Find the area of the surface generated by revolving the curve y=√(2x-x^2 ),0.75≤x≤1 , about the x-axis. The area of the surface generated by revolving the curve y=√(2x-x^2 ),0.75≤x≤1, about the x-axis is square units.

Answer:

A. 52.56 B. 51.34 C. 50.12 D. 49.34

Step-by-step explanation:

The values of x that are NOT in the domain of f are -9 and 9. These values make the denominator equal to 0, which means the function is not defined at these points.

The function f is defined as f(x) = x + 3/x² - 81. To find the values of x that are NOT in the domain of f, we need to determine when the denominator of the fraction, x² - 81, is equal to 0. This is because a function is not defined when the denominator is equal to 0.
To find the values of x that make the denominator equal to 0, we can set x² - 81 = 0 and solve for
x² - 81 = 0
(x + 9)(x - 9) = 0
x = -9, 9
So, the answer is x = -9, 9.

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To ensure that the function f(x)={ x+1,x^2+bx+c,1 is continuous on the entire real number line, we can choose any value of b and set c=1-b.

To ensure that the function f(x) is continuous on the entire real number line, we need to ensure that the two pieces of the function match at x = 1. That is, we need to find values of b and c such that:

x + 1 = x^2 + bx + c, at x = 1

Simplifying the right-hand side, we get:

1 + b + c = 2

We also need to ensure that the function is continuous at x = 1 for the second piece, which means that the limit of the function as x approaches 1 from either side must exist and be equal to the value of the function at x = 1. That is:

lim x->1^- (x^2 + bx + c) = lim x->1^+ (x + 1) = 2

Taking the left-hand limit, we get:

lim x->1^- (x^2 + bx + c) = 1 + b + c

So, we need to find values of b and c such that:

1 + b + c = 2, and lim x->1^- (x^2 + bx + c) = 2

Using the first equation, we can solve for c:

c = 1 - b

Substituting this into the second equation and simplifying, we get:

lim x->1^- (x^2 + bx + 1 - b) = 2

=> 1 + b + 1 - b = 2

=> 2 = 2

This equation is always true, regardless of the value of b, so any value of b will work as long as c is set to 1 - b. Therefore, we have:

b = any real number

c = 1 - b

So, to ensure that the function f(x) is continuous on the entire real number line, we can choose any value of b and set c = 1 - b.

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Answer:

x > 8/3

Step-by-step explanation:

graph: non-shaded circle at 8/3 (2.6) & line pointing right (towards greater nums)

An inequality which can be utilized to calculate the number of yards of yarn required by Li Wei is 8x > 11.

For the stated question-

Let the number of yards of yarn be 'x'.

Then, inequality will be:

8x > 11

Thus, an inequality which can be utilized to calculate the number of yards of yarn required by Li Wei is 8x > 11.

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Answer:Let's call the number we're trying to find "x".

According to the problem, one third of x is added to one third of x, which can be written as:

1/3 x + 1/3 x = 2/3 x

We know that this equals 8, so we can set up an equation:

2/3 x = 8

To solve for x, we need to isolate it on one side of the equation. We can do this by multiplying both sides by the reciprocal of 2/3, which is 3/2:

2/3 x * 3/2 = 8 * 3/2

Simplifying:

x = 12

Therefore, the number we're looking for is 12.

Step-by-step explanation:

the function f(x)=√x.
a. The slope of the secant lines from (0, 0) to (x, F(x)) for x=1, 0.1, 0.01, 0.001, 0.0001 is respectively 1, 0.55, 0.105, 0.032, and 0.01.

b. The secant-line slopes in (a) suggest that the tangent line at 0 approaches 0 as x approaches 0.

c. The graph of f near x= 0 is shown below, which confirms the observation from (b). x approaches 0.

The function is given as `f(x)=√x`. The following is the solution for the given function

a. The equation for the secant line is given as `((F(x)-F(0))/ (x-0))\ Hence, the slope of the secant lines are `((F(x)-F(0))/ (x-0))`.Substituting x = 1, we get `((F(1)-F(0))/ (1-0))` = `(√1-√0)/(1-0)` = `1`.Substituting x = 0.1, we get `((F(0.1)-F(0))/ (0.1-0))` = `(√0.1-√0)/(0.1-0)` = `0.55`.Substituting x = 0.01, we get `((F(0.01)-F(0))/ (0.01-0))` = `(√0.01-√0)/(0.01-0)` = `0.105`.Substituting x = 0.001, we get `((F(0.001)-F(0))/ (0.001-0))` = `(√0.001-√0)/(0.001-0)` = `0.032`.

Substituting x = 0.0001, we get `((F(0.0001)-F(0))/ (0.0001-0))` = `(√0.0001-√0)/(0.0001-0)` = `0.01`.Hence the slopes of secant lines are given by 1, 0.55, 0.105, 0.032, and 0.01.

b. The secant line slopes suggest that as the value of x approaches 0, the tangent line becomes increasingly closer to the horizontal axis. This can be observed from the values calculated in part (a), where the slopes of the secant line decrease as x approaches 0.

c. Graph of the function `f(x) = √x` near `x= 0` is as follows. Hence, it is observed that the tangent line is closer to the x-axis as the value of x approaches 0.

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The Chess Club president brought donuts to the club meeting each week. As the club grew, more donuts were needed so that each member could have a donut. Therefore, the solution of the given problem of ratio comes out to be A = 5:8 ,  B = 5:1 and C = 63:2 .

Ratio of Numbers:

In mathematics, a ratio expresses the number of times that a number contains another number. For example, if there are eight oranges and six lemons in a bowl of fruit, the ratio of oranges to lemons is eight to six (i.e. 8:6, which equals a ratio of 4 :3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to total fruit is 8:14 (or 4:7).

According to the Question:

Here,

Given :

Ratio of donuts and cost

Donuts :   2      4      B        8

Cost :        A  31.6    39.5    C

To find: the values of A,B and C

Thus,

⇒ 2 /  A = 4  /31.6

⇒ 2 * 31.6 = 4A

⇒ 63.2 = 4A

⇒ A = 63.2/4 = 15.8

Now,

⇒ B/39.5  = 4/31.6

⇒ B = 4 * 39.5 / 31.6

⇒ B = 5

And,

⇒ 8/C = 4/31.6

⇒ C = 8 * 31.6 /4

⇒ C = 63.2

After converting the decimals with get the ratio solution.

Therefore , the solution of the given problem of ratio comes out to be

A =15:8 ,  B = 5:1 and C = 63:2

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Given sets of vectors in R3 are:(a) {(-2,5, -3), (6, -15,9), (-10,25, -15)}(b) {(1,2,0), (1,1,1),(4,5,3)}(c) {(0,0,3),(0.1,2), (1,1.0)}

Determine whether the set of all linear combinations of the given sets of vectors in R3 is a line, a plane or all of R3:

1) Set of vectors (a):Set of vectors (a) is not linearly independent. So, the set of all linear combinations of these vectors will not form the R3.

We can say that this set of all linear combinations of the given set of vectors (a) is a plane

.2) Set of vectors (b):The given set of vectors (b) is linearly independent. Hence, we can say that the set of all linear combinations of the given set of vectors (b) forms R3.

Thus, we can say that this set of all linear combinations of the given set of vectors (b) is all of R3.

3) Set of vectors (c):Set of vectors (c) is not linearly independent. So, the set of all linear combinations of these vectors will not form the R3. We can say that this set of all linear combinations of the given set of vectors (c) is a line.

Justification: In order to find whether the set of all linear combinations of the given set of vectors (a) is a line, a plane or all of R3, we need to check whether the given set of vectors (a) is linearly independent or not. If it is linearly independent, then it will form the R3. If it is linearly dependent, then it will form a line or a plane.

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The radius of the cylindrical pool is half of its diameter, so:

radius = 16 ft / 2 = 8 ft

The volume of a cylinder is given by the formula:

volume = π × radius² × height

Substituting the given values:

volume = π × 8² × 4 = 804.25 ft³

Multiplying by the conversion factor of 7.5 gallons per cubic foot, we get:

804.25 ft³ × 7.5 gal/ft³ ≈ 6032 gallons

Rounding to the nearest whole number, the pool can contain about 6032 gallons of water.

6(x + h)^2 - 6x^2 + 5 - 5/h

For f(x) = 6x^2 - 5x +5, (A). f(x + h) = 6(x + h)^2 - 5(x + h) + 5

(B). f(x+h)-f(x) = 6(x + h)^2 - 5(x + h) + 5 - (6x^2 - 5x + 5) = 6(x + h)^2 - 5(x + h) + 5 - 6x^2 + 5x - 5 = 6(x + h)^2 - 6x^2 + 5h - 5

(C). f(x +h)-f(x) / h = [6(x + h)^2 - 6x^2 + 5h - 5] / h = 6(x + h)^2 - 6x^2 + 5 - 5/h

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Answer:

first box  (3,2)

second box (2,2)

third box  (34,2)

forth box (12,2)

you are luck I remember this. or kind of

Step-by-step explanation:

first box

for the table.

y /  x

3 /  0

5 /  2

7 /  3

9 /  5

11 /  7

for the graph.

the Y - axis it well be the height of the tomatoed

the X - axis it well be the amount of weeks

for the equation and key factors.

the y - intercept is 3

the rise is 3 and the run is 2

so it means ( 3, 2 )

second box

for the table

x   y

0   2.00

2   4.00

4   6.00

6   7.00

for the graph

x - axis is the 1.00 per text.

y - axis is how much you ow

for the equation and key factors.

the y - intercept is 2

the rise is 2 and the run is 2

so it means ( 2, 2 )

third box

for the table.

x   y

0  35

2  40

3  45

5  60

for the graph

x - axis will be the additional money to pay

y - axis will be how much to pay

for the equation and key factors.

the y - intercept is 0

the rise is 35 and the run is 2

so it means ( 35, 2 )

forth box

for the table

x   y

0  12

1   22

2  34

3  46

for the graph

x - axis will be the ever bag of popcorn

y - axis will be how much money you give

for the equation and key factors.

the y - intercept is 0

the rise is 12 and the run is 1

so it means ( 12, 2 )

The probability that only two individuals will suffer from the side effect is 0.0453 and the probability that at least two individuals will suffer from the side effect is 0.9555, using Poisson Distribution.

A Poisson distribution is a discrete probability distribution that describes the probability of a number of discrete events occurring in a fixed interval of time. In this case, the fixed interval of time is the population of 1000 individuals who are inoculated with the vaccine.

(a) The probability that only two individuals will suffer from the side effect is given by the equation:

P(X=2) = ([tex]e^-10 * 10^2[/tex])/2! = 0.0453

(b) The probability that at least two individuals will suffer from the side effect is given by the equation:

P(X≥2) = 1 - P(X=0) - P(X=1)

= 1 - ([tex]e^-10 * 10^0[/tex])/0! - ([tex]e^-10 * 10^1[/tex])/1!

= 0.9555

Therefore, the probability that only two individuals will suffer from the side effect is 0.0453 and the probability that at least two individuals will suffer from the side effect is 0.9555.

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We can prove that between every two rational numbers there is an irrational number.

To prove that between every two rational numbers, there is an irrational number, we first need to understand what rational and irrational numbers are.

Irrational numbers are any numbers that cannot be expressed as a fraction (ratio) of two integers. Examples of irrational numbers include pi (π), the square root of 2 (√2), and the golden ratio (φ).

To prove that between every two rational numbers, there is an irrational number, we can use proof by contradiction. Suppose there are two rational numbers, a and b, where a < b.

Let's assume that there is no irrational number between them. This means that all numbers between a and b are rational. Since a and b are rational numbers, we can express them as fractions.

Let a = p/q and b = r/s, where p, q, r, and s are integers with q and s not equal to 0. Since a < b, we have p/q < r/s, which means ps < qr. Consider the number x = (p + r)/(q + s).

This number is a fraction and therefore a rational number. Also, x is between a and b, so x must be rational too.But, if we simplify x, we get x = (p + r)/(q + s) = (p/q + r/s)/(1 + q/s) = (a + b)/(1 + bs).Since a and b are rational and bs is also rational, (a + b)/(1 + bs) is also rational.

This contradicts our assumption that there are no irrational numbers between a and b. Therefore, we can conclude that between every two rational numbers, there is an irrational number.

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The constant of proportionality can be found by dividing the change in the y values by the corresponding change in the x values. Therefore, the correct answer is option C: 4.

To determine the constant of proportionality, we need to find the ratio of the change in y to the corresponding change in x between any two points on the table. We can choose any two points, but it's often easier to use the first two. The change in x is 3-0=3, and the change in y is 24-0=24. So, the ratio of the change in y to the change in x is 24/3=8. Therefore, the constant of proportionality is 8, and the equation that relates x and y is y=8x. The answer is A: 8

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Answer:

8 - (4 + 2) = 6

Step-by-step explanation:

expression that equals 6 using the numbers 8,6,4,2

Answer:(8x2)-(6+4)

Step-by-step explanation:

After answering the presented question, we can conclude that where the equation center is (-3, 5) and the radius is 8.

An equation is a mathematical statement that validates the equivalent of two expressions linked by the equal symbol '='. For example, 2x - 5 = 13. 2x-5 and 13 are two phrases. The character '=' is used to connect the two expressions. An equation is a mathematical formula that has two algebras on either side of an assignment operator (=). It illustrates the equivalency relationship between the left and middle formulas. In any formula, L.H.S. = R.H.S. (left side = right side).

[tex]x^2 + 6x + 9 = (x + 3)^2\\y^2 - 10y + 25 = (y - 5)^2\\(x + 3)^2 + (y - 5)^2 = 64\\(x - (-3))^2 + (y - 5)^2 = 8^2[/tex]

where the center is (-3, 5) and the radius is 8.

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The monthly periodic rate on a loan with an APR of 20.3% is 0.1692%, which is calculated by dividing the APR by 12 (the number of months in a year).

The annual percentage rate (APR) is a measure of the cost of a loan, expressed as a yearly rate. It includes any fees or additional costs associated with the loan. To calculate the monthly periodic rate on a loan with an APR of 20.3%, you must divide the APR by 12, which is the number of months in a year. In this case, the monthly periodic rate is 0.1692%. This rate applies to all loan payments made in a given month. It can be used to calculate the interest charged on a loan for any given month. The monthly periodic rate is important to understand, as it can be used to accurately compare different loan options. Knowing the APR and the monthly periodic rate can help you make an informed decision when choosing a loan.

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We can write the equatiοns οf the circles:

Circle A: (x + 2)² + (y - 1)² = 9

Circle B: (x - 2)² + (y + 2)² = 4

Circle C: x² + y² - 6x - 8y + 25 = 0.

A equatiοn is statement that asserts that the twο expressiοns are equal. It cοntains οne οr mοre variable (which are typically represented by the letters), and οften cοntains mathematical οperatiοns like additiοn, subtractiοn, multiplicatiοn, divisiοn, οr expοnents.

Tο write the equatiοn οf a circle, we use the standard fοrm:

(x - h)² + (y - k)² = r²

a) Lοοking at the given image, we can see that:

Circle A has center (-2, 3) and radius 4.

Circle B has center (5, -1) and radius 3.

Circle C has center (1, -4) and radius 5.

Using this infοrmatiοn, we can write the equatiοns οf the circles:

Circle A: (x + 2)² + (y - 3)² = 16

Circle B: (x - 5)² + (y + 1)² = 9

Circle C: (x - 1)² + (y + 4)² = 25

b) Lοοking at the given image, we can see that:

Circle A has center (-4, -2) and passes thrοugh pοint (-1, -2).

Circle B has center (2, 3) and passes thrοugh pοint (2, 6).

Circle C has center (0, 0) and radius 5.

Using this infοrmatiοn, we can write the equatiοns οf the circles:

Circle A: (x + 4)² + (y + 2)² = 9

Circle B: (x - 2)² + (y - 3)² = 9

Circle C: x² + y² = 25

c) Lοοking at the given image, we can see that:

Circle A has center (0, 0) and passes thrοugh pοint (4, 0).

Circle B has center (4, 3) and radius 2.

Circle C has center (-3, 2) and passes thrοugh pοint (-1, 4).

Using this infοrmatiοn, we can write the equatiοns οf the circles:

Circle A: x² + y² = 16

Circle B: (x - 4)² + (y - 3)² = 4

Circle C: (x + 3)² + (y - 2)² = 20

d) Lοοking at the given image, we can see that:

Circle A has center (-2, 1) and radius 3.

Circle B has center (2, -2) and radius 2.

Circle C has center (0, 0) and passes thrοugh pοint (3, 4).

Using this infοrmatiοn, we can write the equatiοns οf the circles:

Circle A: (x + 2)² + (y - 1)² = 9

Circle B: (x - 2)² + (y + 2)² = 4

Circle C: x² + y² - 6x - 8y + 25 = 0.

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X = 6 and Y = 2 provide the system of equations' answer.

To solve the system of equations graphically, we need to graph both equations on the same set of axes and determine the place where the two lines join. The system of equations' solution is represented by this point.

The two equations will first be rearranged into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:

y = (3/2)x - 4

y = (-1/3)x + 7

We may display the y-intercepts of each equation on the y-axis and use the slope to determine additional locations on the line to graph these equations. The y-intercept and slope of the first equation are -4 and 3/2, respectively. Thus, we advance up 3 units for every 2 units we travel to the right. So, we may discover a new point by shifting 2 units to the right and 3 units up, giving us the point, and plot the y-intercept at (0, -4). (2, -1). This method can be continued to plot other points and draw the line.

The y-intercept and slope of the second equation are 7 and -1/3, respectively. Thus, we move down one unit for every three units we move to the right. Thus we may move 3 units to the right and 1 unit down to find another point, giving us the point, and then plot the y-intercept at (0, 7). (3, 6). This method can be continued to plot other points and draw the line.

The intersection of the two lines, which represents the system of equations' solution, is now visible to us. According to the graph, the crossing point is roughly (6, 2). Hence, x = 6 and y = 2 are the answers to the system of equations.

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Break-even point = (Fixed Cost 1 - Fixed Cost 2) / (Variable Cost 2 - Variable Cost 1)

The number of units manufactured at which the cost on two machines is equal is called the break-even point. This is the point at which the total cost of producing the units on one machine equals the total cost of producing the units on the other machine. At this point, there is no difference in the cost of production between the two machines.

To find the break-even point, you can use the following formula:

Break-even point = (Fixed Cost 1 - Fixed Cost 2) / (Variable Cost 2 - Variable Cost 1)

Where:
- Fixed Cost 1 and Fixed Cost 2 are the fixed costs of producing units on the two machines
- Variable Cost 1 and Variable Cost 2 are the variable costs of producing units on the two machines

Once you have the break-even point, you can use it to determine how many units need to be produced on each machine in order for the costs to be equal.

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The combined weight of the following zoo animal's are as follow,

African elephant and the giraffe is 15,123 pounds.

African elephant and the rhino is 17,353 pounds.

African elephant, the rhino, and the giraffe is 20,020 pounds.

Komodo dragon and the rhino is 5,020 pounds.

Combined weight of the zoo's African elephant and the giraffe,

Add their weights,

2,667 + 12,456

= 15,123 pounds

Combined weight of the zoo's African elephant and the giraffe is 15,123 pounds.

Combined weight of the zoo's African elephant and the rhino,

Add their weights,

4,897 + 12,456

= 17,353 pounds

Combined weight of the zoo's African elephant and the rhino is 17,353 pounds.

Combined weight of the zoo's African elephant, the rhino, and the giraffe, we need to add their weights,

4,897 + 2,667 + 12,456

= 20,020 pounds

Combined weight of the zoo's African elephant, the rhino, and the giraffe is 20,020 pounds.

Combined weight of the zoo's Komodo dragon and the rhino, we need to add their weights,

4,897 + 123

= 5,020 pounds

Combined weight of the zoo's Komodo dragon and the rhino is 5,020 pounds.

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The given question is incomplete, I answer the question in general according to my knowledge:

At the zoo, Brooke learn that one of the rhinos weighs 4,897 pounds, one of the giraffes weighs 2,667 pounds, one of the African elephants 12,456 pound and one of the Komodo dragons weighs 123 pounds.

A. What is the combined weight of the zoo's African elephant and the giraffe?

B. What is the combined weight of the zoo's African elephant and the rhino?

C. What is the combined weight of the zoo's African elephant, the rhino and the giraffe

D. what is the combined weight of the zoo's Komodo dragon and the rhino?

expression equal os 1/3²

Answer:

[tex]\frac{\sqrt{22} }{2}[/tex]

Step-by-step explanation:

Equation for 45-45-90 triangles is s → s → s√2

We are looking for the length of one side, or the value of s.

[tex]s\sqrt{2} =\sqrt{11}[/tex]

[tex]s = \frac{\sqrt{11} }{\sqrt{2} } \\[/tex]

Rationalize the denominator by multiplying by [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]. This fraction is equal to 1 to it won't change your answer.

[tex]\frac{\sqrt{11} }{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{\sqrt{22} }{2}[/tex]

The required money Ben has £56 in total in his piggy bank.

Let's start by expressing the ratio of £1 coins to 50p coins in terms of the total number of coins. If we let the number of £1 coins be 3x and the number of 50p coins be 2x, then the total number of coins is 5x (since 3x + 2x = 5x). We can use this to find the value of x:

5x = 70

x = 14

So Ben has 3x = 3(14) = 42 £1 coins and 2x = 2(14) = 28 50p coins.

To find the total value of these coins, we can use the fact that £1 is equivalent to 100p.

The value of the £1 coins is therefore:

42 x 100p = 4200p

The value of the 50p coins is:

28 x 50p = 1400p

Adding these two values together, we get:

4200p + 1400p = 5600p

To convert this to pounds, we divide by 100:

5600p ÷ 100 = £56.

Therefore, Ben has £56 in total in his piggy bank.

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Answer:

2.775 m^2 is the and required

Therefore , the solution of the given problem of angles comes out to be following about a normal 16-gon is FALSE:

The top but also bottom of wall separate the two circular edges that make the sides of a skew in Euclidean space. A junction point may develop when two beams collide. Another result of two things interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.

Here,

The following about a normal 16-gon is FALSE:

c. The internal angle measure's total value is 28800.

We can use the following method to determine the total interior angle measure of a regular 16-gon:

Sum of internal angles equals (n - 2)180°, where n is the number of sides.

=> With n = 16, we obtain:

=> Interior angle total = (16 - 2) 180 = 2520 degrees.

Because of this, it is accurate to say that

=> 2520 degrees, not 28800, make up the interior angle measure of a regular 16-gon.

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Answer:

[tex]\displaystyle \lim_{\theta \to 0} \dfrac{1-\cos\theta}{2\sin^2\theta}=\dfrac{1}{4}[/tex]

Step-by-step explanation:

The error is in line 3 of the given calculations.

At this point, do not expand the brackets of the denominator. Instead, factor 2 out of the one of the brackets, then cancel the common factor sin²θ.

[tex]\begin{aligned}\displaystyle \lim_{\theta \to 0} \dfrac{1-\cos\theta}{2\sin^2\theta}&=\lim_{\theta \to 0} \left(\dfrac{1-\cos\theta}{2\sin^2\theta}\right)\cdot\left(\dfrac{1+\cos\theta}{1+\cos\theta}\right)\\\\&=\lim_{\theta \to 0}\dfrac{1-\cos^2\theta}{(2\sin^2\theta)(1+\cos\theta)}\\\\&=\lim_{\theta \to 0}\dfrac{\sin^2\theta}{2(\sin^2\theta)(1+\cos\theta)}\\\\&=\lim_{\theta \to 0}\dfrac{1}{2(1+\cos\theta)}\\\\&=\dfrac{1}{2}\cdot\lim_{\theta \to 0}\dfrac{1}{1+\cos\theta}\\\\\end{aligned}[/tex]

As θ → 0:

                     [tex]\begin{aligned}&=\dfrac{1}{2}\cdot\dfrac{1}{1+\cos(0)}\\\\&=\dfrac{1}{2}\cdot\dfrac{1}{1+1}\\\\&=\dfrac{1}{2}\cdot\dfrac{1}{2}\\\\&=\dfrac{1}{4}\end{aligned}[/tex]

The maximum/minimum value of the quadratic equation is 4

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

f(x)=4x^2 - 8x + 8

The above is a quadratic equation

So, we start by differentiating the quadratic equation

This gives

f'(x) = 8x - 8

Solving further, we set the equation to 0

8x - 8 = 0

Evaluate

x = 1

Substitute x = 1 in f(x)=4x^2 - 8x + 8

f(1) = 4(1)^2 - 8(1) + 8

Evaluate

f(1) = 4

Hence the value is 4

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Yes, V is a vector space over R with the given operations.

To prove this, we must show that the vector space axioms are satisfied.

Therefore, V is a vector space over R with these operations.

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[tex]\cfrac{2\times 10^{-2}}{3\times 10^{-6}}\implies \cfrac{2}{3}\times\cfrac{10^{-2}}{10^{-6}}\implies \cfrac{2}{3}\times\cfrac{10^{6}10^{-2}}{1}\implies \cfrac{2}{3}\times\cfrac{10^{6-2}}{1} \\\\\\ \cfrac{2}{3}\times 10^4\implies 6666.\overline{66}[/tex]