Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C.F(x,y) = (e^x -3 y)i + (e^y + 6x)jC: r = 2 cos thetaThe answer is 9 pi.

Answer:

just go with your heart

Answer:

None of them fail the vertical line test.

Step-by-step explanation:

Since each x-value has it's own y-value, they pass the vertical line test. The only time a graph fails the vertical line test is when an x-value has 2 y-values.

Answer:

Vertical lines drawn on the four graphs would touch the graphs at only one point. So, none of the graphs fails the vertical line test.

Answer:65,

Step-by-step explanation:

Where the question?

btw screenshot it if you want me trust you :)

Answer:

(2a^3a^4)^5 simplifies to 32a^35.

Step-by-step explanation:

To simplify (2a^3a^4)^5, we can use the properties of exponents which states that when we raise a power to another power, we can multiply the exponents. Therefore, we can rewrite the expression as:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5

Next, we can simplify the expression inside the parentheses by multiplying the exponents:

a^3a^4 = a^(3+4) = a^7

Substituting this into our expression, we get:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5 = 2^5 * a^35

Finally, we can simplify this expression by using the property of exponents that states that when we multiply two powers with the same base, we can add their exponents. Therefore, we can rewrite the expression as:

2^5 * a^35 = 32a^35

Therefore, (2a^3a^4)^5 simplifies to 32a^35.

The distance it will take to drive from Toronto to buffalo (distance between Toronto and buffalo is 154km) is 1.75 hours.

We are given that;

distance = 154 km speed = 88 km/hr

Now,

we need to use the formula:

time = distance / speed

where time is in hours, distance is in kilometers, and speed is in kilometers per hour.

Plugging these values into the formula, we get:

time = 154 / 88 time ≈ 1.75

Therefore, by speed the answer will be 1.75 hours.

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Answer:

1/15 or 0.0667

Step-by-step explanation:

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bardai

chatgpt

red marble on the first draw is 2/6, or 1/3

red marble on the second draw, given that the first marble was red, is 1/5

(1/3) * (1/5) = 1/15

Given:

Answer:Divied

Step-by-step explanation:

divied both numbers

Donuts left = 3636 - 1932

= 1704

There are 1704 donuts left.

Answer:

18 freshmen, 18 sophomores, 30 juniors, 30 seniors

Step-by-step explanation:

Given ratio

  freshman : sophomores : juniors : seniors

= 320 : 300 : 500 : 510

320 ≈ 300  and  500 ≈ 510

Therefore, 300 : 300 : 500 : 500

Ratio of 300 : 500 = 18 : 30

So  18 : 18 : 30 : 30 best represents the population

Given nos

Ratio:-

Round out

Option A

Ths values of a and b in the equivalent ratio illustrated on the table will be 6 and 12

It should be noted that from the information given, the relationship that exist between the numbers is illustrated as:

y = 0.8x

Therefore, when y is 4.8, the value of x will be:

y = 0.8x

x = 4.8 / 0.8

x = 6

When x = 15, the value of y will be:

y = 0.8x

y = 0.8 × 15

y = 12

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This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

A triangle is a closed, two-dimensional geometric object composed of three line segments, known as sides, that intersect at three locations, known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all sides equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles greater than 90 degrees). The area of a triangle can be computed using the formula A = (1/2)bh, where A is the area, b is the triangle's base, and h is the triangle's height.

Regarding the given diagram, the following claims are always true:

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°\s= m∠2 (the measure of the external angle at angle 2). (the measure of the exterior angle at angle 2). And because angles 2 and 3 are likewise interior triangle angles, we get m2 + m3 = m6, which can be rearranged to yield m5 + m6 = m3 + m4 + m5 = 180°.

m∠2 + m∠3 + m∠5 = 180°

This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

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The area of the triangle with angle B = 128°, side a = 86, and side c = 37 is approximately 2302.7 square units.

To find the area of a triangle when one angle and two sides are given, we can use the formula for the area of a triangle:

Area = (1/2) * a * b * sin(C),

where a and b are the lengths of the two sides adjacent to the given angle C.

In this case, we have angle B = 128°, side a = 86, and side c = 37. To find side b, we can use the law of cosines:

c² = a² + b² - 2ab * cos(C),

where C is the angle opposite side c. Rearranging the formula, we have:

b² = a² + c² - 2ac * cos(C),

b² = 86² + 37² - 2 * 86 * 37 * cos(128°).

By substituting the given values and calculating, we find b ≈ 63.8.

Now, we can calculate the area using the formula:

Area = (1/2) * a * b * sin(C),

Area = (1/2) * 86 * 63.8 * sin(128°).

By substituting the values and calculating, we find the area of the triangle to be approximately 2302.7 square units.

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The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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The ranking based on average speed is 1 > 2 > 4 > 3

(a) Based on the given information, we have:

V1 = V2: The objects on paths 1 and 2 have the same average velocity.

V3 < V4: The object on path 4 has a greater average velocity than the object on path 3.

(b) Average speed is simply the distance traveled divided by the time interval. If the objects move at a constant speed along each path, then the paths with the greatest distances will have the greatest average speeds. Therefore, the ranking based on average speed is:

1 > 2 > 4 > 3

Note that this ranking is based only on the distances traveled along each path, and does not take into account the directions of motion or any changes in direction.

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The cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

To find the cheapest price Sam would pay for 10kg of cake for the party, we need to compare the prices of the available cakes and determine the most cost-effective option.

At Mega Mart, a 5kg cake costs $2500.

Therefore, the price per kilogram for this cake is:

Price per kilogram at Mega Mart = $2500 / 5kg = $500/kg.

At the same time, a 2kg chocolate cake costs $1200.

So, the price per kilogram for this cake is:

Price per kilogram for the chocolate cake = $1200 / 2kg = $600/kg.

Now, let's calculate the total price for 10kg of cake from each option:

Total price at Mega Mart for 10kg = $500/kg \(\times\) 10kg = $5000.

Total price for 10kg of chocolate cake = $600/kg \(\times\) 10kg = $6000.

Comparing the two options, we see that the Mega Mart cake is the more cost-effective choice.

Sam would pay a total of $5000 for 10kg of cake from Mega Mart, whereas the chocolate cake would cost $6000 for the same quantity.

Therefore, the cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

In summary, Sam would pay the cheapest price of $5000 to purchase 10kg of cake for the party from Mega Mart.

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The inequalities which satisfy the number line shown is x>2 and x>=2.

We are given that;

The number line showing inequality

Now,

x>2 satisfies the equation by the given number line

x>=2 satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

Therefore, by the number line the answer will be x>2 and x>=2 .

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We must first find the area of the base, this base is a circle for it we use the equation of the area of a circle.

Where the radius is 2 cm, now we replace and solve this area.

The base area is 12.56 square centimeters

Now we must find the volume of the cylinder with the same base already analyzed, to do this we use the equation for the volume of a cylinder.

Where the radius is 2 cm and the height is 4 cm, now we replace and solve this volume.

The volume is 50.26 cubic centimeters.

In conclusion, the base area and volume are:

Answer:

Associative property, then distributive property

Step-by-step explanation:

The percent of the bags of chips weigh less than 176 grams is b 16%

From the question, we have the following parameters that can be used in our computation:

Mean = 180

Standard deviation = 4

Bags of chips weigh less than 176 grams

This means that

x = 176

So, the z-score is

z = (176 - 180)/4

Evaluate

z = -1

The percent of the bags of chips weigh less than 176 grams is represented as

P = P(z < -1)

Using a graphing calculator, we have

Percentage = 0.15866

So, we have

Percentage = 16%

Hence , the percentage is 16%

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Answer:

(i) x ≤ 1

(ii) ℝ except 0, -1

(iii) x > -1

(iv) ℝ except π/2 + nπ, n ∈ ℤ

Step-by-step explanation:

(i) The number inside a square root must be positive or zero to give the expression a real value. Therefore, to solve for the domain of the function, we can set the value inside the square root greater or equal to 0, then solve for x:

\(1-x \ge 0\)

\(1 \ge x\)

\(\boxed{x \le 1}\)

(ii) The denominator of a fraction cannot be zero, or else the fraction is undefined. Therefore, we can solve for the values of x that are NOT in the domain of the function by setting the expression in the denominator to 0, then solving for x.

\(0 = x^2+x\)

\(0 = x(x + 1)\)

\(x = 0\)     OR     \(x = -1\)

So, the domain of the function is:

\(R \text{ except } 0, -1\)

(ℝ stands for "all real numbers")

(iii) We know that the value inside a logarithmic function must be positive, or else the expression is undefined. So, we can set the value inside the log greater than 0 and solve for x:

\(x+ 1 > 0\)

\(\boxed{x > -1}\)

(iv) The domain of the trigonometric function tangent is all real numbers, except multiples of π/2, when the denominator of the value it outputs is zero.

\(\boxed{R \text{ except } \frac{\pi}2 + n\pi} \ \text{where} \ \text{n} \in Z\)

(ℤ stands for "all integers")

Answer:

(i)  x ≤ 1

(ii)  All real numbers except x = 0 and x = -1.

(iii)  x > -1

(iv)  All real numbers except x = π/2 + πn, where n is an integer.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

\(\hrulefill\)

\(\textsf{(i)} \quad f(x)=\sqrt{1-x}\)

For a square root function, the expression inside the square root must be non-negative. Therefore, for function f(x), 1 - x ≥ 0.

Solve the inequality:

\(\begin{aligned}1 - x &\geq 0\\\\1 - x -1 &\geq 0-1\\\\-x &\geq -1\\\\\dfrac{-x}{-1} &\geq \dfrac{-1}{-1}\\\\x &\leq 1\end{aligned}\)

(Note that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign).

Hence, the domain of f(x) is all real numbers less than or equal to -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x \leq 1\\\textsf{Interval notation:} \quad &(-\infty, 1]\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \leq 1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(ii)} \quad g(x) = \dfrac{1}{x^2 + x}\)

To find the domain of g(x), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.

Set the denominator to zero and solve for x:

\(\begin{aligned}x^2 + x &= 0\\x(x + 1) &= 0\\\\\implies x &= 0\\\implies x &= -1\end{aligned}\)

Therefore, the domain of g(x) is all real numbers except x = 0 and x = -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x < -1 \;\;\textsf{or}\;\; -1 < x < 0 \;\;\textsf{or}\;\; x > 0\\\textsf{Interval notation:} \quad &(-\infty, -1) \cup (-1, 0) \cup (0, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq 0,x \neq -1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iii)}\quad h(x) = \log_7(x + 1)\)

For a logarithmic function, the argument (the expression inside the logarithm), must be greater than zero.

Therefore, for function h(x), x + 1 > 0.

Solve the inequality:

\(\begin{aligned}x + 1 & > 0\\x+1-1& > 0-1\\x & > -1\end{aligned}\)

Therefore, the domain of h(x) is all real numbers greater than -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x > -1\\\textsf{Interval notation:} \quad &(-1, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x > -1\right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iv)} \quad k(x) = \tan x\)

The tangent function can also be expressed as the ratio of the sine and cosine functions:

\(\tan x = \dfrac{\sin x}{\cos x}\)

Therefore, the tangent function is defined for all real numbers except the values where the cosine of the function is zero, since division by zero is undefined.

From inspection of the unit circle, cos(x) = 0 when x = π/2 and x = 3π/2.

The tangent function is periodic with a period of π. This means that the graph of the tangent function repeats itself at intervals of π units along the x-axis.

Therefore, if we combine the period and the undefined points, the domain of k(x) is all real numbers except x = π/2 + πn, where n is an integer.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &\pi n\le \:x < \dfrac{\pi }{2}+\pi n\quad \textsf{or}\quad \dfrac{\pi }{2}+\pi n < x < \pi +\pi n\\\textsf{Interval notation:} \quad &\left[\pi n ,\dfrac{\pi }{2}+\pi n\right) \cup \left(\dfrac{\pi }{2}+\pi n,\pi +\pi n\right)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq \dfrac{\pi}{2}+\pi n\;\; (n \in\mathbb{Z}) \right\}\\\textsf{(where $n$ is an integer)}\end{aligned}}\)

Answer:

14.6°, 165.4°

Step-by-step explanation:

We can say that x is the supplementary angle and x + 150.8 is the other angle

Supplementary angles add up to 180°

x + x + 150.8 = 180

2x = 29.2

x = 14.6 | we found one of the angles

x + 150.8 = 165.4 | find the other angle

The total surface area of solid is,

S = 220 m²

And,  The volume of the prism is, 200 m³

We have to given that;

A solid prism is shown in figure.

Since, The surface area of a prism is,

S = (2 × Base Area) + (Base perimeter × height)

Where, "S" is the surface area of the prism.

Hence, We get;

base area = 5 x 10 = 50 m²

height = 4 m

Base Perimeter = 2 (5 + 10) = 30

Hence, We get;

S = (2 x 50) + (30 x 4)

S = 100 + 120

S = 220 m²

Since, A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is expressed as;

V = base area × height.

Now, For given figure,

Volume of the prism = base area × height

base area = 5 x 10 = 50 m²

height = 4 m

Hence, Volume = 50 × 4 m³

= 200 m³

Thus, The volume of the prism is, 200 m³

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ANSWER

• x = 10.83

• ∡A = 65º

EXPLANATION

The sum of the measures of the interior angles of any triangle is 180º:

Replacing with the angles we know (B and C):

And solving for ∡A:

Then we know that ∡A = 6x, so x is:

We have that This equation simply state that P as a Function of A is equal to 0.97

From the question we are told that

P(A) = 0.97.

Generally

This equation simply state that P as a Function of A is equal to 0.97

i.e P is a Constant equation and A is a variable that changes P to 0.97

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Answer:

49 minutes

Step-by-step explanation:

Volume

v = πr²h

v = π(2.5²)4

v = 78.5 ft³

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

Gallons needed

78.5 * 7.5 = 588.75 gallons

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

Time to fill

588.75 / 12 = 49.0625

Rounded

49 minutes