find the surface area of a cylinder with a height of 20 inches and base radius of 7 inches

The area of the surface generated by revolving the curve about the x-axis is 9664π  / 3 square units.

Given: The equation of the curve is y = 4√x on [21,77]

The formula for finding the surface area of a curve rotated about the x-axis on some interval [a, b] is given by:

\(S = \int\limits^b_a {2\pi f(x)\sqrt{1 +(f'(x))^{2} } } \, dx\)

where S is the surface area,

f(x) is y

a and b is the given interval such that a ≤ x ≤ b or [a, b]

Now in this question,

f(x) = 4√x

a = 21, b = 77

f'(x) = 4 * 1 / 2√x = 2 / √x

f'(x) = 2 /√x

Placing the respective values in the equation we get,

\(S = \int\limits^{77}_{21} {2\pi. 4\sqrt{x} \sqrt{1+(\frac{2}{\sqrt{x} } )^{2} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x} \sqrt{1+\frac{4}{x} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x} * \frac{\sqrt{x + 4} }{\sqrt{x} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x+4} } } \, dx\)

we know the formula for the integral

\(\int\limits^b_a {\sqrt{ax + b} } \, dx = \frac{2}{3a}(ax+b)^{\frac{3}{2} } | { {{b} \atop {{a}}} \right.\)

Therefore, by applying the formula, we get:

\(S = 8\pi *\frac{2}{3}(x+4)^{\frac{3}{2} } | { {{77} \atop {{21}}} \right.\)

\(S = \frac{16\pi }{3} \{ (77+4)^{\frac{3}{2}} - (21+4)^{\frac{3}{2} }\}\)

\(S = \frac{16\pi }{3} \{ (81)^{\frac{3}{2}} - (25)^{\frac{3}{2} }\}\)

\(S = \frac{16\pi }{3} \{729 - 125\}\)

\(S = \frac{16\pi }{3} * 604\)

\(S = \frac{9664\pi }{3}\)

Hence, The area of the surface generated by revolving the curve about the x-axis is 9664π  / 3 square units

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Disclaimer: The given question is incomplete. The complete question is mentioned below:

Find the area of the surface generated when the given curve is rotated about the x-axis y= 4sqrt(x) on [21,77]

The area of the surface generated by revolving the curve about the x-axis is ___ square units (type an exact answer, using pi as needed)

Answer:

2:1

Step-by-step explanation:

We know

To get from F to G, we have to go from -2 to 2, for which the length is 4.

To get from F' to G', we have to go from -2 to 0, for which the length is 2.

What is the ratio of the sides from the big to the small rectangle?

The ratio is 4:2 = 2:1

Answer:

$69 i think im not smart

Step-by-step explanation:

Answer:

823.7

Step-by-step explanation:

No, an objective function P=a x+b y+c can not have the same maximum value at all four vertex points Q, R, S, and T. The objective function P can have the same maximum value at points R and S only.

Explanation: This is because, for a linear programming problem, there are multiple constraints, which form the feasible region for the problem.

For a 2-dimensional linear programming problem, the feasible region is a convex polygon whose vertices are the intersection points of the constraint lines.

In a feasible region, the maximum or minimum value of the objective function is always attained at one of the vertex points or along one of the boundary lines.

The vertex points are the most important points as they are the only points that provide the extreme values of the objective function.

In the given problem, if the objective function P = a x + b y + c has the same maximum value at all four vertex points Q, R, S, and T, then it means that the objective function is parallel to all four sides of the feasible region. This is not possible as the feasible region is a convex polygon.

Therefore, the objective function can have the same maximum value at points R and S only. For example, consider the following feasible region and the objective function P = 3x + 2y.The vertex points of the feasible region are A(0,4), B(2,2), C(4,0), and D(0,0).

At vertex points B and C, the objective function P has the same maximum value of 10.

Therefore, the objective function P can have the same maximum value at points R and S only.

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The solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

To fathom the given differential equation, xy'' + y' = 0, we will begin by expecting a control arrangement of the frame y = ∑(n=0 to ∞) a_nx^n, where a_n speaks to the coefficients to be decided.

Separating y with regard to x, we get:

\(y' = ∑(n=0 to ∞) a_n(nx^[(n-1))] = ∑(n=0 to ∞) na_nx^[(n-1)]\)

Separating y' with regard to x, we get:

\(y'' = ∑(n=0 to ∞) n(n-1)a_nx^[(n-2)]\)

Presently, we substitute these expressions for y and its subsidiaries into the differential condition:

\(x(∑(n=0 to ∞) n(n-1)a_nx^[(n-2))] + (∑(n=0 to ∞) na_nx^[(n-1))] =\)

After improving terms, we have:

\(∑(n=0 to ∞) n(n-1)a_nx^[(n-1)] + ∑(n=0 to ∞) na_nx^[n] =\)

Another, we compare the coefficients of like powers of x to zero, coming about in a boundless arrangement of conditions:

For n = 0: + a_0 = (condition 1)

For n = 1: + a_1 = (condition 2)

For n ≥ 2: n(n-1)a_n + na_n = (condition 3)

Disentangling condition 3, we have:

\(n^[2a]_n - n(a_n) =\)

n(n-1)a_n - na_n =

n(n-1 - 1)a_n =

(n(n-2)a_n) =

From equation 1, a_0 = 0, and from equation 2, a_1 = 0.

For n ≥ 2, we have two conceivable outcomes:

n(n-2) = 0, which gives n = or n = 2.

a_n = (minor arrangement)

So, the solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

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Reed Hopkins received annual dividends of $35.00 and the annual yield was 0.84%.

Reed Hopkins purchased 350 shares of Barber Industries at $11.93 per share, for a total cost of $4,175.50. The company paid annual dividends of $0.10 per share, so Reed received 350 x $0.10 = $35.00 in annual dividends. To calculate the annual yield, we divide the annual dividends by the total cost of the investment and multiply by 100%. Thus, the annual yield is ($35.00 / $4,175.50) x 100% = 0.84%.

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The solution to the equation is p = -72.

The equation, we need to isolate the variable 'p' on one side of the equation. Let's go through the steps:

-p/12 = 6

To get rid of the fraction, we can multiply both sides of the equation by 12:

12 * (-p/12) = 12 * 6

This simplifies to:

-p = 72

To isolate 'p,' we can multiply both sides of the equation by -1:

(-1) * (-p) = (-1) * 72

This gives us:

p = -72

Therefore, the solution to the equation is p = -72.

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Answer:

a

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

7x - 2 + 9x - 2 + 2(5x) = 2(5x + 5) + 2(4x)

7x + 9x + 10x - 4 = 10x + 10 + 8x

7x + 9x + 10x - 10x - 8x = 10 + 4

8x = 14

x = 14/8 = 7/4

So, ST = 5*7/4 + 5

           = 55/4

           = 13 3/4

Answer:

ST = 13.75

Step-by-step explanation:

The perimeter of a trapezium is calculated with the following formula:

P = a + b + c + d (a, b: bases, c, d: sides)

The perimeter of a rectangle is calculated with the following formula:

P= 2(a + b) (a: base, b: side)

we will write the following equation to find the length of ST

7x - 2 + 9x - 2 + 5x + 5x = 2(5x + 5 + 4x) first do the inside the parenthesis

2(9x + 5) = 18x + 10

Now,

7x - 2 + 9x - 2 + 5x + 5x = 18x + 10 add like terms on the left side of the equation

26x - 4 = 18x + 10 transfer like terms to the same side of the equation

26x - 18x = 10 + 4 add/subtract

8x = 14 divide both sides by 8

x = 1.75 replace x with this to calculate the lentgh of ST

5x + 5 = 5*(1.75) + 5 and ST = 13.75

Therefore , the solution of the given problem of unitary method comes out to be Mr. Tan makes a total of $30 Plus $18 = $48.

To finish the job using the unitary technique, the equation from this nano section should be multiplied by two. In essence, when a wanted object is present, both the characterised by either a group and the pigment sections are omitted from the unit method. A variable fee of Inr ($1.01), for instance, would be paid for 40 pens. It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

Let's name the CDs' pre-tax cost "x" for simplicity. The overall cost of the CDs before tax is two times because Lena purchased two of them for the same price. The cost of the Discs, with the addition of the $1.80 sales tax, is:

=> 2x + $1.80

Given that we know the final price, including tax, was $23.40, we can create the following equation:

=> 2x + $1.80 = $23.40

By deducting $1.80 from each half, we arrive at:

=> 2x = $21.60

When you divide both parts by 2, you get:

=> x = $10.80

As a result, each Disc cost $10.80 before taxes.

We can create another equation now that we know his revenues from selling apple juice are $12 higher than his profits from selling lemon juice:

=> 30n - 18n = 12

=> 12n = 12

=> n = 1

As a result, Mr. Tan sells 2n + 5n = 7n = 7 glasses of juice, for a total profit of 30n = $30 from the sale of apple juice and 18n = $18 from the sale of lemon juice.

Therefore, Mr. Tan makes a total of $30 Plus $18 = $48.

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The height of the water increasing at the rate of   \(\frac{1}{12} \frac{m}{min}\) .

What is a function?

In mathematics, a function is a unique arrangement of the inputs (the domain) and their outputs (the codomain), where each input has exactly one output and the output can be linked to the input.

We need a function to connect the two variables when there are associated rates; in this instance, it is unmistakably volume and height. The equation is:

\(V=\) \(\pi r^{2}h\)

Although radius is mentioned in the formula, it is not a variable in this issue because it is constant. We might change the value in

V=\(\pi(6m)^{2}h\)

We must implicitly differentiate wrt (with respect to) time because the rate in this problem is tied to time

\(\frac{dV}{dt} =(36m^{2} )\)  \(\pi\frac{dh}{dt}\)

In the problem, we are given  \(3\frac{m^{2} }{min}\)   which is  \(\frac{dV}{dt}\) .So we substitute this in:

\(\frac{dh}{dt} =\frac{3m^{3}}{min(36m^{2} )\pi }\)

\(=\frac{3}{36\pi} \frac{m}{min}\)

\(=\frac{1}{12} \frac{m}{min}\)

Hence, the height of the water increasing at the rate of  \(\frac{1}{12} \frac{m}{min}\) .

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Answer:

D. K+2K=51

Step-by-step explanation:

Since Lauren is 2 times Kristy's age, Lauren's age=2K

so, if the sum of the two is 51, then 2K+K=51

If you want to solve it, 2K+K=3K=51

51/3=K

17=K

34=L

Answer:

D K + 2K = 51

Step-by-step explanation:

Lauren is twice Kristy's age so it would be 2K cause you want to multi[ly, and then you have to add Kristy's age in the equation because their ages added together is 51

Note that the use of the term "implicitly" in the question suggests that there is some other equation or context that defines y, but without that information, we can only assume that y is an arbitrary function. To differentiate 4/9 with respect to an implicitly defined function, we first need to clarify what that function is.

Let's call it y, so we have: 4/9 = f(y)
Now, we can differentiate both sides with respect to y using the chain rule: d/dy (4/9) = d/dy (f(y))
0 = f'(y)
So, the derivative of 4/9 with respect to an implicitly defined function y is 0. We can write this as:
d/dy (4/9) = 0
Note that the use of the term "implicitly" in the question suggests that there is some other equation or context that defines y, but without that information, we can only assume that y is an arbitrary function.

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The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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\(\text{Plug in and solve:}\\\\2(10)(-5) + -3(10(-5))\\\\2(-50) + -3(10(-5))\\\\2(-50) + -3(-50)\\\\-100+ -3(-50)\\\\-100+150\\\\\boxed{50}\)

Answer:

\(2 + 2 + 2 - 2 = 29\)

Answer:

0.82° C

Step-by-step explanation:

To predict how much change the temperature will be in 20 years time since 2000, simply substitute x = 20 into the given equation, \( y = 0.52 + 0.015x \):

\( y = 0.52 + 0.015(20) \)

\( y = 0.52 + 0.3 \)

\( y = 0.82 \)

✅The temperature change would be 0.82° C.

95% confident that the true population mean backpack weight falls between 49.06 and 54.94 ounces.

To construct a 95% confidence interval for the true population mean backpack weight, we can use the following formula:

Confidence interval = mean weight ± (critical value x standard error)

Where the critical value is determined based on the level of confidence and the degrees of freedom (n-1), and the standard error is calculated as the population standard deviation divided by the square root of the sample size.

In this case, since we have a sample size of 27, the degrees of freedom would be 26. Using a t-distribution table, we can find the critical value for a 95% confidence level with 26 degrees of freedom to be 2.056.

The standard error can be calculated as:

standard error = 7.7 / sqrt(27) = 1.48

Therefore, the 95% confidence interval can be calculated as:

Confidence interval = 52 ± (2.056 x 1.48) = (49.06, 54.94)

This means that we can be 95% confident that the true population mean backpack weight falls between 49.06 and 54.94 ounces, based on the sample of 27 backpacks with a mean weight of 52 ounces and a population standard deviation of 7.7 ounces.

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There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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The required measure of side y = 8

Given : Triangle TUV and triangle XWV are similar

Thus \(\frac{UV}{VW} = \frac{6}{21}\)

this is further equal to \(\frac{2}{7}\)

Thus the ratio UV : VW = 2 : 7

this implies that the ratio TV : VX should also be equal to the ratio of UV : VW = 2 : 7 because of cpst or also called corresponding parts of similar triangles.

Given  UV : VW = 2 : 7

thus TV : VX = \(\frac{y}{28 }\) which on equation will give y as 8

because \(\frac{8}{28}\) when divided by 4 will give us the required ratio that is 2 : 7

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The expression used to calculate how many more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks is 4(700t- 750c) .

What is an expression in math example?

time taken by tatenda to mow a square meter of lawn = t seconds

time taken by Ciara  to mow a square meter of lawn = c seconds

area mowed by tatenda in a week = 700 square meters

area mowed by Ciara in a week = 750 square meters

the expression used to calculate how many more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks

time taken by tatenda for mowing in 4 weeks = 4 * 700 * t seconds

time taken by Ciara for mowing in 4 weeks = 4 * 750 * c seconds

more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks = [4 * 700 * t ] - [4 * 750 * c]

= 4(700t- 750c)

Therefore, the expression used to calculate how many more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks is 4(700t- 750c).

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Answer:

PEg = 196.2 J

Step-by-step explanation:

PEg = mass * gravitational field* height

PEg = 4kg * 9.81m/s² * 5m

PEg = 196.2 kg m²/s²

The marginal cost of the third unit produced is $21.

The average total cost (ATC) is calculated by dividing the total cost (TC) by the number of units produced. From the given table, we can see that when two units are produced, the average total cost is $12.

In order to find the total cost of producing two units, we multiply the average total cost by the number of units: $12 × 2 = $24.

Now, let's move on to the total cost of producing three units. We are given that the average total cost when three units are produced is $15. Therefore, the total cost of producing three units is $15 × 3 = $45.

The change in total cost between producing two units and three units is $45 - $24 = $21.

Finally, we divide the change in total cost by the change in quantity produced to find the marginal cost of the third unit: $21 ÷ (3 - 2)

= $21.

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20 is the possible outputs for the function defined by c(x)=20x for all of the students that would pay for the field trip

The function that is known to represent what would be the cost of the trip of these students is given as C(x)=20x.

The cost of the trip for one of the students is put at 20 dollars each.

We would have x as the total number of those that would be attending this trip. In order to get the output that would show us the cost of the trip.

We take X to be a whole number.

then x = 1

such that that  c(1) = 20(1) = 20

Then the total is 20 per student

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the cost for an upcoming field trip is 20 dollars the cost of the feild trip c is a function of the number of students x select all the possible outputs for the function defined by c(x)=20x

A 20 B 30 c 50

Answer:

32

Step-by-step explanation:

2[18 -(5 + 9) ÷7]

2[18 -14 ÷7]

2[18 -2]

2[16]

32

The remaining sides and angles of the triangle are side c ≈ 18.47 ft, angle B ≈ 23.58 degrees, and angle C ≈ 126.42 degrees.

To find the remaining sides and angles of the triangle given that angle A = 30 degrees, side a = 10ft, and side b = 8ft, we need to determine if the given information represents a valid triangle. Since we have one angle and two sides, we can use the Law of Sines.

The Law of Sines states that (a/sinA) = (b/sinB) = (c/sinC), where a, b, and c are the sides of the triangle, and A, B, and C are the corresponding angles.
Step 1: Use the given information to find angle B.
(10/sin(30)) = (8/sinB)
10/sin(30) = 8/sinB
10/0.5 = 8/sinB
20 = 8/sinB
sinB = 8/20
sinB = 0.4
B = arcsin(0.4)
Angle B ≈ 23.58 degrees
Step 2: Find angle C.
Since the sum of angles in a triangle is 180 degrees:
C = 180 - (A + B)
C = 180 - (30 + 23.58)
C ≈ 126.42 degrees
Step 3: Find side c using the Law of Sines.
(10/sin(30)) = (c/sin(126.42))
10/0.5 = c/sin(126.42)
20 = c/sin(126.42)
c ≈ 20 * sin(126.42)
c ≈ 18.47 ft
So, the remaining sides and angles of the triangle are side c ≈ 18.47 ft, angle B ≈ 23.58 degrees, and angle C ≈ 126.42 degrees.

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Answer:

1571

Step-by-step explanation:

its 1570.8 but you have to round

Answer:

Step-by-step explanation:

sin = opposite leg / hypotenuse

cos = adjacent leg / hypotenuse

Ratios are same