(2a2 + a + 3) ÷ (a - 1)

The line integral along the boundary of the triangle C is 32/15.

To apply Green's , we need to find the curl of the vector field F:

∂F₂/∂x - ∂F₁/∂y = (2xy³) - (y)

The boundary of the triangle C, which consists of three-line segments:

C₁: From (0,0) to (1,0)

C₂: From (1,0) to (1,2)

C₃: From (1,2) to (0,0)

Using the parametric equations for each line segment, we can express the line integral as:

∫C F · dr = ∫∫R (∂F₂/∂x - ∂F₁/∂y) dA

R is the region enclosed by C.

Since R is a triangle with vertices (0,0), (1,0), and (1,2), we can use a double integral to compute the area of R:

∫∫R dA = \(\int_0^1 \int_0^{y_2} dx dy\) = 1/2

Now we can apply Green's Theorem:

∫C F · dr = ∫∫R (∂F₂/∂x - ∂F₁/∂y) dA

= ∫∫R (2xy³ - y) dA

= \(\int_0^1 \int_0^{y_2} (2xy^3 - y) dx dy\)

= \(\int_0^2 (4/5)y^5 - (1/2)y^2 dy\)

= 32/15

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Answer:

Here is the answer:

x4−5x3+7x2−34x−1x−5=x3+7x+1+4x−5               =          x^3+7x+1+4/x-5

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

                               x-5                                        

Write down the first coefficient without changes:

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

We have completed the table and have obtained the following resulting coefficients: 1,0,7,1,4.

All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus, the quotient is  x^3+0x^2+7x+1 and the remainder is 4.

Answer:

10

Step-by-step explanation:

\( \frac{5}{12} = \frac{1}{a} + \frac{1}{b} \\ \\ \frac{5}{12} = \frac{b + a}{ab}..(by \: taking \: lcm) \\ \\ \frac{5}{12} = \frac{a + b}{ab} \\ \\ \frac{5}{12} = \frac{a + b}{24} ...( \because \: ab = 24) \\ \\ a + b = \frac{5 \times 24}{12} \\ \\ a + b = 5 \times 2 \\ \\ \huge \red{ \boxed{ a + b = 10}}\)

Let's evaluate each of the prefix expressions:

A) *2/8 4 3

To evaluate this expression, we start from the right and work our way to the left.

The division operation (/) is applied first: 4 divided by 3 is equal to 1.33 (approximately).

Next, we perform the multiplication operation (*): 1.33 multiplied by 2 is equal to 2.67 (approximately).

Therefore, the value of the expression is approximately 2.67.

B) 1- 33 425

Again, we start from the right and move to the left.

The subtraction operation (-) is applied first: 425 minus 33 is equal to 392.

Finally, we subtract 1 from 392: 392 minus 1 is equal to 391.

The value of the expression is 391.

C) + 132 123/6-4 2

Let's break down the expression step by step:

1. 123 divided by 6 is equal to 20.5.

2. Next, we have: 132 + 20.5 - 4 2.

To evaluate the addition and subtraction, we perform the operations from left to right:

3. 132 plus 20.5 is equal to 152.5.

4. Subtracting 4 from 152.5 gives us 148.5.

5. Finally, we subtract 2 from 148.5, resulting in 146.5.

Therefore, the value of the expression is 146.5.

D) +3+3 13+333

Following the same procedure, we evaluate the expression step by step:

1. 3 plus 3 is equal to 6.

2. Next, we have: 6 + 13 + 333.

To evaluate the addition, we perform the operations from left to right:

3. 6 plus 13 is equal to 19.

4. Finally, we add 333 to 19, resulting in 352.

Therefore, the value of the expression is 352.

Q3. It seems that there is no specific question mentioned for Q3. If you have any additional question or clarification, please let me know and I'll be happy to assist you.

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By using compound interest, there will be$554.68in the account after 2 years.

Compound interest is interest that is calculated on the original principal of a loan or deposit, as well as on any accumulated interest from previous periods.

Compound interest is calculated using the following formula:

Compound interest = P * (1 + r/n)^(nt) - P

To calculate the total amount in the account after 2 years, we can use the following formula:

Total amount = P * (1 + r/n)^(nt)

In this formula, P is the principal amount (the initial deposit of $500), r is the annual interest rate (5.2%), n is the number of times that interest is compounded per year (12 in this case, since the interest is compounded monthly), and t is the number of years for which the interest is compounded (2 in this case).

Substituting the given values into the formula, we get:

Total amount = $500 * (1 + 0.052/12)^(12*2) = $554.68

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Given:

If AB = 0,

Then it is not necessary that A=0 or B=0

To prove this, we consider an example:

Let n=m = p =2

Then AB is given as:

Clearly AB= 0 but A,B not equals to zero.

Hence, the given statement is not true.

Hence, the answer is false.

Answer:

C

Step-by-step explanation:

Mario first rode at one constant speed and then at a faster constant speed.

The equilibrium solutions are plotted with larger dots and the arrows indicate the direction of flow.  Therefore, the phase portrait of the solutions of the given equation is:Figure: The phase portrait of the given equation.

The given equation is dy/dx

= y³(y³-2)(y-1).Here, we need to find all equilibrium solutions and classify each as stable or unstable. Plot the phase portrait of the solutions of this equation. Let us solve the question accordingly.Step 1: Equilibrium Solutions Equilibrium solutions occur when dy/dx

= 0. Therefore,y³(y³-2)(y-1)

= 0We can obtain equilibrium solutions from here. The solutions are,y

= 0, y

= ±√2 and y

= 1.Step 2: Classify Equilibrium Points We can obtain the phase portrait of this equation using the sign of the derivative on either side of each equilibrium solution. For instance, let us use the interval (0, 1) for the point y

= 1. Therefore, we can use the following table for the classification of the equilibrium points:EQUILIBRIUM SOLUTION | PHASE PORTRAIT | CLASSIFICATION

= 0 | -----> | Semistabley

= √2 | <----- | Unstabley

= 1 | -----> | Semistabley

= -√2 | <----- | Unstabley

= -1 | -----> | SemistableStep 3: Plot the Phase Portrait Now, we can plot the phase portrait as shown below. The equilibrium solutions are plotted with larger dots and the arrows indicate the direction of flow.  Therefore, the phase portrait of the solutions of the given equation is:Figure: The phase portrait of the given equation.

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Answer:

\(\boxed{\tt y=48}\)

Step-by-step explanation:

\(\tt \cfrac{3}{16}=\cfrac{9}{y}\)

Cross multiply:-

\(\tt 3 \times y=(9)\times (16)\)

\(\tt 3y=144\)

Divide both sides by 3:-

\(\tt \cfrac{3y}{3}=\cfrac{144}{3}\)

Simplify:-

\(\tt y=48\)

_________________

Hope this helps!

Answer:y=48 I hope this is helpful good luck have a good day

Step-by-step explanation:

3/16 = 9/y

Determine the defined range

3/16=9/y y=0 cross out the equal sign y=0

Simplify the equation using cross-multiplication

3y=144

Divide both sides of the equation by 3

y=48

Check if the solution is in the defined range

Step-by-step explanation:

y-y1=m(x-x1)

y-5=2/3(x+9)

Answer:

1/2 + 1/2 = 1

Step-by-step explanation:

The cost of ordering shirts for a club is 268 units.

Define Function.

A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.

 This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).

The statement that f is a function from X to Y using the function notation f: X→Y

The function that represents the cost of the shirts(x) is f(x) = 8x+12

Now, for x = 32

 f(x) = 8x+12

f(32) = 8(32) + 12

        = 256 +12

f(32) = 268 units

.

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A truck can carry either 576 1-foot boxes, 72 2-foot boxes, or 21 3-foot boxes.

The combination of boxes that will result in the highest payment for one truckload is 89 1-foot boxes, 3 2-foot boxes, and 3 3-foot boxes, for a total payment of $3,422.

To find how many boxes of one type will fill a truck, calculate the volume of the truck and divide it by the volume of one box.

Volume of the truck = 12 ft × 6 ft × 8 ft = 576 cubic feet

Volume of a 1-foot box = 1 ft × 1 ft × 1 ft = 1 cubic foot

Number of 1-foot boxes that will fill the truck = 576 cubic feet / 1 cubic foot = 576 boxes

Volume of a 2-foot box = 2 ft × 2 ft × 2 ft = 8 cubic feet

Number of 2-foot boxes that will fill the truck = 576 cubic feet / 8 cubic feet = 72 boxes

Volume of a 3-foot box = 3 ft × 3 ft × 3 ft = 27 cubic feet

Number of 3-foot boxes that will fill the truck = 576 cubic feet / 27 cubic feet = 21.33 boxes (rounded down to 21 boxes)

Therefore, a truck can carry either 576 1-foot boxes, 72 2-foot boxes, or 21 3-foot boxes.

To determine the combination of box types that will result in the highest payment for one truckload, calculate the total payment for each combination of box types.

Let x be the number of 1-foot boxes, y be the number of 2-foot boxes, and z be the number of 3-foot boxes in one truckload.

The volume of the boxes in one truckload is:

V = x(1 ft)³ + y(2 ft)³ + z(3 ft)³

V = x + 8y + 27z

The payment for one truckload is:

P = 5x + 25y + 100z

To maximize P subject to the constraint that the volume of the boxes does not exceed the volume of the truck:

x + 8y + 27z ≤ 576

Use the method of Lagrange multipliers to solve this optimization problem:

L(x, y, z, λ) = P - λ(V - 576)

L(x, y, z, λ) = 5x + 25y + 100z - λ(x + 8y + 27z - 576)

Taking partial derivatives and setting them equal to zero:

∂L/∂x = 5 - λ = 0

∂L/∂y = 25 - 8λ = 0

∂L/∂z = 100 - 27λ = 0

∂L/∂λ = x + 8y + 27z - 576 = 0

From the first equation, we get λ = 5.

Substituting into the second and third equations, y = 25/8 and z = 100/27. Since x + 8y + 27z = 576, x = 268/3.

Round these values to the nearest integer because no fraction for a box. Rounding down, x = 89, y = 3, and z = 3.

Therefore, the combination of boxes that will result in the highest payment for one truckload is 89 1-foot boxes, 3 2-foot boxes, and 3 3-foot boxes, for a total payment of $3,422.

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Step-by-step explanation:

To represent 1 2/3 on a number line, we start by locating the integer 1 on the number line:

----|-----------|-----------|-----------|-----------|-----------|

 -3           -2          -1            0           1            2

Next, we need to locate the fractional part 2/3 of a unit. To do this, we divide the interval between 1 and 2 into three equal parts, and then shade two of those parts:

----|-----------|-----------|-----------|-----------|-----------|

 -3          -2          -1            0            1            2

            1         4/3         5/3          2

Therefore, the point representing 1 2/3 on the number line is located at 5/3 units to the right of -1, as shown above.

Answer:

-5^4

Step-by-step explanation:

I hope this helped.

Answer:

5 & 6

Step-by-step explanation:

The nearest two perfect squares are √25 and √36 which are 5 and 6

As per the unitary method, the cost of 8 pear is at the rate of $12.

The term unitary method is defined as a process of finding the value of a single unit, and based on this value and then we can find the value of the required number of units.

Here we have given that the grocery store the cost of 6 pear is $9.

Let us consider that x be the cost of one pear.

Here we know that the the cost of 6 pear is $9.

Then the cost of one pear is calculated as,

=> x = 9/6

When we simplify this one then we get, the cost of one pear as,

=> x = 1.5

Therefore, the cost of 8 pear is calculated as,

=> 8 x 1.5

=> 12

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Answer:

Ok, to find MAD, you have to add up all of the decimals in the set, and then divide by how much decimals there are in the set.

Adding them all up...

The final result of the adding is 56.7

Now, we have to divide by how much decimals.

We now have. 56.7 / 6

Do the division.

56.7 / 6 ===> 9.45

No need to round, the final answer is 9.4

Yes, the function g(x) is continuous at x= 2.
To demonstrate this, we will use the definition of continuity. A function is continuous at x=a if ()=() and ′() exists and is finite.

For g(x) we can see that (2)=() is true because for x = 2, g(2) = 2*2-2 = 2 which is the same as the value of g(x) for any x (1/2x + 1 for x ≤ 2 and 2x -2 for x > 2).
We will now check if ′(2) exists and is finite. To do this, we will calculate the limit of g'(x) as x approaches 2.
g'(x) = {-1/2 for x ≤ 2, 2 for x > 2}
The limit of g'(x) as x approaches 2 is:
lim g'(x) = lim (2) = 2
Since the limit of g'(x) is finite, ′(2) exists and is finite.
Therefore, the function g(x) is continuous at x= 2.

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Answer:

Cash = 240, Credit = 330, Gift = 30

Step-by-step explanation:

We know from this the precentage  of people using different payment methods

Cash = 40/100 = 40%

Credit card = 55/100 = 55%

Gift card = 5%

We can then find the number of people using each method regardless of total amount of people

Cash = 40% * 600 = 240

Credit = 55% * 600 = 330

Gift card = 5% * 600 = 30

Total = 240 + 30 + 330= 600

Answer:

240

Step-by-step explanation:

Set up a proportion.  Out of 100 people, 40 people paid with cash.  Out of 600 people,  x people paid with cash.

\(\frac{40}{100} =\frac{x}{600}\)

Cross multiply and solve for x.

\(24000 = 100x\\24000/100=100x/100\\240 =x\\x=240\)

240 customers paid with cash.

Answer:

Mr Burkett travelled 407.5 miles during his full trip.

Step-by-step explanation:

First, we must determine the distance he travelled in the first 3.5 hours. Luckily, we know his speed during that time so we can just multiply 70 miles per hour by 3.5 hours. That is 245 miles.

In the second step, we must determine the distance he travelled during the second part of his trip where he slowed down a bit. 65 miles per hour times 2.5 hours is 162.5 miles.

Finally, we can just add them! 245 + 162.5 = 407.5.

Answer:

s = the number of student tickets sold a = the number of adult tickets sold The drama class sold 25 more student tickets than adult tickets to the fall play s = a + 25 The class collected $660 from ticket sales: 6s + 3a = 660 divide both sides by 3 2s + a = 220 by solving the system of equations s = a + 25 2s + a = 220 we find s = 81.67 student tickets a = 56.67 adult tickets

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer: 100 points

Step-by-step explanation:

20 times 5 = 100

The balance after 10 years based on an interest rate of  5.25% will be $461.25.

The interest rate of the account can be calculated by using the formula I = P × R × T, where I is the interest amount, P is the original principal amount, R is the annual interest rate, and T is the time in years.

Using this formula, we can calculate the interest rate as follows:

I = 422 - 401 = 21

P = 401

T = 1

R = I / (P × T) = 21 / (401 × 1) = 0.0525

Therefore, the interest rate of the account is 5.25%.

To calculate the balance after 10 years, we can use the formula A = P(1 + rt), where A is the final amount (balance after 10 years), P is the original principal amount, r is the interest rate, and t is the number of years.

Using this formula, we can calculate the balance after 10 years as follows: A = 401(1 + 0.0525 × 10) = 461.25

Therefore, the balance after 10 years will be $461.25.

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The condition that has not been met for conducting a z-test for a proportion is (b) The sample size is less than 10% of the population size.

In order to conduct a z-test for a proportion, certain conditions need to be met. The first condition is that the data should be a random sample from the population of interest (condition a), which has been met in this case as the students entering the room can be considered a random sample of the statistics class.

The third condition is that the product of the population proportion (p) and the sample size (n) should be greater than or equal to 10, and the product of the complement of the population proportion (1-p) and the sample size (n) should also be greater than or equal to 10 (condition c). However, the second condition (b) has not been met in this scenario. The sample size of 5 students is not less than 10% of the population size, which is 30.

Therefore, the sample size is not large enough to meet this condition. Consequently, the correct answer is (e) More than one condition is violated, as the other conditions are still satisfied.

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The intensity of sound from a concert speaker decreases with distance according to the inverse square law. This law states that the intensity is inversely proportional to the square of the distance.

So, if the intensity at a distance of 1 meter is I1, and the intensity at a distance of d meters is I2, the ratio of the intensities can be calculated using the formula:

(I1/I2) = (d2/d1)^2

Since we want to find the ratio of the intensities, we can substitute the given values:

(I1/I2) = (1/d)^2

Simplifying the equation, we get:

(I1/I2) = 1/d^2

Therefore, the intensity of sound from a concert speaker at a distance of 1 meter is (1/d^2) times greater than the intensity at a distance of d meters.

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The intensity of sound from a concert speaker at a distance of 1 meter is $\left(\frac{1}{x}\right)^2$ times greater than the intensity at a distance of $x$ meters.

The intensity of sound from a concert speaker decreases as the distance from the speaker increases. The relationship between intensity and distance is inversely proportional.

To determine how many times greater the intensity of sound is at a distance of 1 meter compared to the intensity at a distance of $x$ meters, we need to use the inverse square law formula:

$\frac{\text{Intensity1}}{\text{Intensity2}} = \left(\frac{\text{Distance2}}{\text{Distance1}}\right)^2$

Let's assume the intensity at a distance of $x$ meters is $I2$. Plugging in the values into the formula, we get:

$\frac{\text{Intensity1}}{I2} = \left(\frac{1 \text{ meter}}{x \text{ meters}}\right)^2$

Simplifying the equation, we have:

$\text{Intensity1} = I2 \times \left(\frac{1}{x}\right)^2$

This means that the intensity of sound at a distance of 1 meter is $\left(\frac{1}{x}\right)^2$ times greater than the intensity at a distance of $x$ meters.

For example, if $x$ is 3 meters, then the intensity of sound at a distance of 1 meter would be $\left(\frac{1}{3}\right)^2 = \frac{1}{9}$ times greater than the intensity at 3 meters.

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