Question 6: Integration (12 marks) a. Which of the following definitions best describes the result of integrating a positive function f(x)? A The value of f(x) when == 0 B. The area between the curve of f(x) and the x-axis. C. The difference between the minimum of f(x) and the maximum of f(x). D. The gradient of f () at the point where x = 0. (1 mark) b. Which of the following is the general antiderivative of the function f(x) = 23+8x?? A 10x4 + 24x2 B. 2x° (x2 + 4) C. 2x6 + 8x4 D. 32° +2x4+C (1 mark) Which of the following statements is true for an odd function 9(2) ? 1 C. A. B. В S 0-2500 S = g(x) = 0 5 (2) = 0 Soo-a C. D (1 mark) d. By using the substitution 4x + 2 = u, show that the expression below is true. 1 +1 dx +C (4x + 2) 1600 + 8 (5 marks) e. Find the volume of the solid obtained when the area bounded by the curves below is rotated about the x-axis. Use the result shown in part (e) to assist you. Sa+gads 1 O x 1 = 0 (4 marks)

Answer:

Step-by-step explanation:

Answer:

3%

Step-by-step explanation:

percent of two numbers x and y

x as a percent of y is given by x/y * 100

given

Total bill = $11.18

in the bill , tax amount = $0.33

thus,

tax as percent of total bill is =  tax amount /Total bill  * 100

tax as percent of total bill is = 0.33 /11.18  * 100= 2.95 %

Thus,

tax percentage is 2.95%

tax percentage to nearest whole number is 3%

The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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Answer:B

Step-by-step explanation:

If the air is colder than the water you would have -2-9 because if you keep,Change and flip it it it is -2+-9 which is -11.

Given:

The radius of the circle is r=2 mi.

To find the diameter of the circle:

The formula is,

Thus, the diameter of the circle is 4 mi.

Answer: 4mi

Step-by-step explanation:

diameter = 2 x radius

2x2 = 4

Answer:

*does

Step-by-step explanation:

Answer:

92?

Step-by-step explanation:

2x9=18 100-18+10=92

Answer:

60/24

Step-by-step explanation:

Answer:

StartFraction 60 hours Over 1 EndFraction times StartFraction 24 days Over 1 hour EndFraction

Step-by-step explanation:

I'm sorry if this is wrong

 a) The function P(x) is equal to -0.3x^2 + 57x - 13.
b) R(90) = 5310, C(90) = 253, and P(90) = 5057.

a) To find P(x), we substitute the given expressions for R(x) and C(x) into the equation P(x) = R(x) - C(x). Therefore, P(x) = (60x - 0.3x^2) - (3x + 13). Simplifying, we get P(x) = -0.3x^2 + 57x - 13.
b) To find R(90), C(90), and P(90), we substitute x = 90 into the respective functions.
- For R(90), we have R(90) = 60(90) - 0.3(90)^2 = 5400 - 2430 = 5310.
- For C(90), we have C(90) = 3(90) + 13 = 270 + 13 = 253.
- For P(90), we have P(90) = R(90) - C(90) = 5310 - 253 = 5057.
Therefore, R(90) = 5310, C(90) = 253, and P(90) = 5057.

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the complete question is:
Total profit is defined as total​ revenue, R(x), minus total​cost, C(x), and is given by the function ​P(x)=​R(x)−​C(x). Given​R(x)=60x - 0.3x^2 and C(x)=3x+13​, find each of the following:
​a) P(x) ​(type in desending powers of x)
b) ​R(90​), ​C(90​), and ​P(90​)

The first step is to subtract $500 from $2000 and then you end up with $1500 which you then divide by 5.

Each payment will have to be $300

Answer:

2.915 × 10^9

Step-by-step explanation:

you count the from right to left since its a positive number until you get one number in front. That's where you place your decimal. Since there's 9 numbers behind the 2 it will be 10 to the power of 9.

The Simplification of the expression 7 exponent 7/7 exponent 4 is 7³

7 exponent 7/7 exponent 4

= 7^7 ÷ 7^4

Using the law of indices which states that:

7^7 ÷ 7^4

= 7^(7-4)

= 7^3

Therefore, the Simplification of the expression 7 exponent 7/7 exponent 4 is 7³

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By the remainder theorem, if p(x) = x³ - 3x² + kx - 1 and x - 1 is a factor p(x), then the remainder upon dividing p(x) by x - 1 is p (1) = 0.

So we have

p (1) = 1³ - 3 • 1² + k - 1 = 0

Solve for k :

1 - 3 + k - 1 = 0

k = 3

Answer:

Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Step-by-step explanation:

Answer:

1 1/3 tubs per min.

2 mph.

50 mph.

9 cups per bag.

Step-by-step explanation:

Multiply the numerator of the first number by the denominator of the second number, then divide the product by the denominator of the first number. Hope this helps :)

Answer:

AC ≈ 11.0 cm

Step-by-step explanation:

Using Pythagoras' identity in Δ CDE and Δ ADE

CE² + DE² = DC²

CE² + 7² = 8²

CE² + 49 = 64 ( subtract 49 from both sides )

CE² = 15 ( take the square root of both sides )

CE = \(\sqrt{15}\)

-------------------------------------------------------

AE² + DE² = DA²

AE² + 7² = 10²

AE² + 49 = 100 ( subtract 49 from both sides )

AE² = 51 ( take the square root of both sides )

AE = \(\sqrt{51}\)

Then

AC = AE + CE = \(\sqrt{15}\) + \(\sqrt{51}\) ≈ 11.0 cm ( to the nearest tenth )

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The expectation is -$9.6

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes.

Expected winning per ticket :

Σ(X × p(X)) = [(1000 × 1/1000) + (600 × 2/1000) + (300 × 2/1000) + (200 × 5/1000) - price per ticket

= 1 + 1.2 + 0.6 + 1 - 7

= 3.8-7

= -$3.2

Expected winning if 3 tickets are purchased :

3 × (-3.2) = -$9.6

Hence, the expectation is -$9.6

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The domain of f /g consists of numbers x for which g(x) does not equal to 0 that are in the domains of f and g.

According to the statement

we have given that the The domain of f /g consists of numbers x And we have to find the value of the g(x).

So, For this purpose, we know that the

Domain of a function is the set of all possible inputs for the function.

And according to definition it is clear that the , domain is the input value of the function,

And it is impossible that the function have a 0 zero input value in the functions f(x) and the g(x).

Every function have at least 1 domain or input value.

So, The domain of f /g consists of numbers x for which g(x) does not equal to 0 that are in the domains of f and g.

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Answer:

4 liters

Step-by-step explanation:

6+4+6 = 16

16/4 = 4

Answer:

\(\huge\boxed{V=729m^3}\)

Step-by-step explanation:

The formula of a volume of a cube:

\(V=s^3\)

\(s\) - an edge

We have \(s=9m\).

Substitute:

\(V=9^3=729(m^3)\)

Answer:

Step-by-step explanation:

2/6 = 1/3  so we just need to know what is more 3/5 or 5/8

3/5 = (3•8)/(5•8) = 24/40

5/8 = (5•5)/(8•5) = 25/40

25 > 24  so 5/8 > 3/5

so Cristiano walked farther

They walk for 1/3 of a day so in a whole day they walk three times the distance

3/5 • 3 = 9/5 = 1 4/5 = 1.8 mile

5/8 • 3 = 15/8 = 1 7/8 = 1.875 mile

A tree diagram can be drawn to represent all possible outcomes of drawing two marbles without replacement. The probability of drawing two red marbles is 3/4. The probability of drawing at least one green marble is 11/14.

Tree diagram is shown.

Let R1 be the event of getting a red marble on the first draw, and R2 be the event of getting a red marble on the second draw. Then the probability of getting two red marbles is

P(R1 and R2) = P(R1)P(R2|R1)

= (4/8)(3/7)

= 6/28

= 3/14

The probability of picking at least one green marble is equal to 1 minus the probability of picking two red marbles. So

P(at least one green) = 1 - P(R1 and R2)

= 1 - 3/14

= 11/14

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The missing number of the series is 21.

The given sequence appears to follow the pattern of the Fibonacci sequence, where each number is the sum of the two preceding numbers. The Fibonacci sequence starts with 0 and 1, and each subsequent number is obtained by adding the two previous numbers.

Using this pattern, we can determine the missing number in the sequence.

0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55

Looking at the pattern, we can see that the missing number is obtained by adding 8 and 13, which gives us 21.

Therefore, the completed sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.

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The missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55 is 21.

To find the missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55, we can observe that each number is the sum of the two preceding numbers. This pattern is known as the Fibonacci sequence.

The Fibonacci sequence starts with 0 and 1. To generate the next number, we add the two preceding numbers: 0 + 1 = 1. Continuing this pattern, we get:

Therefore, the missing number in the sequence is 21.

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That implies after 12 feet down the hallway pain can be felt.

What is Distance?

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Based on the triangle midpoint theorem, the statement which must be shown is that: B. the length of GH is half the length of KL.

Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.

Based on the triangle midpoint theorem, we can infer and logically deduce that the statement which must be shown is that the length of GH is half the length of KL.

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Answer:  B. The length of GH is half the length of KL.

Step-by-step explanation:   TRUST ME!  The answer is correct on Edge.  :)

Answer: B) \(f\left(x\right)=\frac{1}{3}\left(-x-1\right)^{5}\)

Step-by-step explanation:

When graphing x5 the parent function and plugging in the equation for B the only equation that fits the criteria of

*shifting left 1 unit

*vertically compressed by 1/3

*reflect over the y-axis

So the answer is B

The function after the transformation is f ( x ) = ( 1/3 ) ( -x + 1 )⁵

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x⁵

On reflecting over the y axis , we get

f ( x ) = ( -x )⁵

On vertically compressing by a factor of ( 1/3 ) , we get

f ( x ) = ( 1/3 ) ( -x )⁵

And , shifting 1 unit to the left , we get

f ( x ) = ( 1/3 ) ( -x + 1 )⁵

Hence , the transformed function is f ( x ) = ( 1/3 ) ( -x + 1 )⁵

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When something decreases by 15.7%, the growth factor is about 1.182 and when something decreases by 0.12%, the growth factor is about 1.00012.

In math, what is the definition of multiplying?

Multiplication is a mathematical process that shows the amount of times a number has been added to itself. It is represented by the multiplication symbols (x) or (*). Division is a mathematical process that shows how many equal amounts add up to a given quantity.

If something decreases by 15.7%, the increase in the factor is 100 / (100 - 15.7) Equals 1.182.

As a result, when something decreases by 15.7%, the growth factor is about 1.182.

When something falls by 0.12%, the expansion factor is 100 / (100 - 0.12) = 1.00012.

As a result, when something decreases by 0.12%, the growth factor is about 1.00012.

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Answer: I think your answer would be A. (-2,8) and (2,-8)

I hope it's right

The value of x from the given linear function is -11/6

Linear equations are expression that has a leading degree of 1

Given the linear equation below

-2/3(3x - 4) +3x =5/6

Expand

-2/3(3x) - 2(-4) + 3x = 5/6

-2x + 8/3  + 3x = 5/6

Collect the like terms

x = 5/6 - 8/3

x = (5-16/6

x = -11/6

Hence the value of x from the given linear function is -11/6

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