Part A Ignoring the mass of the spring; what is the mass m of the fish? View Available Hint(s) Azd m =_______ kg

The approximation of the integral ∫ sin(√x) dx using the Midpoint Rule with n = 4 is approximately 17.5614 when rounded to four decimal places.

To approximate the integral ∫ sin(√x) dx using the Midpoint Rule with n = 4, we first need to determine the width of each subinterval. The width, denoted as Δx, can be calculated by dividing the total interval length by the number of subintervals:

Δx = (b - a) / n

In this case, the total interval is from 0 to 24, so a = 0 and b = 24:

Δx = (24 - 0) / 4

   = 6

Now we can proceed to compute the approximation using the Midpoint Rule. We evaluate the function at the midpoint of each subinterval within the given range and multiply it by Δx, summing up all the results:

∫ sin(√x) dx ≈ Δx * (f(x₁) + f(x₂) + f(x₃) + f(x₄))

Where:

x₁ = 0 + Δx/2 = 0 + 6/2 = 3

x₂ = 3 + Δx = 3 + 6 = 9

x₃ = 9 + Δx = 9 + 6 = 15

x₄ = 15 + Δx = 15 + 6 = 21

Plugging these values into the formula, we have:

∫ sin(√x) dx ≈ 6 * (sin(√3) + sin(√9) + sin(√15) + sin(√21))

Now, let's calculate this approximation, rounding the result to four decimal places:

∫ sin(√x) dx ≈ 6 * (sin(√3) + sin(√9) + sin(√15) + sin(√21))

≈ 6 * (0.6908 + 0.9501 + 0.3272 + 0.9589)

≈ 6 * 2.9269

≈ 17.5614

Therefore the answer is 17.5614

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Answer:

C

Step-by-step explanation:

A 1 2-liter bottle for $0.89

1 liter = .89 /2 = $0.445

B 3 1-liter bottles for $1.50

1 liter = $1.50/3 = $0.50

C 24 0.5-liter bottles for $5.25

1 liter = 5.25 / 12  = $0.4375

D 36 0.25-liter bottles for $4.75

1 liter = $4.75 / 9  = $0.53

Give me brainllest

Answer:

C is the best buy

Step-by-step explanation:

0.89/2 = 0.445

3 * 1 litre bottles = 3 litres

1.50/3 = 0.5

24 * 0.5 litres = 12 litres

5.25/12 = 0.4375

36 * 0.25 liters = 9 liters

4.75/9 = 0.52777777

Answer:

202.5

Step-by-step explanation:

180+180*12.5% or 180*112.5%

Answer:

£202.50

Step-by-step explanation:

First convert 12.5% into a decimal by dividing it by 100 to get 0.125.

Then we work out 12.5% of 180 by multiplying them: 180 * 0.125 = 22.5

Then we are increasing so add it back to the original: 180 + 22.5 = 202.5

Because we are using £ we add it back on and add a 0 for the pennies.

Answer

So changing 1/4 by multiplying top and bottom by 9 gives 9/36 and changing 2/9 by multiplying top and bottom by 4/4 gives 8/36 and adding 9/36 to 8/36 gives 17/36 - a rational number.

Step-by-step explanation:

The value of Erica's investment after 6 years is approximately $4,939.05.

To find the value of Erica's investment after 6 years, we can use the compound interest formula. The formula for compound interest is given as:

A = P\((1 + r/n)^(nt)\)

Where:

A is the final amount or value of the investment.

P is the initial principal or investment amount.

r is the annual interest rate (as a decimal).

n is the number of times the interest is compounded per year.

t is the number of years.

In this case, Erica's initial investment is $4000, the annual interest rate is 4% (or 0.04 as a decimal), and the investment is growing annually. Therefore, we have:

P = $4000

r = 0.04

n = 1 (since the interest is compounded annually)

t = 6 years

Plugging these values into the compound interest formula, we can calculate the final value of the investment:

A = $4000(1 + \(0.04/1)^(1*6)\)

A = $4000(1 + 0.04)^6

A = $4000(1.04)^6

Evaluating this expression, we find:

A ≈ $4,939.05

Therefore, the value of Erica's investment after 6 years is approximately $4,939.05.

This calculation assumes that no additional investments or withdrawals were made during the 6-year period and that the interest rate remains constant at 4% per year.

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The extremum of the function f(x, y) = x^2 + 4y^2 - 4xy subject to the constraint x + y = 9 is a maximum at the point (0, 9).

To find the extremum of the function f(x, y) = x^2 + 4y^2 - 4xy subject to the constraint x + y = 9, we can use the method of Lagrange multipliers. The method involves finding critical points of the function while considering the constraint equation.

Let's define the Lagrangian function L as follows:

L(x, y, λ) = f(x, y) - λ(g(x, y))

where g(x, y) represents the constraint equation, g(x, y) = x + y - 9, and λ is the Lagrange multiplier.

We need to find the critical points of L, which occur when the partial derivatives of L with respect to x, y, and λ are all zero.

∂L/∂x = 2x - 4y - λ = 0 .............. (1)

∂L/∂y = 8y - 4x - λ = 0 .............. (2)

∂L/∂λ = x + y - 9 = 0 .............. (3)

Solving equations (1) and (2) simultaneously, we have:

2x - 4y - λ = 0 .............. (1)

-4x + 8y - λ = 0 .............. (2)

Multiplying equation (2) by -1, we get:

4x - 8y + λ = 0 .............. (2')

Adding equations (1) and (2'), we eliminate the λ term:

6x = 0

x = 0

Substituting x = 0 into equation (3), we find:

0 + y - 9 = 0

y = 9

So, we have one critical point at (x, y) = (0, 9).

To determine whether this critical point is a maximum or minimum, we can use the second partial derivative test. However, before doing so, let's check the boundary points of the constraint equation x + y = 9.

If we set y = 0, we get x = 9. So we have another point at (x, y) = (9, 0).

Now, we can evaluate the function f(x, y) = x^2 + 4y^2 - 4xy at the critical point (0, 9) and the boundary point (9, 0).

f(0, 9) = (0)^2 + 4(9)^2 - 4(0)(9) = 324

f(9, 0) = (9)^2 + 4(0)^2 - 4(9)(0) = 81

Comparing these values, we see that f(0, 9) = 324 > f(9, 0) = 81.

Therefore, the extremum of the function f(x, y) = x^2 + 4y^2 - 4xy subject to the constraint x + y = 9 is a maximum at the point (0, 9).

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Answer:  x > 0   x = (0, ∞)

Step-by-step explanation:

The domain (x-values) are the number of ounces the package weighs.

The package must weigh greater than 0 but there doesn't appear to be a maximum weight. Therefore, x > 0

The domain is the set of values for which the given function is defined. The domain of the given relation is (0,∞).

The domain is the set of values for which the given function is defined.

The range is the set of all values which the given function can output.

Given the postal service charges $2 to ship packages up to 5 ounces in weight and $0.20 for each additional ounce up to 20 ounces. After that, they charge $0.15 for each additional ounce. Therefore, the independent variable in this relationship is the weight of the postal.

Since the weight of the postal can be anything greater than 0.

Therefore, the domain of the relation is (0,∞).

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John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer:

∠I ≅ ∠F

Step-by-step explanation:

Since, F is common vertex in the sides GF and FE of triangle FGE and I is common vertex in the sides IJ and IH of triangle IJH.

Hence, ∠I ≅ ∠F will be the required information to prove that △FGE ~ △IJH by the SAS similarity theorem.

The other information needed to prove that △FGE ~ △IJH by the SAS similarity theorem will be  ∠I ≅ ∠F

The ratio of similar sides of similar triangles are equal.

According to the given question, the angle F serves as a common vertex with the sides GF and FE of triangle FGE and also I serve as the common vertex with the sides IJ and IH of triangle IJH.

The other information needed to prove that △FGE ~ △IJH by the SAS similarity theorem will be  ∠I ≅ ∠F

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The dot product is a scalar quantity that represents the projection of one vector onto another, and can be used to calculate the angle between two vectors.

The cross product is a vector quantity that represents the magnitude and direction of the orthogonal projection of one vector onto another. Orthogonality is related to both results in that the dot product of two orthogonal vectors is zero, while the cross product of two parallel vectors is also zero. In addition to that, the cross product of two non-zero vectors results in a third vector that is orthogonal to both.

The dot product is a scalar product that calculates the projection of one vector onto another. The cross product is a vector product that calculates the orthogonal component of one vector with respect to another.

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Step-by-step explanation:

(x-85.2)/7.4=2/5

(x-85.2)=18.5

x=18.5+85.2=103.7cm

Using equations, we can find that he purchased 6 footballs.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example.

Here in the question,

Let the number of footballs purchased be f.

Let the number of basketballs purchased be b.

Cost of each football = $60.

Cost of each basketball = $30.

Total amount spent = $450

Now,

60f + 30b = 450

Given,

2b = f

⇒ b = f/2

Putting the value of b in the equation,

60f + 30(/2f) = 450

⇒ 60f + 15f = 450

⇒ 75f = 450

⇒ f = 6

Therefore, he purchased 6 footballs.

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The system is a consistent system with an infinite solutions.

There are two types of system of equations - consistent and inconsistent.

Inconsistent means that it has no solution , i.e. the solution does not exist.

Consistent system means a solution of the equation exists.

Further, this is of type , a consistent system may have a unique solution or an infinite number of solutions where we need to assign an arbitrary value to a free variable.

For e.g. let us consider the system -

x + y+ z = 0

2x + 3y + 4z = 1

Since , (0,0,0) is a solution to this system , we can't say its an inconsistent system .

Also, for a system to be consistent , either a unique solution exists or an infinite solutions exist. There is no particular number of solutions.

Also, we see that (-1,1,0) is also a solution other than the zero solution.

So, such a system is a consistent system with infinite solutions.

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Answer:

hope this helped!

Answer:

Hello! :) Have a good day!

It will be 30!

Answer:

Basically the statment is saying that in order to get P (A and B) you have to multiply P(A) by P(B).

Answer:

I think it means the probability of selecting (AnB) is equal to Probability of selecting A × probability of selecting B

Step-by-step explanation:

Please rate bainliest if you think I deserve

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Answer:

the first one because Albert sat on apple tree and discovered u don't have a father

Answer: A

Step-by-step explanation:

Answer 2 1/10

work is shown in the picture above. I hope this helps.

Answer:

15,392 pencils.

Step-by-step explanation:

If a factory can make 3,848 pencils in an hour, then the factory can make 15,392 pencils in 4 hours.

Simply multiply 3,848 by 4.

\(3,848*4=15,392\)

Therefore, the factory can make 15,392 pencils in 4 hours.

Answer:

Approximately 16,000 pencils

Step-by-step explanation:

Round 3,848 pencils to the nearest thousand.

That'll turn 3,848 to 4,000.

Since it's 4 hours:

4,000 * 4 = 16,000 pencils

The value of expression is,

1) log₃ 2 = 0.64

2) log ₁₂ 24 = 1.29

3) log₄ 18.7 = 2.12

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

1) log₃ 2

2) log ₁₂ 24

3) log₄ 18.7

Now, We can simplify as;

1) log₃ 2

= log 2 / log 3

= 0.3 / 0.47

= 0.64

2) log ₁₂ 24

= log 24 / log 12

= 1.38 / 1.07

= 1.29

3) log₄ 18.7

= log 18.7 / log 4

= 1.27 / 0.60

= 2.12

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Answer:

I don't understand what is your question?

Answer:

see explanation

Step-by-step explanation:

(sinA + cosA)² + (sinA - cosA)² ← expand using FOIL

= sin²A + 2sinAcosA + cos²A + sin²A - 2sinAcosA + cos²A ← collect like terms

= 2sin²A + 2cos²A

Answer: top: x= -15     bottom: x= -37

Step-by-step explanation: First you need to get x by itself so for example on the top one you would do 8-8 to get x alone and then you would also do -7- 8 because whatever you do to one side you have to do to the other.

Hope this helped!!!

Answer:  \(2(4)^{x+8}-2\)

======================================================

Explanation:

To translate or shift 7 units to the left, we replace x with x+7

So,

\(f(x) = 2(4)^{x+1}-2\\\\f(x+7) = 2(4)^{x+7+1}-2\\\\f(x+7) = 2(4)^{x+8}-2\\\\g(x) = 2(4)^{x+8}-2\\\\\)

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

Extra info:

If you're wondering "why x+7 and not x-7?" it's because we effectively moved the xy axis 7 units to the right while keeping the f(x) curve fixed in place. This gives the illusion the f(x) curve is moving 7 units to the left.

The graph of each is shown below. I used GeoGebra to make the graph.

Answer: See attached.

Step-by-step explanation:

        We see from the given values that for every table there is 3* the number of guests and vise versa (for every 3 guests there is one table). Using this information we can complete the other values by multiplying or dividing.

3 tables * 3 = 6 guests

15 guests / 3 = 5 tables

9 tables * 3 = 27 guests

30 guests / 3 = 10 tables

118.4 - 6.4 = 112

314.944 - 3.7 = 311.244

1,840.5072 + 23.56 = 1864.0672

325 - 2.5 = 322.5

196 + 3.5 = 199.5

405 + 4.5 = 409.5

3,437.5 +5.5 = 3443

393.75 +5.25 = 399

2,625 + 6.25 = 2631.25

231 + 8.25 = 239.25

92 + 5.75 = 97.75

196 + 12.25 = 208.25

117 - 6.5 = 110.5

936 + 9.75 = 945.75

305 + 12.2 = 317.2

Answer:

elsa can do 150 in 3 minutes.

so together they can do 450 in 3 minutes, or 150 in 1 minute

they would need two minutes

Answer:

4.5 minutes long to do their job.

Answer:

14

Step-by-step explanation:

scale factor = 4/8 which is to 2.

therefore, x = 7×2

x = 14

Answer:

(-487.48, 85.96)

Explanation:

The component form of the velocity can be found as

(vx, vy)

Where

vx = vcos(170)

vy = vsin(170)

So, replacing the velocity v by 495 mph, we get:

vx = (495)cos(170)

vx = -487.48

vy = 495sin(170)

vy = 85.96

Therefore, the answer is

(-487.48, 85.96)