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choli [55]
3 years ago
6

Calculate the average rate of change of f(x) = x2 - 1 x - 4 for 2 ≤ x ≤ 6.

Mathematics
2 answers:
hoa [83]3 years ago
8 0

Answer:

Hence, the average rate of change is:

\dfrac{97}{12}

Step-by-step explanation:

We are asked to calculate the average value of the function:

f(x)=x^2-\dfrac{1}{x}-4 in 2 ≤ x ≤ 6

The average rate of change of the function f(x) in the interval 2 ≤ x ≤ 6  is given as:

\dfrac{f(6)-f(2)}{6-2}\\\\=\dfrac{f(6)-f(2)}{4}

Now,

f(6)=36-\dfrac{1}{6}-4\\\\f(6)=32-\dfrac{1}{6}\\\\f(6)=\dfrac{191}{6}

f(2)=4-\dfrac{1}{2}-4\\\\\\f(2)=-\dfrac{1}{2}

Hence, the average rate of change is:

\dfrac{\dfrac{191}{6}-\dfrac{-1}{2}}{4}\\\\=\dfrac{194}{6\times 4}\\\\=\dfrac{97}{12}

Hence, the average rate of change is:

\dfrac{97}{12}

rusak2 [61]3 years ago
5 0

Answer:

Step-by-step explanation:

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A cuboid with dimensions 45 cm by 16 cm by 12 cm is cut to form smaller cubes of
LenKa [72]

Answer:

<u>135 cubes</u>

Step-by-step explanation:

Volume of cuboid :

  • 45 x 16 x 12
  • 720 x 12
  • 8,640 cm³

Volume of a small cube :

  • (4)³
  • 64 cm³

Number of cubes :

  • n = 8,640/64
  • n = <u>135 cubes</u>
4 0
2 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
Paula's house is assessed at $213,000, and her property tax rate is 2.9%. How
NARA [144]

Answer:A

Step-by-step explanation:

She is taxed at a rate of 2.9%, so each year she is taxed 213000 * 2.9% . calculating this, we find that every year, she must pay 6177 in taxes. However, we need the amount in a month, so we divide by 12, to get 6177/12= 514.75, or A

3 0
3 years ago
Read 2 more answers
13 add 2x equals 3 what does x equal??
Anastasy [175]
13 + 2x = 3
subtract 13 from both sides of the equation
2x = -10
divide by 2 on both sides 
x = -5
5 0
3 years ago
Read 2 more answers
Solve the problem. Make sure your answer is in simplest form. 3/16 x 4/21 = ?
Irina18 [472]

Answer:

\frac{1}{28}

Step-by-step explanation:

The result is given by means of some algebraic handling:

\frac{3}{16}\times \frac{4}{21}

\frac{12}{336} - Multiplication of rationals.

\frac{6}{168} - Dividing each term by 2.

\frac{3}{84} - Dividing each term by 2.

\frac{1}{28} - Dividing each term by 3.

8 0
3 years ago
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