Can someone PLEASE help me out??!!!!!!!

The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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Answer:

its 3.05

Step-by-step explanation:

The coordinates of A will be at (-10, -5) when the transformation (x,y) → (x + 10, y + 5) is  performed on point A.

Given the coordinate of the resulting image after the transformation is A'(0, 0). We need to get the coordinate of the original image A.

Since the transformation (x,y) → (x + 10, y + 5) is performed on A.

A = (0 - 10, 0 - 5)

If we are going from the pre-image to the image, we will translate to the left and downwards

A = (-10, -5)

Hence the coordinates of A will be at (-10, -5)

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Answer:

124.4

Step-by-step explanation:

Perimeter of ∆HIJ = IJ + HJ + HI

IJ = 40

HJ = 37.6

HI = ?

Let's find HI

∆HIJ and ∆EFG are similar. Since they have equal corresponding angles. Therefore, the ratio of their corresponding sides would be equal.

Thus:

EF/HI = FG/IJ

EF = 117 (given)

HI = ?

FG = 100 (given)

IJ = 40 (given)

Plug in the values

117/HI = 100/40

117/HI = 2.5

117 = HI*2.5

117/2.5 = HI

HI = 46.8

✔️Perimeter of ∆HIJ = IJ + HJ + HI

= 40 + 37.6 + 46.8

= 124.4

Answer: greaterright

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

Let \(x\) be equal to the decimal when multiplied by 2 equals 1

\(2x=1\)

Divide both sides by 2

\(\frac{2x}{2} =\frac{1}{2} \\x=0.5\)

Multiply the decimal by 100 to get a percent

0.5×100=50%

I hope this helps!

It takes the second marathoner 4 hours and 40 minutes to complete the marathon.

Let's assume the distance of the marathon is "d" miles.

The first marathoner runs at a constant speed for 4 hours, so we can find their speed as:

speed = distance / time = d / 4

The second marathoner starts by running at 4 times the speed of the first marathoner, so their speed is:

speed = 4(d / 4) = d

For the second half of the race, the second marathoner's speed drops to 3/4 of the first marathoner's speed. Let's assume it takes "t" hours for the second marathoner to complete the second half of the race. Then, we can write:

d / 2 = (3/4)(d / 4)(t)

Simplifying this equation, we get:

t = (2/3) hours

So the total time it takes the second marathoner to finish the race is:

4 + (2/3) = 4 2/3 hours = 4 hours and 40 minutes.

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Answer:

208080

Step-by-step explanation:

Answer:

(8×10^2)⋅(2.5×10^2) = 200,000

Step-by-step explanation:

How I know this is because 10^2 is 100. And if you multiply 8*100 it equals 800. After if you multiply 2.5*100 it equals 250. Lastly if you multiply 800 by 250 you get 200,000

I hope this is correct

Answer:

7.2 x \(10^{6}\)

Step-by-step explanation:

7.2 x \(10^{6}\)

To write the number in scientific notation, you need to move the decimal from where it is at at the end of the number so that the number will be 1 or greater than 1, but less than 10.

7,200,000.  If we do not see a decimal, it is at the end of the number.   We moved the decimal between the 7 and 2.  How many places did we move the decimal.  It was at the end of the number and now it is between the 7 and the 2.  We moved it 6 places.  That tells us what the exponent will be.

The orthogonal complement to S has dimension 0 when the dimension of the vector space is equal to the dimension of S.

We have,

The orthogonal complement to a subspace S of a vector space is the set of all vectors in the vector space that are orthogonal (perpendicular) to every vector in S.

The dimension of the orthogonal complement is given by the difference between the dimension of the vector space and The dimension of S.

If S spans the entire vector space, then its orthogonal complement consists only of the zero vector and therefore has dimension 0.

Thus,

The orthogonal complement to S has dimension 0 when the dimension of the vector space is equal to the dimension of S.

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Answer:

Reflection across the x-axis

Step-by-step explanation:

The points are the same, just opposite of one another. The image looks as if it is a reflection. Think of the x-axis like a puddle and the shape looking into it; try to picture the image seeing its reflection to help.

Answer:

Reflection across the x-axis.

Step-by-step explanation:

The triangles mirror each other with the x-axis acting like said mirror.

To find the volume of a triangular-based pyramid, you can use the following formula:

\(V = (1/3) * A_{base} * h\)

\(V = (1/3) * A_{base} * h\)

where:

- V represents the volume of the pyramid

- \(A_{base\) represents the area of the triangular base

- h represents the height of the pyramid

1. Determine the measurements: Measure the length of the base of the triangle (b) and the height of the triangle (\(h_{base\)). If the triangle is not right-angled, use trigonometric calculations to determine the height.

2. Calculate the area of the base: Use the formula for the area of a triangle, which is

\((1/2) * b * h_{base,\)

to find the area of the triangular base.

3. Determine the height of the pyramid: Measure the vertical height (h) from the base of the pyramid to the apex (top point). Make sure to use consistent units with the base measurements.

4. Apply the volume formula: Plug the values of the base area (\(A_{base\)) and the height (h) into the volume formula:

\(V = (1/3) * A_{base} * h.\)

5. Simplify and calculate: Multiply the base area by the height, and then divide the result by 3 to calculate the volume of the pyramid.

Make sure to use consistent units throughout the calculations. The resulting volume will be in cubic units (e.g., cubic centimetres, cubic inches, etc.), reflecting the three-dimensional space occupied by the pyramid.

Remember to double-check your measurements and calculations to ensure accuracy in determining the volume of the triangular-based pyramid.

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Answer:

Z - 4/4 + 8

=> Z - 1 + 8

=> Z - 9

If my answer helped, please mark me as the brainliest!!!

Thank You!!

Answer:

Z - 4/4 + 8

=> Z - 1 + 8

=> Z - 9

Step-by-step explanation:

If there are 6 red blocks and 4 blue blocks and a child is arranging them in a row, then there will be total of 210 possible arrangements.

In this scenario, there are a total of 10 blocks (6 red and 4 blue).

To determine the number of different arrangements possible, you'll need to find the combinations of these 10 blocks.

Using the formula for combinations (n! / (r! (n-r)!)), where n is the total number of blocks and r is the number of one type (e.g. red):

Total possible arrangements = 10! / (6!4!) = 210

So, there are 210 different possible arrangements of the 6 red blocks and 4 blue blocks in a row.

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Answer:

$10

Step-by-step explanation:

Unit rate

$8/4cup = $2/cup

Therefor

5 cups * $2/cup = $10

Answer:18$

Step-by-step explanation:first you wanna see the rate 8 dollars for 4 cups so 8/4 gives you 2.The rate is 2 dollars per cup.

So now we have to find how much 5 cups is worth.Since we know how much each lemonade cost we just have to plug it all in!So 5*2.Is 10 and we also made 8 bucks from the first 4 cups.

Now that we know that we sold 8$ the first time and 10$ the second we add them all up to give you “18$“total

The values of the variables for the parallelogram include the following;

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In this context, we can reasonably infer and logically deduce that this parallelogram has both pairs of opposite sides parallel to each other and the opposite angles (vertical angles) are equal and congruent.

By CPCTC, the variable x can be calculated as follows;

15x = 45°

x = 45°/15

x = 3

Since the diagonals of a parallelogram are perpendicular to each other, we have:

m<1 = 3y - 9 = 90

3y = 99

y = 33

15x = 18z

15(3) = 18z

45 = 18z

z = 45/18

z = 2.5

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The Length of perimeter of the shaded shape is; 24 - 8π

Let us first find the rectangle measurements that contains the shaded portions.

Width of rectangle = 2 * 4 = 8

Length of rectangle = 2 + 2 = 4

Perimeter of rectangle = 2(8 + 4) = 24 units

Now, let us find the perimeter of all semi circles and quarter circles that fall into into this rectangle region;

Perimeter of semi circles = πr + πr + πr + πr/2 + πr/2 = 4πr

Perimeter of semi circles inside the rectangle = 4π * 2 = 8π

Thus;

Length of perimeter of shaded shape = 24 - 8π

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The Anne  to deposit  $208.33 each month in order to accumulate $10,000 by the time she is 20 years old, assuming a 0% interest rate.

To calculate how much Anne's monthly deposits  to be in order to accumulate $10,000 by the time she is 20,  to consider the time frame and the interest rate.

Let's assume that Anne has 4 years to save the money (from 16 to 20 years old) and that the interest rate is 0% for simplicity.

To determine the total number of months Anne has to save. Since there are 12 months in a year and she has 4 years, the total number of months is:

Total months = 4 years × 12 months/year = 48 months

Next, calculate how much she needs to save each month:

Amount to save = Total amount desired / Total months

= $10,000 / 48

≈ $208.33

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The break-even point for the given equation c = 15n + 269,000  , r = 95n  representing cost and revenue is equal to Option c. 3363units ( round up to nearest whole unit ).

As given in the question,

Cost equation is represented by :

c = 15n + 269,000

Revenue equation is given by ;

r = 95n

For the break-even point the cost is always equal to the revenue as there is no profit no loss.

c = r

15n + 269,000 = 95n

⇒ 95n - 15n = 269,000

⇒ 80n = 269,000

⇒ n = 269,000 / 80

⇒ n = 3362.5

⇒ n = 3363 units ( round up to nearest whole unit )

Therefore, the break-even point for the given cost and revenue is equal to Option c.  3363units ( round up to nearest whole unit ).

The above question is incomplete , the complete question is:

Find the break-even point for the given cost and revenue equations. round to the nearest whole unit. c = 15n + 269,000  , r = 95n

a. 80                          c. 3363        

b. 2445                      d. 110

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Answer:

The polygon has 13 sides.

Step-by-step explanation:

The sum of the interior angles of a polygon is (n - 2) * 180, where n is the number of sides. This formula can be set equal to the sum of the interior angles to determine how many sides it has.

(n - 2) * 180 = 1980

180n - 360 = 1980

180n = 2340

n = 13

Answer:

1/216

Step-by-step explanation:

probability of rolling a 2 and a 2 and a 2 = 1/6(1/6)(1/6) = 1/216

\(slope = \frac{rise}{run}\\\\m = \frac{y2 - y1}{x2 - x1}\)

Lets US population be x

ATQ

\(\\ \sf\longmapsto \dfrac{x}{10}=32\)

\(\\ \sf\longmapsto x=32(10)\)

\(\\ \sf\longmapsto x=320million \)

Canada has a population that is about 1/10 as large as the United States. If Canada's population is about 32 million, about how many people live in the United States? Explain the number of zeros in your the answer.

Given,

Population of Canada = 32 million (1/10 of that of the USA)

=> Let the population of the USA be 'x'.

Now,

→ x/10 + 32 (million)

→ x = 32 × 10

→ x = 320 million.

(The number of zeros in 1 million is 6, so the number of zeros in 320 million will be 7)

320000000 or 320 million.

Answer:

4x^2+x

Step-by-step explanation:

(x)(4x+1)=(x)(4x)+(x)(1)

Hope this helped :)

Answer:

the answer to what?

Step-by-step explanation:

The amount to be invested is c. $14,200.39.

The formula for calculating of simple interest is -

Simple Interest = Principal × Rate × Time ÷ 100

Keep the values in formula to find the principal amount to be invested to earn mentioned interest.

5896 = Principal × 6.92 × 6/100

Rewriting the equation

Principal = (5896 × 100) ÷ (6.92 × 6)

Performing multiplication in numerator and denominator on Right and Side of the equation

Principal = 589600 ÷ 41.52

Performing division on Right and Side of the equation

Principal = 14,200.39

Thus, the principal amount should be $14200.39.

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Answer:

14.49

Step-by-step explanation:

14 * 0.035 = 0.49

14 + 0.49 = 14.49

Using area of a rectangle, it is found that the area of the iPad's screen is of 45.2 square inches.

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

The area of a rectangle of length l and width w is given by:

\(A = lw\)

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

The diagonal of a rectangle is the hypotenuse of a right triangle, in which the sides are the length and the width.

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

\(x^2 + (\frac{4x}{3})^2 = (9.7)^2\)

\(x^2 + \frac{16x^2}{9} = 94.09\)

Multiplying everything by 9:

\(9x^2 + 16x^2 = 846.81\)

\(25x^2 = 846.81\)

\(x^2 = \frac{846.81}{25}\)

\(x = \sqrt{\frac{846.81}{25}}\)

\(x = 5.82\)

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

\(A = lw = 7.76(5.82) = 45.2\)

The area of the iPad's screen is of 45.2 square inches.

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