+2(n-1))

d=4+2n-4-2(n-1)

d=4+2n-4-2n+2

d=2.

The common difference is 2

Now, the first term is when n=1

an=4+2(n-1)

a1=4+2(1-1)

a1=4+2(0)

a1=4

This is an arithmetic progression of common difference 2 and first term 4.

5. I think this correct sequence so we will use it.

an = 2 + 3(n - 1)

Let find an+1

an+1= 2+3(n+1-1)

an+1= 2+3n

This is not GP

Let find common difference(d) which is an+1 - an

d=an+1-an

d=2+3n-(2+3(n-1))

d=2+3n-2-3(n-1)

d=2+3n-2-3n+3

d=3.

The common difference is 3

Now, the first term is when n=1

an=2+3(n-1)

a1=2+3(1-1)

a1=2+3(0)

a1=2

This is an arithmetic progression of common difference 3 and first term 2.

6. I think this correct sequence so we will use it.

an = 3 + 4(n - 1)

Let find an+1

an+1= 3+4(n+1-1)

an+1= 3+4n

This is not GP

Let find common difference(d) which is an+1 - an

d=an+1-an

d=3+4n-(3+4(n-1))

d=3+4n-3-4(n-1)

d=3+4n-3-4n+4

d=4.

The common difference is 4

Now, the first term is when n=1

an=3+4(n-1)

a1=3+4(1-1)

a1=3+4(0)

a1=3

This is an arithmetic progression of common difference 4 and first term 3.

5 0

3 years ago

Prove that the sum of all natural numbers is -1/12.

ankoles [38]

This is not true. The infinite series

$\displaystyle\sum_{n=1}^\infty n$

converges if and only if the sequence of its partial sums converges. The $k$ -th partial sum is

$\displaystyle\sum_{n=1}^kn=\frac{k(k+1)}2$

but clearly this diverges as $k$ gets arbitrarily large.

5 0

3 years ago

Our school has 6 Grade and 786 students. What is the average number of students in each grade

Harrizon [31]

Answer:

The average number of students in each grade is 131 students

Step-by-step explanation:

In order to get this answer, you will divide 786 by 6 because 768 is the number of students in your school and 6 is the number of grades. Once you divided 786 and 6, you should get 131. Hope this helps! :)

<h3>CloutAnswers</h3>

3 0

3 years ago

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Which number sentence is true?​

Which number sentence is true?