Let C[infinity](R) be the vector space of all infinitely differentiable functions on R (i.e., functions which can be differentiated infinitely many times), and let D : C[infinity](R) → C[infinity](R) be the differentiation operator Df = f ‘ . Show that every λ ∈ R is an eigenvalue of D, and give a corresponding eigenvector

Answer:

Dilation of 3

Step-by-step explanation:

Note \(DE=2\) and \(D'E'=6\).

The scale factor is defined as the ratio of the length of the side of the image to the length of the corresponding side of the preimage.

So, the scale factor is \(\frac{6}{2}=3\).

Answer: x=2   DS=10   SE=10   DE=20

Step-by-step explanation:

\(7x-4=16-3x\\7x-4+3x=16-3x+3x\\10x-6=16\\10x-4+4=16+4\\10x=20\\\)

Divide the equation by 10:

\(x=2\)

Hence,

\(DS=(7)(2)-4\\DS=14-4\\DS=SE=10\\DE=DS+SE\\DE=10+10\\DE=20\)

Answer:

180° in a triangle

180 = (2x + 3) + (4x + 2) + (2x - 1)

180 = 8x + 4

180 - 4 = 176

176 = 8x

176/8 = x

X = 22

proof:

A = 2 X 22 + 3 = 47

B = 4 X 22 + 2 = 90

C = 2 X 22 - 1 = 43

47 + 90 + 43 = 180°

The population size at t = 6 hours is approximately 1349.9 individuals.

To solve this differential equation, let's denote the population at time t as P(t). We know that the growth rate is proportional to the current population, so we can write the differential equation as:

dP/dt = k * P

where k is the proportionality constant.

To solve the equation, we can separate variables and integrate both sides:

1/P dP = k dt

∫1/P dP = ∫k dt

ln|P| = kt + C

where C is the constant of integration.

To find the value of C, we can use the initial condition that the population starts with 1000 individuals at t = 0:

ln|1000| = 0 + C

C = ln|1000|

Substituting the value of C back into the equation, we have:

ln|P| = kt + ln|1000|

ln|P| - ln|1000| = kt

ln(P/1000) = kt

\(P/1000 = e^(kt)\\P = 1000 * e^(kt)\)

Now, if the growth rate is 0.05 per hour, we have k = 0.05. So the equation becomes:

P = 1000 * e^(0.05t)

To find the population size at t = 6 hours, we substitute t = 6 into the equation:

\(P(6) = 1000 * e^(0.05*6)\\P(6) ≈ 1000 * e^0.3\)

P(6) ≈ 1000 * 1.3499

P(6) ≈ 1349.9

The population size at t = 6 hours is approximately 1349.9 individuals.

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Complete question:

A population of bacteria starts with 1000 individuals and grows at a rate proportional to the current population. If the growth rate is 0.05 per hour, find the equation that models the population growth and determine the population size at t = 6 hours.

Answer:

e. 7.2 > 7

f. -7.2 < -7

Step-by-step explanation:

Refer to number line

Answer:

The correct option is;

B. P VP Jenna Todd Jenna Annie Jenna Luis Todd Luis Todd Annie  

Step-by-step explanation:

The candidates running for president of the school club = Jenna and Todd

The candidates running for vice president of the school club = Todd, Annie, and Luis

If Todd is elected president = Todd can't be elected vice president

The list of all the possible outcome is therefore;

P            \({}\)            VP

Jenna       \({}\)          Todd

Jenna       \({}\)          Annie

Jenna       \({}\)          Luis

Todd       \({}\)           Annie

Todd       \({}\)           Luis

The proportion for the problem is 28 cm by 24 cm

From the question, we have the following parameters that can be used in our computation:

Scale: 2 cm = 1 foot

Also, we have

Dimensions = 14 ft by 12 ft

using the above as a guide, we have the following:

Scale dimensions = 2 * 14 cm by 12 * 2 cm

Evaluate

Scale dimensions = 28 cm by 24 cm

Hence, the proportion is 28 cm by 24 cm

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Using basic geometry and area formula for calculation of length, Apply fencing on only 3 side , The answer is 109.54 feet.

A subfield of mathematics called geometry examines the dimensions, placements, angles, and sizes of objects.

A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.

Area of rectangle is:

A= l x b

area=750 square feet.

for attaining minimum area , these area must be fitted in square,

so, \(l = \sqrt {750}\)

=27.38 feet

since, one side is taken by barn, l should be extended 4 times, 2 on 1 side and 2 on sides each.

Total length of fence = 4 * 27.38

= 109.54 feet

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True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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The value of the given expression is -1.

Given is an expression 1/4 (-4/1) (3/5) (-5/6) (-2) we need to simplify it,

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

so,

1/4 (-4/1) (3/5) (-5/6) (-2)

= 1/4 × -4 × 3/5 × -5/6 × -2

= -1 × -1/2 × -2

= -1

Hence the value of the given expression is -1.

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Answer:

(1,8.5)

Step-by-step explanation:

x=(-1+3)÷2

=1

y=(9+8)÷2

=8.6

(1 , 8.5)

D - 16/1

Since the value of the rest is less than one, that means that it's a reduction but since D is more than one, it means that it's an enlargement.

Step-by-step explanation:

teyrucjq kfuq teyrucjq

Answer:

The answer is 7 plus ½ a number

Answer:

given,triangle EFG is congruent to triangle HIJ,THEIR corresponding sides are equal,

so, 10x=x+45

10x_x=45

or,9x=45

therefore , x=5

again,

3y = y+14

or, 3y_y=14

or, y=14/2

therefore the value of y is 7.

so the value of x is 5 and y is 7.

hope its helpful to uh...

10,000 records have 30 predictor variables, each with 5% of the values missing, resulting in 15,000 missing values. The predictive model drops any row with even a single missing value, so 5,000 records would be dropped from the analysis.

1. There are 30 predictor variables.

2. Each variable has 5% of the values missing.

3. 5% of 10,000 records = 500 records.

4. 30 variables x 500 records = 15,000 missing values.

5. 10,000 records - 15,000 missing values = 5,000 records dropped from the analysis.

The data set has 10,000 records and 30 predictor variables. Each variable has 5% of the values missing, so 500 records are missing for each variable. This results in 15,000 missing values spread randomly and independently throughout the data set. The analyst uses a predictive model that drops any row (record) with even a single missing value, so 5,000 records would be dropped from the analysis.

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I am sorry but i wont be able to help you with that question because it is too complex for me. perhaps you would like to ask again to another tutor or post it on brainly.com.

Answer:

∠QPS and ∠RSP

Step-by-step explanation:

Answer:

Explanation:

Given the function, g(x) below:

We evaluate g(x) for x=1,2 and 3:

We see that whenever x increases by 1, the value of g(x) triples.

Question

Farmer Jim keeps 12 hens in every cooper if farmer Jim has 20 coops

a) how many hens does she have ?

b) if every hens lays 9 eggs on Monday how many eggs will farmer Jim collect on Monday

Answer:

a) 240 hens

b) 2160 eggs

Step-by-step explanation:

a) Farmer Jim keeps 12 hens in every cooper if farmer Jim has 20 coops

Hence,

1 coop = 12 hens

20 coops = y hens

Cross Multiply

y hens = 20 coops × 12 hens/1 coop

y hens = 240 hens

Therefore Farmer Jim has 240 hens

b) We are told in question b that: if every hens lays 9 eggs on Monday how many eggs will farmer Jim collect on Monday?

From question a) we determine that the number of hens that Farmer Jim has:

240 hens

Hence,

1 hen = 9 eggs

240 hens = z eggs

z eggs = 240 hens × 9 eggs/1 hen

z eggs = 2160 eggs

Therefore, on Monday Farmer Jim will collect 2160 eggs

Answer: .17 m/h

Step-by-step explanation: One centimeter is .01 meters/one hundredth of a meter, so you just need to move the decimal two digits to the right to convert.

Answer:

245π = 770cm³

Step-by-step explanation:

so V=πr ²h

input the numbers

V=π x 7² x 5

Type into your calculator and use the pi symbol to get the exact number or type in 3.142.

You should get around 245π which is approximately 770cm³

Hope that helps :)

Answer:

219.8cu in

Step-by-step explanation:

7x3.14=21.98

21.98x10=219.8

Answer:

.21 cents

Step-by-step explanation:

To get .21 do 1.68 divided by 8

1.68 ÷ 8 = .21

Hope this helps ya!!

The ratio of the vertical change to the horizontal change between any two points on a line is called the slope of the line.

A ratio is a relationship between two or more numbers that shows how much bigger or smaller one value is compared to another. In mathematics, ratios are often used to compare quantities or amounts, such as the amount of money spent on two different items or the distance traveled over a certain period of time. The ratio of the vertical change to the horizontal change to any two points on a line is called the slope of the line.

This is a fundamental concept in geometry and algebra, and it is used to describe the steepness of a line. The slope is often denoted by the letter m, and it is calculated as follows:m = (y₂ - y₁) / (x₂ - x₁)Where (x₁, y₁) and (x₂, y₂) are two points on the line. The slope is positive if the line is increasing from left to right, negative if the line is decreasing from left to right, and zero if the line is horizontal.

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Answer:

All Factors of 340: 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170 and 340.

Prime Factors of 340: 2, 5, 17.

Prime Factorization of 340: 22 × 51 × 171

Sum of Factors of 340: 756.

Step-by-step explanation:

This question is incomplete because it lacks the picture of the graph. Find attached to the answer, the picture of the graph.

Question:

Which function does the graph represent?

a) f(x) = (x + 3)(x + 7)

b) f(x) = (x – 3)(x – 7)

c) f(x) = 3(x – 3)(x – 7)

d)f(x) = 11(x + 3)(x + 7)

Answer:

c) f(x) = 3(x – 3)(x – 7)

Step-by-step explanation:

The function of a graph or the the graph of a function is when

f(x) = y

From the attached graph, after reading it,

They are three specific points on the x - axis, where x = 3 and x = 7, x = 8

So, where x = 3 on the x axis, y =

f(3) = 0

where x = 7 on the x axis, y =

f(7) = 0

So, where x = 8 on the x axis, y =

f(8) = 15

Looking at the options in the question,

a) f(x) = (x + 3)(x + 7)

f(x) = y

where x= 3

f(3) = (3+3)(3+7)

= 60

where x= 7

f(7) = (7+3)(7+7)

= 140

where x= 8

f(8) = (8+3)(8+7)

= 165

This option is wrong

b) f(x) = (x – 3)(x – 7)

f(x) = y

where x= 3

f(3) = (3-3)(3-7)

= 0

where x= 7

f(7) = (7-3)(7-7)

= 0

where x= 8

f(8) = (8-3)(8-7)

= 5

This option is wrong.

c) f(x) = 3(x – 3)(x – 7)

f(x) = y

where x= 3

f(3) = 3(3-3)(3-7)

= 0

where x= 7

f(7) =3(7-3)(7-7)

= 0

where x= 8

f(8) = 3(8-3)(8-7)

= 3(5)(1)

= 15

This option is correct

d)f(x) = 11(x + 3)(x + 7)

f(x) = y

where x= 3

f(3) = 11(3+3)(3+7)

= 660

where x= 7

f(7) = 11(7+3)(7+7)

= 1540

where x= 8

f(8) = 11(8+3)(8+7)

= 1815

Therefore, function the graph represents is Option c) f(x) = 3(x – 3)(x – 7)

Answer: The answer is C. f(x)= 3(x-3)(x-7)

Step-by-step explanation: