The condition [tex]f^{\prime}(2)[/tex] = 0 to form a subspace of [tex]\mathbb{R}^{(0,3)}[/tex] is that f ∈ S is that otherwise, S wouldn't be closed under addition and thus would not be a subspace of [tex]\mathbb{R}^{(0,3)}[/tex].
What is additive identity?An identity element (like 0 in the collective of whole numbers under operation of addition) that leaves unaffected any element that it is added in a provided mathematical system.
Now, for the given question.
I'd just like to comment on the paragraph about intuition as well as the additive identity: That instinct is incorrect.
First, we could perhaps define a object that we need to confirm is a subspace of [tex]\mathbb{R}^{(0,3)}[/tex] in a more precise manner than the translation in which it is initially presented. We want to look at a set, S.
Where,
[tex]S=\left\{x, f \mid 0 < x < 3, f \in \mathbb{R}^{(0,3)} \wedge f^{\prime}(x)=0\right\}[/tex]
We are specifically tasked with having to prove the restriction just on derivative of f, which is best accomplished in the manner made reference.
The fact that S, as described above, describes a functional space explains why my initial intuition about problem is ultimately incorrect. I was hindering myself by viewing it solely as a geometric space.
As a result, I missed the fact that zero function (the additive identity in such a functional space) is indeed a natural member of S.
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The complete question is-
I'm working my way through Axler's "Linear Algebra Done Right", and I've run into a proposition that I don't understand. Namely:
The set of differentiable real-valued functions f on the interval (0, 3) such that [tex]f^{\prime}(2)[/tex] = b is a subspace of [tex]\mathbb{R}^{(0,3)}[/tex] if and only if b = 0.
My intution is that this has something to do with the fact that a subspace requires an additive identity, but that because the domain of the differentiable functions is open and exludes 0, we have to make some concessions (i.e. [tex]f^{\prime}(2)[/tex] = 0), though I'm unsure of how to work up a proof that backs this.
Why must [tex]f^{\prime}(2)[/tex] = 0 to form a subspace of [tex]\mathbb{R}^{(0,3)}[/tex]?
A road is 8/9 of a mile long. A crew needs to replace 4/5 of the road how long is the section that needs to be repaved
Answer:
4/45
Step-by-step explanation:
8 - 4
9 5
= 8 × 5 - 4 × 9
9 × 5 5 × 9
= 40 - 36
45 45
= 40 – 36
45
= 4
45
8/9 - 4/5
= 4/45
HELP PLS!!!!!!!!!!!!!!!!
Answer:
4x^3 (3)_/x + 10x^3 (3)_/x
Step-by-step explanation:
First lets solve the first term
When you multiply exponents you add them, so x^10 can be split into:
x^3 * x^3 * x^3 * x^1
We can then take it out.
4x^3 (3)_/x
Then for the other part we can also factor it.
2*2*2 is 8 so we can take that out and multiply it by 5 =10
You can keep x in there since you can factor it into smaller pieces.
The final answer you get when you add all of it together is :
4x^3 (3)_/x + 10x^3 (3)_/x
Manny took home a couple of his friends after soccer practice. he originally had 4 gallons of gas in his car. he used 1.05 gallons of gas to take one friend home and three tenths gallon to take the other friend home. how much gas did he have left in his car after taking both friends home? 1.04 gallons 2.95 gallons 3.70 gallons 2.65 gallons
Answer:
2.65 gallons
Step-by-step explanation:
He originally had 4 gallons and he used 1.05 gallons.
4 - 1.05 = 2.95
He then used another three-tenths to take another friend home.
Three-tenths is equal to 3/10 or 30/100 or 0.30
2.95 - 0.30 = 2.65 gallons
5. YOU BE THE TEACHER Your friend identifies
the terms and like terms in the expression
3x-5-2x + 9x. Is your friend correct?
Explain your reasoning.
SIMPLIFYING ALGEBRAIC EXPRESSIONS Simplify the
16. 12g + 9g
17. 11x 9-7
O
The correct form of the expression is 5(2x - 2)
How to solve the expression?It should be noted that the expression that is given is illustrated as:
3x-5-2x + 9x.
To solve this, collect the like terms
3x - 2x + 9x - 5
= 10x - 5
= 5(2x - 1)
The correct form of the expression is 5(2x - 1)
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which is the slope of the line y=-3x+2
Answer:
3
Step-by-step explanation:
y=mx+b
m is the slope
WILL CHOOSE THE BRAINLIEST ANSWER!!!
Answer:
A. 25°
Step-by-step explanation:
In triangle ABC:
<A + <B + <C = 180°
=> 45° + (2x - 15)° + 4x° = 180°
=> 6x° + 30° = 180°
=> 6x° = 150°
=> x° = 25°
Choose A.25°
Answer:
A. 25 degrees
x = 20
2(20) - 15 = 25 degrees
Help with math problems
In the given picture there is a graph and we have to find out is that graph is one to one or not.
It is a one to one graph.
In the graph there is line.
To know is the line is one to one or not we have to check 1st that the line is a function or not.
To check the line is function or not we have to do by vertical line test.
Graphically, the vertical line test is a way to determine if a line is a function or not.
To perform the vertical line test, we pass the vertical lines arrows the graph and if it does not intersect the graph more then one point it passes the vertical line then it can say as a function.
In the given figure1 we can see the vertical lines does not touch the line in the graph more then one point so it is a function.
Now, we know the line is a function so now we have to check if the line is one to one or not.
To check the line is one to one or not we have to do by horizontal line test.
Graphically, the horizontal line test is a way to determine if a line is a one to one or not.
To perform the horizontal line test, we pass the horizontal lines arrows the graph and if it does not intersect the graph more then one point it passes the horizontal line then it can say as a one to one function.
In the given figure2 we can see the horizontal lines does not touch the line in the graph more then one point so it is a one to one function.
Therefore, The graph is a one to one function.
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Simplify this expression.
2d + 1 + d-5
[?]d + []
Answer:
3d-4
Step-by-step Explanation:
2d+1+d-5 Combine like terms 2d and d together which is 3d. That leaves you with 1-5 which is -4. so then you end up with 3d-4 as your answer.
Before the break at swim-team practice, Nicole swam 1,200 yards. After the break, she swam 1,600 yards. What is the percent of increase in the number of yards Nicole swam? Round to the nearest tenth if necessary.
The percent of the increase in the number of yards Nicole swam will be 33.33%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Nicole swam 1,200 yards during the swim rookie minicamp before the break. She swam 1,600 yards after the break.
Then the percent of the increase in the number of yards Nicole swam will be
P = [(1600 - 1200) / 1200] x 100
P = (400 / 1200) x 100
P = 0.3333 x 100
P = 33.33%
The percent of the increase in the number of yards Nicole swam will be 33.33%.
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Help me solve these please
Answer:
See picture below
Step-by-step explanation:
Answer:
7. 2^-5= 1/2^5= 1/32
8. (4/5)^-3= (5/4)^3=125/64
9. 8^-4/8^-7=8^-4+(-7)=8^11=216
10. (1/3)^-2 x (1/3)^2=(1/3)^-2+2=(1/3)^0=1
Which is a correct representation of x + 5 using algebra tiles?
The correct representation of x + 5 using algebra tiles is one green rectangle box and one small yellow box.
What are algebra tiles?Algebra tiles are the tiles or square or rectangular boxes which are use to represent the polynomial expression whether of linear , monomial or quadratic.
There are three types of algebra tiles :
Small squares : Small squares are generally use to represent a constant value which is a letter or any symbol. Rectangles : Rectangles are use to represent a monomial or linear expression such as x ,y , z etc.Large squares : They are use to represent quadratic expressions such as x^2 , y^2 , z^2 etc.All of these tiles has different color to represent positive and negative value :
Square Type Positive color Negative Color
Small squares Yellow Red
Rectangles Green Red
Large Squares Blue Red
For the given question, Expression is x + 5
that means, there is one Green rectangle and one Yellow small square.
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Can someone please help mee (20 points + brainliest!!!)
Work out the difference between 88.1 and 2.81
16 ones 24 tens 1 hundred
The standard form for given values is 12416.
What are form of numbers?A number has two form . First is standard form and another is expended form of numbers.
What is standard form?It is a form in which we write number as a whole without describing the places for the numbers.
The numbers such as 456, 17817, 9009, 32 etc all are the standard form of the numbers.
What is Expended form?In the case of expended form we generally write number with its describe places of value or with the plus (+) symbol between them.
For example, 16 ones 24 tens 1 hundred is the expended form of numbers.
In the given question the form given is :
16 ones 24 tens 1 hundred
so, we have to place 16 at ones place , 24 at tens place and 1 at hunderedth place value .
Therefore, the standard form becomes : 12416.
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The complete question is:
Convert to standard form
16 ones 24 tens 1 hundred
Please help it’s argent!!
5 employees are working on Saturday and get their base pay $125 per day plus an additional $40. How much will the company pay their employees to work on Saturday?
Answer:
=($25×5)+($125×5)
=$125+$625
=$750
3. A local charity wants to purchase a classic 1975 Chevy Monte Carlo for use as a prize in a fundraiser.
They find the following eight prices in the paper
$18,000
$16,000
3090
$18,888
b. What is the range?
a. What is the best measure of central tendency to use to get a reasonable estimate for
the cost of the car? Explain.
ill in the missing numbers along the sides of the triangle so that it contains each of the numbers from through exactly once. furthermore, each side of the triangle should contain four numbers whose sum is .
Each side of the triangle should contain four numbers whose sum is 28.
3+5+9+11=28
3+10+8+7=28
11+6+9+7=28
The pain of numbers that can be used for A and B is [5,9] The pain of numbers that can be used for C and D is [10,8] and the pain of numbers that can be used for E and f is [6,4].
What are the 3 sides of a triangle?The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question; and its "adjacent" side is the one that faces it. We use special terminology to define the sides of right triangles.
We use special terminology to define the sides of right triangles.
The side opposite the right angle is always the hypotenuse of a right triangle. It is the longest side in a right triangle.
The opposing and neighboring sides are the other two sides. The labels on these sides relate to an angle.
One side is across from another at a particular angle.
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solids that can made by equilateral triangle
Answer:
the tetrahedron, octahedron and icosahedron
Answer:
tetrahedron, octahedron, icosahedron
SOMEONE PLEASE HELP ME I REALLY NEED HELP ON THIS
The volume of the square frustrum, the volume of the pyramid and the volume of the obelisc are 1018791.667 ft³, 22019.625 ft³ and 1040811.292 ft³, respectively.
How to determine the volume of the Washington Monument
In this problem we must determine the volume of a obelisc, which is equal to the sum of the volumes of a square frustrum and a pyramid with a square base. First, sum the volumes of the frustrum and the pyramid:
V' = (1 / 3) · 500 · (55² + 55 · 34.5 + 34.5²)
V' = 1018791.667 ft³
V'' = (1 / 3) · (34.5)² · 55.5
V'' = 22019.625 ft³
Second, calculate the volume of the obelisc:
V = V' + V''
V = 1018791.667 ft³ + 22019.625 ft³
V = 1040811.292 ft³
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Question 2(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Approximate -8+√√20 to the nearest tenth.
O 4.5
03.5
O-35
O-4.5
The approximation of -8 plus the square root of 20 is given by:
-3.5.
How a number is rounded to the nearest tenth?To round a number to the nearest tenth, it will have only one decimal digit, and the rule is as follows:
If the second decimal digit is less than 5, the first decimal digit remains constant.If the second decimal digit is of 5 or greater, one is added to the first decimal digit.The square root of 20 is given by:
sqrt(20) = 4.47.
7 > 5, hence, rounded to the nearest tenth:
sqrt(20) = 4.5.
Then:
-8 + 4.5 = -3.5.
Which is the approximation.
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x
-3
-2
-1
0
Intro
2
f(x)
-16
-1
2
-1
-1
Analyze the table of values for the continuous function,
f(x), to complete the statements.
A local maximum occurs over the interval
A local minimum occurs over the interval
4 of 10
Done
A local maximum occurs over the interval (-2,0).
A local minimum occurs over the interval (0,2).
If the graph of the function increases first and decreases after a particular point, then the function acquires a local maximum at that point.
Similarly, if the graph of the function decreases first and then increases after a point, then the function acquires a local minimum at that point.
Here the given x and f(x) values for the continuous function f(x) are:
x f(x)
-3 -16
-2 -1
-1 2
0 -1
1 -4
2 -1
As we can see by examining the table values, the function is increasing in the intervals (-3,2) and (-2,-1).The function acquires value f(x) = 2 at x = -1 and then it starts to decrease. So this value f(x) = 2 is the local maximum and is acquired on the interval (-2,0).
The graph is then decreasing from x = -1 to x = 1. The function has the value f(x) = -4 at x = 1. Then the function starts to increase from x = 1 to x = 2. So f(x) = -4 is the local minimum of the function and is acquired on the interval (0,2).
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The area of the parallelogram is 4 times the area of the triangle.
The perpendicular height of the parallelogram is h cm.
Find the value of h.
*HOMEWORK QUESTION*
Answer:
13
Step-by-step explanation:
Area of triangle = 0.5 × base × height
= 0.5 × 6 × 13
= 39
Area of parallelogram = 4 × Area of triangle
Note - Area of parallelogram = base × perpendicular height
Hence,
Base × perpendicular height = 4 × 39
12 × H = 156
H = 156 ÷ 12
= 13
Answer = 13
Answer:
h = 13 cm
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 6 and h = 13 , then
A = [tex]\frac{1}{2}[/tex] × 6 × 13 = 3 × 13 = 39 cm²
Then the area (A) of the parallelogram = 4 × 39 = 156 cm²
the area (A) of the parallelogram is calculated as
A = bh ( b is the base and h the height )
here b = 12 , then
12h = 156 ( divide both sides by 12 )
h = 13
Is Figure B a scale copy of figure A?
Yes, figure B is a scale copy of figure A.
As per the question statement and its reference diagram attached thereby, we are provided with two geometrical figures of same shape but different sizes.
We are required to determine if figure B is a scale copy of figure A or not.
To solve this question, we need to carefully compare the lengths of the corresponding sides from both the figures.
We can clearly see that, the dimension of every side of figure B is twice that of the corresponding side of Figure A, i.e.,
[tex](1*2)=2\\(2*2)=4\\(3*2)=6\\(4*2)=8[/tex]
Hence, it is proved that figure B is a scale copy of figure A.
Scale copy: In geometry, a scale copy of a figure is another figure having same shape, but the dimensions of all the sides of the scale copy are equal multiples of the dimensions of the corresponding sides of the original figure.To learn more about Scale Copy, click on the link below.
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Write a program that promptsthe user for their quarterly water bill for the last four quarters. the program should find and output their average monthly water bill. if the average bill exceeds $75, the output should include a message indicating that too much water is being used. if the average bill is at least $25 but no more than $75, the output should indicate that a typical amount of water is being used. finally, if the average bill is less than $25, the output should contain a message praising the user for conserving water. also show input validation for the first entry. you may have to apply all the programming constructs that you have learned so far, as needed, to complete this exercise. (decisions, loops, input validation). sample run 1: please input your water bill for quarter 1: 300 please input your water bill for quarter 2: 200 please input your water bill for quarter 3: 225 please input your water bill for quarter 4: 275 your average monthly bill is $83.33. you are using excessive amounts of water
calculate the total of the bills= 300+200+225+275 =1000
the average monthly bill= 1000/12 = 83.333
Total =0
for i in range(4):
bill = float(input("Enter bill for quarter " + str (i+1) + ": "))
total += bill
average = total / (4 * 3)
if average > 75:
print("Average monthly bill is $" + str(average) + ". Too much water is being used")
if 25 <= average < 75:
print("Average monthly bill is $" + str(average) + ". A typical amount of water is being used")
if average < 25:
print("Average monthly bill is $" + str(average) + ". Thank you for conserving water")
calculate the total of the bills= 300+200+225+275 =1000
the average monthly bill= 1000/12 = 83.333
Total =0
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The length of a rectangle is twice the width. The area of the rectangle is 90 square units. Note that you can divide the rectangle into squares. A. Which irrational number represents the length of each side of the square? B. Estimate the length and width of the triangle
Answer: A. [tex]3\sqrt{5}[/tex]
B. l=[tex]6\sqrt{5}[/tex], w=[tex]3\sqrt{5}[/tex]
Step-by-step explanation:
A. A=l*w
l=2w
A=2w*w
90=2w*w
w*w=45
w=[tex]\sqrt{45}[/tex]
w=[tex]\sqrt{9*5}[/tex]
w=[tex]3\sqrt{5}[/tex] ==> Square length and the rectangle width
B. 90=l*w
90=l*[tex]3\sqrt{5}[/tex]
30=l[tex]\sqrt{5}[/tex]
l=[tex]\frac{30}{\sqrt{5} }[/tex]
l=[tex]\frac{30\sqrt{5} }{5}[/tex]
l=[tex]6\sqrt{5}[/tex], w=[tex]3\sqrt{5}[/tex]
Please helpp
−5(−2/3)
Answer:
[tex]\frac{10}{3}[/tex] or 3.3333.....
Hope this helps.
Step-by-step explanation:
( negative ) * ( negative ) = ( positive )
5 * [tex]\frac{2}{3}[/tex] = [tex]\frac{5*2}{3}[/tex] = [tex]\frac{10}{3}[/tex]
Factor: x^2 - 169
please and thank you
Answer:
13,-13 are the factors
The steps are
x²-13²=(x+13)*(x-13)
so the factors are 13,-13
A random sample of 92 sophomores are asked whether they plan to attend Homecoming. Of these, 51 sophomores said they will attend. What is the margin of error at 90% confidence and its interpretation?
The margin of error at 90% confidence and its interpretation is 0.085. 90% confident that the true proportion of sophomores who will attend Homecoming is within 0.085 of the sample proportion.
The margin of error is defined as a term used in statistics to find the confidence interval. It is denoted by E.
Given, random sample of 92 .
The formula for margin of error is;
[tex]E = z(\sqrt{(p(1 - p)/n} )[/tex]
The parameters are given as;
Sample size; n = 92
Sample of success; x = 51
Sample proportion:
p = 51/92
= 0.554
z at 90% CL = 1.645
Thus;
[tex]E = 1.645(\sqrt{(0.554(1 - 0.554)/92} )[/tex]
[tex]E = 0.085[/tex]
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what is the value of arccos(-sqrt3/2)
the answer is 5pi/6
PLEASE HELP!!! Julie is helping her mom carry groceries. The bag she is carrying has everything they need to make spaghetti for dinner tonight. It has 450 grams of spaghetti, 750 grams of tomato sauce, and 0.5 kilograms of ground beef. How many kilograms does her bag of groceries weigh?
Answer:
1.7 kilograms
Step-by-step explanation:
750 + 450 + 0.5kg ( 1kg = 1000) so 0.5 would be 500g.
=1,700g (1.7kg) :)