Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.y = 6/7 x2, y = 13/7 − x2; about the x-axis

Answer:

The answer is B and c.

Step-by-step explanation:

first thing you need to do is  look at slopes

the slopes are different then look at  the y intersects there the same

and finally they both intersect at the same point.

the correct answer is B and C.

the area of the shaded part is 30. 89 cm²

We have the shape to be a rectangle

The area of the shaded part should be;

Area of rectangle - 2 ( area of a semi circle)

The formula for area of a rectangle

Area = length × width

Area = 12 × 12

Area = 144 cm²

Area of a semicircle = 1/2 πr²

Area = 1/ 2 × 3. 142 × 6²

Area = 56. 56 cm²

Area of shaded part = area of rectangle - 2( area of semicircle)

Area of shaded part = 144 - 2(56. 56)

Area of shaded part = 144 - 113. 11

Area of shaded part = 30. 89 cm²

Thus, the area of the shaded part is 30. 89 cm²

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Answer:

\(x^{2} -pqx+pq\)

Step-by-step explanation:

Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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The value of function f(7) is approximately 14.857.

To find the value of f(7), we can use the information given about f(1), the continuity of f', and the definite integral involving f'.

Let's go step by step:

1. We are given that f(1) = 12. This means that the value of the function f(x) at x = 1 is 12.

2. We are also given that f' is continuous. This implies that f'(x) is continuous for all x in the domain of f'.

3. The definite integral 7 ∫ f'(x) dx from 1 to 7 is equal to 20. This means that the integral of f'(x) over the interval from x = 1 to x = 7 is equal to 20.

Using the Fundamental Theorem of Calculus, we can relate the definite integral to the original function f(x):

∫ f'(x) dx = f(x) + C,

where C is the constant of integration.

Substituting the given information into the equation, we have:

7 ∫ f'(x) dx = 20,

which can be rewritten as:

7 [f(x)] from 1 to 7 = 20.

Now, let's evaluate the definite integral:

7 [f(7) - f(1)] = 20.

Since we know f(1) = 12, we can substitute this value into the equation:

7 [f(7) - 12] = 20.

Expanding the equation:

7f(7) - 84 = 20.

Moving the constant term to the other side:

7f(7) = 20 + 84 = 104.

Finally, divide both sides of the equation by 7:

f(7) = 104/7 = 14.857 (approximately).

Therefore, f(7) has a value of around 14.857.

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Answer:

Area of the sheet = 2×2 = 4 feet2

Step-by-step explanation:

The probability of choosing a black token from the bag is 31.25% and the probability of choosing a red token from the bag is also 31.25%.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A bag contains 80 colored tokens. Of all the tokens in the bag, 25 are black and 5/16 are red.

There are total tokens are 80 in which black token are 25 black tokens. Thus, the probability of choosing black token is,

\(P=\dfrac{25}{80}\\P=0.3125\\P=31.25\%\)

There are total 5/16 tokens in bag. Thus, the number of red tokens in bag is,

\(n=\dfrac{5}{16}\times80\\n=25\)

Thus, the probability of choosing red token is,

\(P=\dfrac{25}{80}\\P=0.3125\\P=31.25\%\)

Thus, the probability of choosing a black token from the bag is 31.25% and the probability of choosing a red token from the bag is also 31.25%.

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If this trend continues, the total books the author would have sold over the first 12 months is 157,810 books.

In this scenario, we would calculate the total books sold by this author over the first 12 months as follows;

First month = 19,000 books.

Second month; 19,000 × (1 - 7)% = 19,000 × 93/100 = 17,670 books.

Third month; 17,670 × (1 - 7)% = 17,670 × 93/100 = 16,433 books.

Fourth month; 16,433 × (1 - 7)% = 16,433 × 93/100 = 15,283 books.

Fifth month; 15,283 × (1 - 7)% = 15,283 × 93/100 = 14,213 books.

Sixth month; 14,213 × (1 - 7)% = 14,213 × 93/100 = 13,218 books.

Seventh month; 13,218 × (1 - 7)% = 13,218 × 93/100 = 12,293 books.

Eigth month; 12,293 × (1 - 7)% = 12,293 × 93/100 = 11,432 books.

Ninth month; 11,432 × (1 - 7)% = 11,432 × 93/100 = 10,632 books.

Tenth month; 10,632 × (1 - 7)% = 13,218 × 93/100 = 9,888 books.

Eleventh month; 11,432 × (1 - 7)% = 11,432 × 93/100 = 9,196 books.

Twelveth month; 9,196 × (1 - 7)% = 9,196 × 93/100 = 8,552 books.

Next, we would add all of the books sold in each month together;

Total books sold = 19,000 + 17,670 + 16,433 + 15,283 + 14,213 + 13,218 + 12,293 + 11,432 + 10,632 + 9,888 + 9,196 + 8,552

Total books sold = 157,810 books.

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The formula that can be used to describe the sequence is:\(a(n) = (-1)^(n+1) * 3^(n) * 4.\)

The given sequence is -81, 108, -144, 192.

The formula that can be used to describe the sequence is:  \(a(n) = (-1)^(n+1) * 3^(n) * 4\), where n is the nth term in the sequence.

This formula is a geometric sequence formula that can be used to describe the given sequence.

The formula represents the nth term of the sequence as a function of the position of the term in the sequence.

Here, n represents the position of the term in the sequence

.For the given sequence, the first term is -81, which corresponds to the first position in the sequence (n = 1).

The second term is 108, which corresponds to the second position in the sequence (n = 2).

The third term is -144, which corresponds to the third position in the sequence (n = 3).

The fourth term is 192, which corresponds to the fourth position in the sequence (n = 4).

Therefore, the formula that can be used to describe the sequence is: \(a(n) = (-1)^(n+1) * 3^(n) * 4.\)

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Answer:

Step-by-step explanation:

Lets call the number n.

So the cube of this number is \(n^3\) and the sum of 7 and the cube of this number is \(7+n^3\)

Step-by-step explanation:

So

Total money = 20

Entrance fee = 1.75

Food = 2.50

Ride = 1.05

Amount spend = 1.75 + 2.05 = 3.8

Left for rides = 20 - 3.8 = 16.2

So rides = 16.2 ÷ 1.05 = 15

I think atleast 15 rides

Note: Consider "÷" sign instead of "=".

Given:

\((x^3-3x^2+5x-3)\div (x-1)\)

To find:

The quotient.

Solution:

We have,

\((x^3-3x^2+5x-3)\div (x-1)\)

It can be written as

\(=\dfrac{x^3-3x^2+5x-3}{x-1}\)

Splitting the middle terms, we get

\(=\dfrac{x^3-x^2-2x^2+2x+3x-3}{x-1}\)

\(=\dfrac{x^2(x-1)-2x(x-1)+3(x-1)}{x-1}\)

Taking out the common factor (x-1), we get

\(=\dfrac{(x-1)(x^2-2x+3)}{x-1}\)

Cancel the common factors.

\(=x^2-2x+3\)

The quotient is \(x^2-2x+3\).

Therefore, the correct option is D.

Answer:

D

Step-by-step explanation:

The percentage represented is 72%, and the decimal is 0.72

First lets find the decimal, it will be equal to the quotient between the total number of shaded squares and the total number of squares.

There are 200 squares in total, and of these 200, there are 144 shaded ones, then the decimal is:

d = 144/200  = 0.72

To find the percentage, you only need to multiply the decimal by 100%, we will get:

p = 100%*0.72 = 72%

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6 more than y :    

3 times a number:

x ← a number    

5 less than the product of 10 and c :

10c   ← the product of 10 and c

14 more than 6 times t :

6t  ← six times t

The sum of x and y is 18:

x+y    ← the sum of x and y

A number minus 12 is y:

x - a number

The domain of the function is all real numbers and  range is  y ≥ -1.

Since the vertex is at (1,-1), the axis of symmetry is x = 1.

This means that the domain of the function is all real numbers.

To find the range, we need to consider the y-values of the graph. Since the vertex is the lowest point of the graph, the range must be all y-values greater than or equal to -1.

However, since the parabola opens upwards, there is no upper bound on the y-values.

Therefore, the range is given by y ≥ -1.

Hence, the domain of the function is all real numbers and  range is  y ≥ -1.

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Answer:

2nd graph above the one you chose

Answer:

$400

Step-by-step explanation:

We will make this question into a function by setting 'p' as the initial price before sale and converting the percent to a decimal (60*0.01).

Because the final price was calculated by multiplying the initial price by 60%, we can represent that with the function:

0.6p=240

All we need to do now is isolate p by dividing out 0.6.

p=400

Giving us an answer of $400 (that's an expensive jacket )

Please find attached a diagram with the completed table

In order to determine which number is  a counterexample of the conjecture, we are to divide each number by 2 and 4. A counterexample of this conjecture would only be divisible by either 2 or 4 but not both of them

Dividing the numbers by 2

12 / 2 = 6

19 / 2 = 9.5

22 / 2 = 11

28 / 2 = 14

30 / 2 = 15

Dividing the numbers by 4

12 / 4 = 3

19 / 4 = 4.75

22 / 4 = 5.5

28 / 4 = 7

30 / 4 = 7.5

22 and 30 are counterexamples because they are divisible by 2 but not by 4

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Answer:

-6

Step-by-step explanation:

Hello!

Since we are finding f(-1) we put -1 in for x

2(-1)^2 + 8(-1)

Follow PEMDAS

2 * 1 + 8(-1)

2 * 1 + -8

2 + -8 = -6

The answer is -6

Hope this helps!

my answer is (a) I think

Answer:

Step-by-step explanation:

1000*PI*4/3

4000/3*PI

1333.3 (3 REPEATING)*PI

4186.6 (6 REPEATING)

BRAINLIEST PLSSSSSSSSSSSSS

Answer:

4186.67

Step-by-step explanation:

volume of sphere = 4πr³/3

4 × 3.14 × 10 × 10 × 10 ÷ 3 = 4186.67cm³

Answer:

A

Step-by-step explanation:

The triangle NLM has corresponding angles with triangle LND

Answer:

t pounds = 3.5 (or just t = 3.5c)

Step-by-step explanation:

2 pounds of tomatos for 7$ means that one pound of tomatos for 3.5$. Therefore, t pounds = 3.5 c

The equation which represents the sales of tomatoes will be ( t = 3.5c).

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

2 pounds of tomatoes for 7$ means that one pound of tomatoes for 3.5$. Therefore, t pounds = 3.5 c

Let t represent tomatoes and c represents cost then the expression will be written as below:-

t = 3.5c

Therefore, the equation which represents the sales of tomatoes will be ( t = 3.5c).

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\(\dfrac{z-1}3 = \dfrac8{z+1}\)

Eliminate the denominators.

\(3(z+1)\cdot\dfrac{z-1}3 = 3(z+1)\cdot\dfrac8{z+1}\)

\(z^2 - 1 = 24\)

Solve for \(z\).

\(z^2 = 25\)

\(\boxed{z = \pm5}\)

The volume of the triangular prism as described is; 15 cubic foot.

A triangular pyramid simply refers to any geometric solid with a triangular base, and all three lateral faces are also triangles with a common vertex

It follows from the formula for calculating the volume of a triangular prism that;

Volume = (1/3) × base area × height.

Consequently,

volume of the prism is; = (1/3) ×9 × 5

Volume = 15 cubic foot

Therefore, volume of the triangular prism as described is; 15 cubic foot.

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Answer:

3(6g - 5)

Step-by-step explanation:

1. First, find the GCF of 15 and 18.

Factors of 15:

1, 3, 5, 15

Factors of 18:

1, 2, 3, 6, 9, 18

The GCF of 15 and 18 is 3.

2. Factorize

3(6g - 5)

3. Check you answer:

3(6g) + 3(-5)

18g - 15

Hope this helps!

\(\large{\mathcal{ANSWER:}}\)

Let initially he had x No. of apples

ATQ :-

x-40% of x=420

x-2/5x=420

=> 3x=420×5

x= 700

\(\underline{\boxed{\purple{\tt{©⚘MissyRiel}}}}\)

Hope this helps!

we know that the average for six numbers can be writen like:

So if 5 of them are -3.20 and the average is -3.65 we can replace that values and find the missing one:

and we solve for x so:

So the missing value is -6