Write a formula for function h in terms of function f.

a) The infinite series in sigma notation is described by this expression:

[tex]y = \sum \limits_{i=1}^{\infty} \frac{1}{i\cdot (i+2)}[/tex]     (1)

b) The explicit formula for the n-th partial sum is represented by the following expression:

[tex]y = \frac{1}{i\cdot (i+2)}[/tex], i ∈ [tex]\mathbb{N}[/tex]     (2)

An infinite series is monotonous when it is bounded, that is, when the limit of the infinite series exists. In this case, we have an evidence of monotony in the denominators of the terms of the given series. In two consecutive terms, the latter always have a denominator greater than the former.

a) The series in sigma notation is now described below:

[tex]y = \sum \limits_{i=1}^{\infty} \frac{1}{i\cdot (i+2)}[/tex]

b) The explicit formula for the n-th partial sum is defined by the expression within the sum, which is now presented below:

[tex]y = \frac{1}{i\cdot (i+2)}[/tex], i ∈ [tex]\mathbb{N}[/tex]  

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Answer:

1,804

Step-by-step explanation:

106 - 60 = 44

44/2 = 22

60 + 22 = 82

82*22 = 1,804

Step-by-step explanation:

when you are on that level of math that you get this type of question - this is totally easy.

we get the extreme point(s) of a function by finding the zeros of the first derivative of the function.

f'(x) = 4x - 8

so,

0 = 4x - 8

8 = 4x

x = 2

to determine whether it is a minimum or a maximum, we have 2 choices :

the quick way for a quadratic (parabola) equation by looking at the factor of x² : is it >0, then the parabola opens up upwards, and the extreme point is therefore a minimum. if it is <0, then it opens downward, and the extreme point is a maximum.

in our case : 2 is larger than 0, therefore minimum.

or the formal way for any type of function : create the second derivative and see, if it is >0 (minimum) or <0 (maximum) for the extreme x.

in our case

f''(x) = 4

this is larger than 0 for all x, so the extreme point is a minimum.

AnswerI dont know

Step-by-step explanation:

how do you expect me to k

I'm pretty sure it's water bro

Answer:

2/3 or .66 repeated

Step-by-step explanation:

1 1/3= 1.33

1.33 + .66..7 is 2

Answer:

[tex]\huge\boxed{\sf x = \frac{2}{3}}[/tex]

Step-by-step explanation:

Let the number be x

Given condition:

[tex]\displaystyle 1 \frac{1}{3} +x=2\\\\Subtract\ 1\frac{1}{3} \ to \ both \ sides\\\\x = 2-1\frac{1}{3} \\\\x = \frac{2 \times 3}{1 \times 3} - \frac{4}{3} \\\\x = \frac{6}{3} - \frac{4}{3} \\\\x=\frac{6-4}{3} \\\\\boxed{x = \frac{2}{3}} \\\\\rule[225]{225}{2}[/tex]

Answer:

x= -4/3

Step-by-step explanation:

Steps

7x +8 = 4X + 4

Subtract 8 from both sides

7x+ 8-8= 4x + 4-8

Simplify

7x=4x-4

Subtract 4x from both sides

7x-4x=4x-4-4x

Simplify

3X = -4

Divide both sides by 3

3X/3 = -4/3

Simplify

x= -4/3

Answer:

Step-by-step explanation:

Solution

7x+8=4x+4                          Subtract 4x from both sides

7x - 4x + 8 = 4                     Combine

3x + 8 = 4                            Subtract 8 from both sides

3x + 8 - 8 = 4 - 8                 Combine

3x = - 4                                Divide by 3

3x/3 = -4/3  

Answer: x = -4/3

Answer:

-3k + 10

Step-by-step explanation:

you have to combine -8 and 2 because they are like terms, but since -8 is being subtracted from -3k the minus sign and the negative sign basically combine to make a positive sign so it would make it -3k + 8 + 2 which gives you -3k + 10

Answer: Heyaa! ~

Your Answer is... − 3k+10

Step-by-step explanation:

Hopefully this helps you! ~

Answer:

a

Step-by-step explanation:

f(x)-g(x)=2x square-3x+6-(3x square +4x-8)

2x square-3x+6-3x square-4x+8

-x square-7x+14

Answer:

15

Step-by-step explanation:

15-6=9 so a-6=9

Answer:

17

Step-by-step explanation:

17-6=9 (to double check your work and make sure it's right you do the opposite [9+6=17] )

Answer:

y ≤ 4

Step-by-step explanation:

Solving :

Answer:

C. -2(9 + 32n)

Step-by-step explanation:

-2(9 + 32n)

= -2*9 - 2*32n

= (-18) - 64n.

Answer:

360

Step-by-step explanation:

from the survey:

32/80 - 0.4 love math

0.4*900

= 360

Answer:

<6 and <16 are alternate exterior angles.

Answer:

42 with 4 extra ounces

Step-by-step explanation:

since we know we can't do 256/6

256, when downed, is 252

252/6 = 42

the most she can make is 42 with 4 more ounces leftover

Based on the amounts Julia paid and the percentage rates, the missing amounts are:

Julia's social security taxes were:

= 6.2% x 2,000

= $124.

Medicare amount:

= 1.45% x 2,000

= $29

Federal income tax:

= 260 / 2,000 x 100%

= 13%

State income tax:

= 120 / 2,000 x 100%

= 6%

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Answer:

75% because the ratio is 1:4 so the probability of the next being minestrone is high.

Answer:

6

Step-by-step explanation:

#1

As this is a scatter plot so we have to draw a suitable line then have to find the equation of line inorder to fulfill our requirements.

#2

Put temperature as 21(x)

#3

0 is the y intercept or the initial amount of sales

It's denoting to the fact that there were initially 0 boxes

Answer:

14.

Step-by-step explanation:

42 = 2 8 3 * 7

Largest prime factor = 7

28 = 2 * 2 * 7

Smallest prime factor = 2

Answer = 2*7 = 14.

Answer:

x= -30

Step-by-step explanation:

Step-by-step explanation:

so, you did not pay attention to even the simplest of facts in the class ?

the radius is always half of the diameter, or (in other words), the diameter is always twice the radius.

that is really all there is to this.

please tell me you need actual help to divide something by 2 ?

you need me to be your calculator ? posting the questing and then typing the results in from here is more effort than just to use your own calculator.

1. 12.6/2 = 6.3 cm

2. 31.08/2 = 15.54 ft

3. (10 7/11)/2 = (110/11 + 7/11)/2 = 117/11 / 2 =

= 117/22 = 5 7/22 cm

(you noticed something ?)

4. sqrt(54)/2 = sqrt (54/4) = sqrt(27/2) = sqrt(13.5) =

= 3.674234614... m

5. 10.125/2 = (10 1/8)/2 = 5 1/16 = 5.0625 in

(see again under 3.)

Answer:

6 sqrt 2 , 3pi / 4

Step-by-step explanation:

Find magnitude   sqrt ( (-6)^2 + 6^2 ) = sqrt (72) = 6 sqrt 2

Then the since the x and y are = magnitude and quadrant II

 it is   3 pi/4

6 sqrt (2) , 3pi/ 4

Answer:

D) He has a 67% chance of getting a 1, 3, 5, or 6.

The period of the given function is  2π/3, the phase shift is 4, and the vertical shift is 6 units.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a trigonometric function:

y = csc[3(x+ 4)]+ 6

Every each revolution of 2π the function repeats the same value for every x.

The period of the original function is 2π

For the given function plug 2π

y = csc[3(x+ 4)+2π]+ 6

y = csc[3(x+ 2π/3+4)]+ 6

The period of the function will be 2π/3

From the function, the phase shift = 4

And vertical shift = 6

Thus, the period of the given function is  2π/3, the phase shift is 4, and the vertical shift is 6 units.

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Option 3

Step-by-step explanation:

Answer:

  200 miles

Step-by-step explanation:

Each inch represents 50 miles, so 4 times 1 inch will represent 4 times 50 miles.

  4(1 in) ⇔ 4(50 mi)

  4 in ⇔ 200 mi

It is about 200 miles from Chelsea to New York City according to the map.

Answer:

First number = 20

Second number = 12

Explanation:

Let the 1st number be x

Let the 2nd number be y

=====================

Condition 1

[tex]\sf \rightarrow x + 7 + \dfrac{y}{6} = 29[/tex]

[tex]\rightarrow \sf x=-\dfrac{y}{6}+22[/tex]

=====================

Condition 2

[tex]\rightarrow \sf 2y - (x - 5) = 9[/tex]

[tex]\rightarrow \sf x = 2y -4[/tex]

=====================

Substitute equations

[tex]\rightarrow \sf -\dfrac{y}{6}+22 = 2y-4[/tex]

[tex]\rightarrow \sf y=12[/tex]

=====================

Find value of 1st number

[tex]\rightarrow \sf x = 2y - 4[/tex]

[tex]\sf \rightarrow x = 2(12) - 4[/tex]

[tex]\rightarrow \sf x = 20[/tex]