!!!!

larisa [96]

Answer:

For a polynomial of the form ax2+bx+c a x 2 + b x + c , rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅−2=−4 a ⋅ c = 2 ⋅ - 2 = - 4 and whose sum is b=−3 b = - 3 . Factor −3 - 3 out of −3x - 3 x .

Step-by-step explanation:

6 0

2 years ago

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Assume that f(x)=ln(1+x) is the given function and that Pn represents the nth Taylor Polynomial centered at x=0. Find the least

WINSTONCH [101]

Answer:

the least integer for n is 2

Step-by-step explanation:

We are given;

f(x) = ln(1+x)

centered at x=0

Pn(0.2)

Error < 0.01

We will use the format;

[[Max(f^(n+1) (c))]/(n + 1)!] × 0.2^(n+1) < 0.01

So;

f(x) = ln(1+x)

First derivative: f'(x) = 1/(x + 1) < 0! = 1

2nd derivative: f"(x) = -1/(x + 1)² < 1! = 1

3rd derivative: f"'(x) = 2/(x + 1)³ < 2! = 2

4th derivative: f""(x) = -6/(x + 1)⁴ < 3! = 6

This follows that;

Max|f^(n+1) (c)| < n!

Thus, error is;

(n!/(n + 1)!) × 0.2^(n + 1) < 0.01

This gives;

(1/(n + 1)) × 0.2^(n + 1) < 0.01

Let's try n = 1

(1/(1 + 1)) × 0.2^(1 + 1) = 0.02

This is greater than 0.01 and so it will not work.

Let's try n = 2

(1/(2 + 1)) × 0.2^(2 + 1) = 0.00267

This is less than 0.01.

So,the least integer for n is 2

7 0

3 years ago

Look at the graph below and answer the following.

bearhunter [10]

Answer:

Part 1) The graph has three (3) x-intercepts and has one (1) y-intercept

Part 2) The y-value of the minimum point is -3

Part 3) f(4)=3

Part 4) f(0)=3

Part 5) f(5)=1.5

Part 6) x=-6

Part 7) The horizontal line y=-1 intersects the graph three times

Part 8) The value of the function for f(6) is equal to zero

Part 9) The function is increasing on the interval (-6,-2) and (8,11) and the function is decreasing on the interval (2,8)

Part 10) The function is positive on the interval (-3,6) and (10,11) and is negative on the interval (-6,-3) and (6,10)

Step-by-step explanation:

Part 1) Find the number of x-intercepts and y-intercepts of the graph

we know that

The<u> x-intercepts</u> are the values of x when the value of y (the function) is equal to zero

Look at the graph

The graph has 3 x-intercepts

The x-intercepts are the points (-3,0), (6,0) and (10,0)

The<u> y-intercepts</u> are the values of y when the value of x is equal to zero

Look at the graph

The graph has 1 y-intercept

The y-intercept is the point (0,3)

Part 2) The y value of the minimum point on the graph is?

we know that

Look at the picture

The minimum point is (-6,-3)

therefore

The y-value of the minimum point is -3

Part 3) f(4) is equal to?

we know that

f(4) is the value of the function when the value of x is equal to 4

Look at the graph

For x=4

The value of the function is equal to y=3

therefore

f(4)=3

Part 4) f(0) is equal to?

we know that

f(0) is the value of the function when the value of x is equal to 0

Look at the graph

For x=0

The value of the function is equal to y=3

therefore

f(0)=3

Part 5) f(5) is equal to?

we know that

f(5) is the value of the function when the value of x is equal to 5

Look at the graph

For x=5

The value of the function is about y=1.5 (see the attached figure)

therefore

f(5)=1.5

Part 6) The value of x when f(x)= -3 is?

Look at the graph

we have the point (-6,-3)

when the value of f(x)=-3

the value of x is equal to x=-6

Part 7) The horizontal line y = -1 intersects the graph _____ times?

Look at the graph

The horizontal line y=-1 intersects the graph three times (see the attached figure)

Part 8) f(6) is positive or negative?

Look at the graph

we have the point (6,0)

For x=6

The value of the function is equal to zero

Part 9) Is the graph increasing or decreasing on the interval -6?

Look at the graph

The function is increasing on the interval (-6,-2) and (8,11) and the function is decreasing on the interval (2,8)

Part 10) Is the graph positive or negative on the interval 6

Look at the graph

The function is positive (f(x) > 0) on the interval (-3,6) and (10,11) and is negative (f(x) < 0) on the interval (-6,-3) and (6,10)

4 0

2 years ago

Decompose 5/15 and 8/12

AnnZ [28]

Answer:

:)

Step-by-step explanation:

5/15 divided by 5 is equal to 1/3 and

8/12 divided by 2 is 4/6 divided by 2 is 2/3

You have to divide the numerator with the same number that you divide the denominator with.

6 0

1 year ago

Zoya asked the students of her class their baseball scores and recorded the scores in the table shown below: Baseball Scores Sco

nlexa [21]

Answer:

4.06

Step-by-step explanation:

Given :

Scores Number of students

0 1

1 2

2 5

3 3

4 6

5 7

6 9

To Find: Mean

Solution:

Mean = $\frac{\text{Sum of all scores}}{\text{number of students}}$

Mean = $\frac{0 \times 1+1\times 2+2\times 5+3\times 3+4\times 6+5\times 7+6\times 9}{1+2+5+3+6+7+9}$

Mean = $\frac{134}{33}$

Mean = $4.06$

Hence, The Mean of baseball score is 4.06 .

4 0

2 years ago

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