let [a; b] be a non-degenerate closed interval in r, and let f : [a; b] ! r. for ant x 2 [a; b] and any t 2 [a; b] s.t. t 6

Answers

Answer 1

According to the given data the non - degenerated closed interval in r is calculated as [tex]\int\limits^t_s[/tex]f(t) - f(s).

What is the degenerated interval?

Any set that only contains one real number is known as a degenerate interval (i.e., an interval of the form [a,a]).  an interval is measured in terms of numbers. An interval is any integer that falls between two specific numbers. This range encompasses all real numbers between those two. Real numbers can be any number anyone can think of. A degenerate interval is any set that contains only one real number (i.e., an interval of the form [a, a]). The empty set is included in this definition by some authors. A suitable interval is one that is either empty or degenerate and has an infinite number of elements.

According to the given data:

f(x[tex]_r[/tex]) - f(x[tex]_r[/tex]₋₁)  = F' (e[tex]_r[/tex])(x[tex]_r[/tex] - x[tex]_r[/tex]₋₁)

By summating the equation it becomes.

f(t) - f(s) [tex]\int\limits^t_s[/tex] f < = f(t) - f(s) --------->

[tex]\int\limits^t_s[/tex] ts < = f(t) - f(s)  ------------->2

From 1 and 2

[tex]\int\limits^t_-s < ={f(t) - f(s) < = \int\limits^t_d {f}[/tex]

So, it finally becomes

[tex]\int\limits^t_s[/tex]f < = f(t) - f(s)

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Related Questions

Graph the function h(x)=-3/x by completing the table of values and plotting points.How does the graph compare to its parent function, f(x)=1/x? Describe any change for each of the following

Answers

Using translation concepts, the graph of h(x) = -3/x is given at the end of the answer. Compared to the parent function, it was vertically stretched by a factor of 3 and reflected over the x-axis.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the parent and translated functions are given, respectively, by:

f(x) = 1/x.h(x) = -3/x.

The translations are described as follows:

Multiplication by a negative number, hence it was reflected over the x-axis.Multiplication by a number with absolute value of 3, hence the function was vertically stretched by a factor of 3.

The graph of h(x) is given at the end of the answer, containing points such as:

(-3,1).(-1,3).(1,-3).(3,-1).

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Evaluate the expression for the given values.
m² +7 n if m=4 and n=-2

Answers

Answer: -82

Step-by-step explanation: Substitute the values  then do order of operations

I have looked from answer sheet but i still didn’t get it…

Answers

Answer:

Xyz E number

Step-by-step explanation:

I think Xyz is right

Answer:

  A.  AB = xyzx

Step-by-step explanation:

You want AB when A = BC, B = x, and C = yz.

Substitution

You can evaluate the unknown expression by making substitutions until you can't anymore.

  AB = (BC)(B) . . . . . . . . substitute BC for A

  AB = ((x)(yz))(x) . . . . . . substitute x for B (2 places), yz for C

  AB = xyzx . . . . . . . . . . remove the unnecessary parentheses

Please help due today

Answers

The correct answer should be D

What is the fewest number of intersection points that two planes can have?

Answers

Answer: 4 points

Step-by-step explanation:

The minimum number of points needed to define two distinct planes is 4 points. Two distinct planes can be defined by 4 points under the conditions that the two distinct planes intersect at a line, and two points exist on that line that are shared between the planes.

Answer:

One line of intersection (three points of intersection)

Step-by-step explanation:

When two planes intersect, they don't form points of intersection, but they form a line of intersection.

From equation of a line,

[tex]{ \tt{ax + by + cz = 0}}[/tex]

x, y, z are points of intersection

A customer wants to buy 0.3 pounds of mulch that cost $7.30 per pound. if the customer has a coupon for $0.50 off the total cost, how much will they pay for the mulch?

Answers

Answer:  The customer will pay 1.69$ for the mulch.

Step-by-step explanation:

7.30 = 1 Pound

0.3 = 3/10

3/10 x 7.30 or 3/10 of 7.30 = 2.19

2.19

2.19 = without coupon

1.69 = with coupon.

The total with 50 cents off is 1.69$.

xy = 4
y = 2x + 2

Solve linear systems by substitution

Answers

Answer:

Step-by-step explanation:

8+(-7)^2-(7∙-2+1)
help. please
I know the answer is 70 but just show me how you get 70????

Answers

The simplified form of the expression 8 + (-7)² - (7 × (-2) + 1 ) is 70.

What is the simplified form of the expression?

Given the expression in the question;

8 + (-7)² - (7 × (-2) + 1 )

Simplify each term, raise -7 to the power 2

8 + (-7)² - (7 × (-2) + 1 )

8 + 49 - (7 × (-2) + 1 )

Multiply 7 by -2

8 + 49 - ( -14 + 1 )

Add -14 and 1

8 + 49 - ( -13)

Remove parenthesis by multiplying -1 by -13

8 + 49 + 13

Now, simplify by adding the number

8 + 49 + 13

57 + 13

70

Therefore, the simplified form of the expression 8 + (-7)² - (7 × (-2) + 1 ) is 70.

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Need help asap my test is done in 5 minutes

Answers

Hello,

[tex] \frac{8 {}^{5} }{8 {}^{ - 9} } = 8 {}^{5 - ( - 9)} = 8 {}^{5 + 9} = 8 {}^{14} [/tex]

Brosss pleaseee help me

Answers

Answer:

Below.

Step-by-step explanation:

a. True - it states that 4 is an element of Set P.

b False - 5 is an element of set Q .

   5 ∈ Q.

c. P ∩ Q = Ф True - This says that there are no common elements in P and Q   which is true.  Ф is the 'empty set'.

d. True: n(P) = 4 means there are 4 elements in P.

e. True: there are 4 elements in P and in S.

   S can be written as {3, 4, 5, 6} - that is the integers which are greater      than 2 and less than or equal to 6. The Z means the set of integers.

Sarah bought a drink for $4 and bought 8 candy bars. She spent a total of 44 dollars. How much did each candy bar cost?

Answers

Answer: $5 for each candy bar.

Step-by-step explanation: Sarah bought a drink for $4 so, $44-$4=$40(leftover), now she bought 8 candy bars for $40:8=$5 (each candy bar cost)

how do you solve the equation 3(9/4 + 1/4y)-5y=11

Answers

Step-by-step explanation:

Hope that helps!!

(-4,-11) coordinates over the x axis

Answers

The plotting of (-4,-11) coordinates is given below in the graph .

In mathematics, a graph can be defined as a graphical representation or chart that systematically represents data or values. A point on a graph often represents a relationship between two or more things. In mathematics, graph theory is the study of graphs. A graph is a mathematical construct used to model pairwise relationships between objects. In this context, a graph consists of vertices (also called nodes or points)  connected by edges (also called links or lines).

We have given a coordinate (-4,-11) which means that x - coordinate is -4 and y- coordinate is -11 .

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The complete question is mention below :

Plot (-4,-11) coordinates over the x -axis and y-axis .

What is the total area of this figure (I am in middle school and a 7th grader just for notes)

Answers

Answer:12?

Step-by-step explanation:

A=L x W

Answer:

the total area is 20

Step-by-step explanation:

next time you can just count the boxes that's how I answer these types of questions.

Today is Amanda's birthday. She is 6 years old. How old is Amanda in months?

Answers

Answer:

72 months

Step-by-step explanation:

6 x 12 = 72

HELPP PLSSSSSSSSSS i would really appreciate it

Answers

Applying exponential properties, we have that the solution to the given expression is:

[tex]-\frac{125}{343}[/tex]

How do we proceed when a fraction is elevated to the exponent?

When a fraction is elevated to the exponent, we apply the exponent to both the numerator and the denominator.

In this problem, we have that:

The numerator is of 5, hence 5³ = 125.The denominator is of 7, hence 7³ = 343.

Negative base with odd exponent, hence the solution is negative and given as follows:

[tex]-\frac{125}{343}[/tex]

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A triangle with vertices A(1,1), B(3,4), C(6,3) is rotated counterclockwise about the origin 90°. What are the coordinates of the vertices of the new triangle?]

Answers

The coordinates of the vertices of the new triangle are A'(-1,1) ,B'(-4,3), C'(-3,6)

Rotation means the circular movement over the object around the center.

Rotation can be done in both directions like clockwise as well as counter clockwise It requires rotation implies negative magnitude A counter clockwise turns has a positive magnitude

Vertices of triangle = A(1,1) , B(3,4), C(6,3)

Triangle is rotated counterclockwise about the origin 90°.

In counterclockwise rotation (x,y) becomes (-y,x)

Then

the new coordinates of triangle are A', B', C'

A(1,1) = A'(-1,1)

B(3,4) = B'(-4,3)

C(6,3) = C'(-3,6)

The coordinates of the vertices of the new triangle are A'(-1,1) ,B'(-4,3), C'(-3,6)

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The sum of 2 integers is 7 and the sum of their squares is 37 what is the integers

Answers

Answer:

[tex]1[/tex] and [tex]6[/tex].

Step-by-step explanation:

Let [tex]x[/tex] denote one of the integers. Since the two integers add up to [tex]7[/tex], the other integer would be [tex](7 - x)[/tex].

The sum of the squares of these integers is [tex]37[/tex]. In other words:

[tex]x^{2} + (7 - x)^{2} = 37[/tex].

Expand [tex](7 - x)^{2}[/tex] using binomial expansion. Simplify and rewrite this equation and solve for [tex]x[/tex].

[tex]2\, x^{2} - 14\, x + 12 = 0[/tex].

[tex]x^{2} - 7\, x + 6 = 0[/tex].

Using the quadratic formula or factorization, [tex]x = 1[/tex] or [tex]x = 6[/tex]. Thus, the two integers are [tex]1[/tex] and [tex]6[/tex].

41. The Boca Grande Causeway in Florida is about
14 times as long as the Golden Gate Bridge
in San Francisco. The Golden Gate Bridge is
about 9,000 feet long. About how long is the
Boca Grande Causeway?

Answers

The length of the  Boca Grand Causeway is  126,000 feet

What is the length of the Boca Grand Causeway?

Multiplication is the continual addition of two or more numbers of equal sizes. The value gotten after multiplication is the product. Multiplication is one of the basic mathematical operations. The sign used to denote multiplication is x. Other basic mathematical operations include addition, subtraction and division.

Length of the Boca Grand Causeway = length of the golden gate bridge x 14

9,000 x 14 = 126,000 feet

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what is the answer to 34^5+6%7=

Answers

Answer:

ik what you ment

this is your answer 45,435,439.87

Step-by-step explanation:

The Answer is 45435430

-8 You burn 6 grams of carbon in plenty of air: C(s) + O₂(g) →→→ CO₂ (g) a What volume of gas will form (in dm³ at rtp)? b What volume of oxygen will be used up?


Answers

    a) Gas has a volume of 12 liters.

    b) 12 liters of oxygen gas will be consumed during the reaction.

Step-by-step explanation:

Moles of Substances:

We measure the quantity of atoms and molecules in moles, which is equal to 6.022 ×10²³, Avogadro's number, because they are too small to be counted or weighed individually. A substance's atomic mass is multiplied by Avogadro's number to get its mass in grams.

Here, Half a mole of carbon is equal to six grams of carbon. since 12 grams make up one mole of carbon. Since carbon dioxide has the chemical formula CO2, when a mole of carbon is fully combusted, it will result in the production of a mole of carbon dioxide gas.

a) Half a mole of gas has a volume of 12 liters because one mole of gas at RTP consumes 24 liters.

b) Due to the fact that each oxygen molecule contains two oxygen atoms and each carbon dioxide molecule contains two oxygen atoms, 12 liters of oxygen gas will be consumed during the reaction.

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How do I write A number is equal to twice the sum of the same answer and ten write as an equation that matches the verbal sentence

Answers

The number that fits in the given situation is -20.

What exactly are equations?An equation, in its most basic form, is a mathematical statement that shows that multiple mathematical expressions are equal.For example, 3x + 5 = 14 is an equation in which 3x + 5 and 14 are two expressions detached by a 'equal' sign.

Now,

Let us suppose the number is x.

The sum of the same number and ten will be written as x + 10.

As a result, the next condition is twice the sum, which can be written as:

2 × (x + 10)

As a result of the condition, we can write the equation as:

x= 2 × ( x + 10 ) or 2x + 20 = x

Solve for x: x = 2x + 20

2x + 20 = x

Taking 20 off both sides:

2x + 20 - 20 = x - 20 2x = x- 20 2x - x = -20 x  = -20

Therefore, the number that fits in the given situation is -20.

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how to solve 3x-2
…………..

Answers

First you set the equation to zero 3x-2=0 then decide both sides by three which cancels 3 out and leaves you with 2/3 and you divide that which gives you 0.6

PLease help me on this

Answers

Answer:

C. [tex]2^{3} x3^{2}[/tex]

Step-by-step explanation:

[tex]2^{3} x3^{2}[/tex]

[tex]2^{3} =8[/tex]

[tex]=8x[/tex]·[tex]3x^{2}[/tex]

[tex]3^{2} =9[/tex]

[tex]=8x[/tex]·[tex]9[/tex]


Then multiply 8 · 9 = 72


[tex]=72[/tex]


hopefully this helps you !

laura obtained the plans to create a chair. the seat of the chair calls for six pieces that are 1'10 1/2". what total length will she need if she is planning on making four chairs?

Answers

The total length will she need if she is planning on making four chairs is 42 inches.

How to calculate the value?

It should be noted that the chair calls for six pieces that are 10 1/2" , therefore, the total length will she need if she is planning on making four chairs will be:

= 10 1/2 × 4

= 10.5 × 4

= 42 inches.

The total length is 42 inches.

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Complete question

laura obtained the plans to create a chair. the seat of the chair calls for six pieces that are 10 1/2". what total length will she need if she is planning on making four chairs?

If you have piano lessons every 7 days and tuba lessons s every 3 days, how many days before you have them together

Answers

21 days before I had both the lessons together.

For the occurrence of two events at the same time we will find the least common multiple.

If I have piano lessons on every 7th day and tuba lessons on every 3rd day,

Least common multiple of 3 and 7 will be,

Multiples of 3 = 1 × 3

Multiples of 7 = 1 × 7

Least common multiple (LCM) of 3 and 7 = 3 × 7

                                                                   = 21

Therefore, 21 days before I had both the lessons together.

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a test shows that 10 out of 100 gadgets are defective. in a random sample of two gadgets are chosen the probability that both are defective is

Answers

The probability of selecting both defective gadgets out of 100 gadgets is 1/110, which is calculated using the basic concepts of probability theory.

What is a random experiment?

An experiment that is repeated several times and produces more than one possible outcome is called as the random experiment. It contains a well-defined set of values which constitutes a sample space. Eg: Rolling a die, tossing a coin etc.

Calculation of the probability of selecting both gadgets as defective

The total amount of gadgets = 100

Number of defective gadgets = 10

The probability of selecting a defective gadget is 10 / 100 or 1 / 10

Now, the total number of gadgets and defective gadgets are decreased by 1

So, the probability of selecting another gadget as defective is 9 / 99 or 1 / 11

P(E) = P(when two selected gadgets are defective) = 1 / 10 x 1 / 11

P(E) = 1 / 110

Hence, the probability of selecting both defective gadgets is 1/110.

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Rick's chore list shows that he is responsible for washing the dishes after dinner this week. Last night, he washed 4 plates in 2 minutes. Tonight, his grandparents are coming to dinner, and Rick will wash 6 plates.
If he washes plates at the same rate, how many minutes will it take Rick to wash the plates tonight?

Answers

Answer:

3 minutes

Step-by-step explanation:

there are many ways to answer this question you can on it later but im going to write the easiest here

4 plates is 2 minutes

find how many minutes for one plate and times it by 6

2 ÷ 4 = 1/2 minutes or 30 seconds

therefore;

1/2 × 6 = 3 minutes

please rate brainliest if helps

Write the slope-intercept equation of a line that passes through the points (-2,5) and (6,-4)

Answers

The slope-intercept equation of a line that passes through the points (-2,5) and (6,-4) is [tex]y=-\frac{9}{8}x+\frac{11}{4}[/tex]

We know that the slope-intercept form of the line is y =  mx + c, where m is the slope of the line and c is the y-intercept of the line.

For given question we have been given two points (-2,5) and (6,-4)

We need to find the slope-intercept equation of a line that passes through the points (-2,5) and (6,-4).

Using two-point form the equation of the line is,

[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex]

Let (x1, y1) = (-2,5) and (x2, y2) = (6,-4)

So, the equation of the line is,

[tex]\frac{y-5}{-4-5} =\frac{x-(-2)}{6-(-2)}\\\\ \frac{y-5}{-9} =\frac{x+2}{6+2}\\\\\frac{y-5}{-9} =\frac{x+2}{8}\\\\ 8(y-5)=-9(x+2)\\\\8y-40=-9x-18\\\\8y=-9x-18+40\\\\8y=-9x+22\\\\y=-\frac{9}{8}x+\frac{11}{4}[/tex]

above equation is in the slope-intercept form.

Therefore, the slope-intercept equation of a line that passes through the points (-2,5) and (6,-4) is [tex]y=-\frac{9}{8}x+\frac{11}{4}[/tex]

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PLEASE HELP

later Paul drew 2 solid figures and 5 plain figures. in his drawing what was the ratio of solid figures to plain figures

Answers

Answer:

2:5

Step-by-step explanation:

WHichever one they ask you for first is the first number in the ratio. Meaning 2 solid figures are 2:1 plain figures.

Answer: 2:5 have a good day
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