How does quantitative information differ from qualitative information.

We conclude that f(x) is discontinuous at x = 0 for the given f(x) having properties-limit lim x→3 f(x) = 5 lim x→[infinity] f(x) = -1 lim x→0 f(x) x-0 does not exist. f(0) = 15. f(x) is never equal to zero.

Given that, Suppose f(x) has ALL of the following properties:

lim x→3 f(x) = 5 lim x→[infinity] f(x) = -1 lim x→0 f(x) x-0 does not exist.

f(0) = 15.

f(x) is never equal to zero.

We need to explain why f(x) is discontinuous.

For a function to be continuous, it must meet three requirements:

that the function is defined,

that the limit exists, and

that the function and limit are equal at every point.

If any one of these requirements isn't met, the function is discontinuous.

As per the given values, f(0) = 15, which is a finite value.

But, the left-hand limit and right-hand limit of f(x) as x approaches zero do not exist.

Thus, the function is discontinuous at x = 0.

Hence, we conclude that f(x) is discontinuous at x = 0.

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The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second

The length of the ladder = 17

Consider the length of the base as x and the height is h

The rate at which the ladder is sliding = 5 feet per second

dx/dt = 5

Apply the Pythagorean theorem

x^2 + h^2 = 17^2

h^2 = 289 - x^2

h = \(\sqrt{289-x^2}\)

The rate of change of height with respect to x is

dh/dx = - x / (289 - x^2)^(1/2)

dh/dt = dh/dx × dx/dt

Substitute the values in the equation

= - 15 / (289 - 15^2)^(1/2) × 5

= -15/8 × 5

= -75/8 feet per second

Therefore, the rate of change of height when x = 15 is -75/8 feet per second

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Answer:

Step-by-step explanation:

bearing is the angle which a line makes with the north.

Answer:

C.)

Step-by-step explanation:

A function defines one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) means that y varies according to whatever value x takes on. A causal relationship is often implied (i.e. "x causes y"), but does not *necessarily* exist.

Answer:

|3x+4| +6

Step-by-step explanation:

f(x) = |3x+4| +2

g(x) =4

f(x) + g(x) =  |3x+4| +2 +4

               =  |3x+4| +6

These three vectors satisfy proj_w u = proj_w v = ⟨0, 2, 5⟩.

To find three different nonzero vectors u, v, and w in R^3 such that proj_w u = proj_w v = ⟨0, 2, 5⟩, we can use the properties of vector projection and the given information.

Let's start by finding u and v.

We know that the projection of vector u onto vector w is ⟨0, 2, 5⟩, so we can write:

proj_w u = (u · w) / ||w||² * w = ⟨0, 2, 5⟩

Since the dot product (u · w) is involved, we can choose any vector u that is orthogonal to ⟨0, 2, 5⟩. For simplicity, let's choose u = ⟨1, 0, 0⟩.

Now, let's find v.

We know that the projection of vector v onto vector w is also ⟨0, 2, 5⟩, so we can write:

proj_w v = (v · w) / ||w||² * w = ⟨0, 2, 5⟩

Again, we can choose any vector v that is orthogonal to ⟨0, 2, 5⟩. Let's choose v = ⟨0, 1, 0⟩.

Now, we have u = ⟨1, 0, 0⟩ and v = ⟨0, 1, 0⟩. To find vector w, we need to ensure that the projections of both u and v onto w are equal to ⟨0, 2, 5⟩.

For proj_w u, we have:

(1a + 0b + 0c) / (a² + b² + c²) * ⟨a, b, c⟩ = ⟨0, 2, 5⟩

Simplifying, we get:

a / (a² + b² + c²) * ⟨a, b, c⟩ = ⟨0, 2, 5⟩

From the x-component, we have:

a / (a² + b² + c²) * a = 0

This equation suggests that a must be 0 since we want a non-zero vector. Therefore, a = 0.

Now, we have:

0 / (0² + b² + c²) * ⟨0, b, c⟩ = ⟨0, 2, 5⟩

From the y-component, we have:

b / (b² + c²) = 2

From the z-component, we have:

c / (b² + c²) = 5

Solving these two equations simultaneously, we can find suitable values for b and c. One possible solution is b = 1 and c = 5.

Therefore, we have the following vectors:

u = ⟨1, 0, 0⟩

v = ⟨0, 1, 0⟩

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As per the angle sum property of quadrilateral, then values of x is 245 and the value of y is 341

Angle sum property of quadrilateral:

The angle sum property states that the sum of all the angles of the quadrilateral is 360 degree.

Given,

The angles of the quadrilateral are 5x degrees, (4y minus 2 )degrees, (13x plus 10 )degrees, and 10y degrees.

Now we have to write and solve a system of linear equations to find the values of x and y.

While we looking into the given angles, then we get the values

=> 5x°

=> (4y - 2)°

=> (13x + 10)°

=> 10y°

We know that, the sum of all the angles of the quadrilateral is 360°.

So, it ca be written as,

=> 5x° + (4y - 2)° + (13x+ 10)° + 10y° = 360°

=> 18x° + 14y° - 8° = 360°

=> 18x° + 14y° = 354°

When we divide all of them by 2, then we get the equation as,

=> 9x° + 7y° = 177°

Now we have to rewrite the given equation as,

=> 9x° = 177° - 7y°

=> x° = (177° - 7y°)/9

Apply these value on the angles, then we get,

=> 13(177 - 7y)/9 = -10

=> 13(177 - 7y) = 90

=> -7y = -90 - 2301

=> 7y = 2391

=> 341

Then the value of x is

=> 245

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Answer:

1.50    1.5

Step-by-step explanation:

beacuse its both of the wingspans together

Answer:

i think 1.5 inch

Step-by-step explanation:

0.75*2

this is because 1 wing is . 75 inch ACROSS so if two wings you will multiply it into two

Answer:

Assuming you mean "American History V World History"

American History tends to focus on the history of the United States, beginning largely with the colonial era and tracking forwards towards the present. It's largely a national history. World History, on the other hand, is far more encompassing, both geographically as well as temporally.

Assuming you mean "Global History V World History"

World history encompasses a history that is not necessarily completely interconnected through globalization, while global history examines this specific history of inter-connectivity. World History examines the individual histories of different locations around the world, whereas Global History examines how those locations are connected.

Answer:

World history encompasses a history that is not necessarily completely interconnected through globalization, while global history examines this specific history of interconnectivity. ... Furthermore, the fluid nature of what world and global histories mean ensures a number of disagreements with these definitions.

Answer:

12

Step-by-step explanation:

Divide both sides by 6 to isolate x

Answer:12

Step-by-step explanation:

divide 6 from 72

The implicit equation for the plane passing through the points (−4,−1,1) , (0,3,−4) , and (0,3,6) is: 2x - y + 3 = 0

To find the implicit equation for the plane passing through the points (−4,−1,1), (0,3,−4), and (0,3,6), we can first find two vectors that lie on the plane. We can choose the vectors formed by subtracting the first point from the other two points:

v1 = <0 - (-4), 3 - (-1), -4 - 1> = <4, 4, -5>

v2 = <0 - (-4), 3 - (-1), 6 - 1> = <4, 4, 5>

We can then find the normal vector of the plane by taking the cross product of these two vectors:

n = v1 x v2 = <4, 4, -5> x <4, 4, 5> = <-40, 20, 0>

The equation of the plane can then be written in the form:

-40(x - x0) + 20(y - y0) = 0

where (x0, y0, z0) is any point on the plane. We can use any of the three points given to find the equation of the plane. Let's use the point (0, 3, -4):

-40(x - 0) + 20(y - 3) = 0

Simplifying this equation, we get:

-40x + 20y - 60 = 0

Dividing both sides by -20, we get the final implicit equation of the plane:

2x - y + 3 = 0

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Answer: B) 37.68

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

Plugging in the given radius of 6 centimeters, we get:

C = 2πr

C = 2π(6)

C ≈ 37.68

Answer:

$1.56

Step-by-step explanation:

1.50 times 0.04 is 0.06

1.50+0.06

$1.56

Answer:

ANswer is $2.10.

Step-by-step explanation:

The tax is $.60 and you add that to $1.50.

Answer:

D. 74⁻⁶ (74^-6)

Step-by-step explanation:

Looking at the expression, I remember the following: 1 over an exponent (as a fraction) is the same thing as a negative exponent. None of these answers involve an exponent except for D (although A does involve a negative number). So D, which is 74⁻⁶, is the answer here.

Answer:

40.9

Step-by-step explanation:

In ΔRST, the measure of ∠T=90°, ST = 71 feet, and RS = 94 feet. Find the measure of ∠S to the nearest tenth of a degree.

To write a number in scientific notation you must know:

1. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10

2. A number can be converted to scientific notation by increasing the power of 10 by one for each place the decimal point is shifted to the left.

Then so:

Answer: Margo does 48 activities in 4 weeks.

Step-by-step explanation:

In the calendar,

Red dots represent homework, yellow dots represent work, and green dots represent practice.

On a typical week , she uses 5 red dots, 3 yellow dots, and 4 green dots.

That means , total activity he does in a week = 5+3+4=12

Then, total activities in 4 weeks = 4 x 12 = 48

Hence, Margo does 48 activities in 4 weeks.

Solution:

If we choose a usual coordinate axis, an object going down would be traveling a negative distance, so a possible answer would be:

C. skiing 161 ft down a mountain.

On the other hand, An expense of money involves a waste of money, which is negative. So another possible answer would be:

D. spending $spending $161 on vacation.

Then, we can conclude that the correct answer would be:

C. skiing 161 ft down a mountain.

D. spending $spending $161 on vacation.

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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The answer would be 27/8.

D. None of these, as neither option B nor option C can be obtained using the Law of Detachment.

The Law of Detachment states that if a conditional statement "if p, then q" is true and p is true, then q must also be true.

Analyzing the given options:

A. The conclusion "There is no school" can be obtained by applying the Law of Detachment to the given information, as it matches the format of the law: "If today is Saturday (p), then there is no school (q)." Since today is Saturday (p), the conclusion that "There is no school" (q) can be derived using the Law of Detachment.

B. The conclusion "He is able to buy a new set of headphones" is not directly obtained by using the Law of Detachment. It involves an additional conditional statement and is not in the form of the given "if p, then q" structure.

C. The conclusion "George lives in both Brick and Ocean County" cannot be derived using the Law of Detachment. It is not in the form of a conditional statement, and there is no given information that connects George's residence to the conditional statement provided. Therefore, D is the right answer. None of them are possible utilizing the Law of Detachment, as neither option B nor option C can be obtained. Therefore, Option D is correct.

The question was incomplete. find the full content below:

Which of the following conclusions is true AND obtained by using the Law of Detachment

A. If today is Saturday, then there is no school.

Today is Saturday.

There is no school.

B. If you work 8 hours, then you'll earn $100.

If you earn $100, you'll be able to buy a new set of headphones.

Jonathan works 8 hours.

He is able to buy a new set of headphones.

C. If a person lives in Long Beach Island, then they live in Ocean County.

Brick is in Ocean County.

George lives in both Brick and Ocean County

D. None of these.

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The union of  sets a and b is a ∪ b, includes all the numbers that satisfy conditions of either a or b. Here a ∪ b consists all real numbers that fall within ranges −3 ≤ x ≤ 0 or −1 < x < 2, resulting in the interval −3 ≤ x < 2.

Set a is defined as {x ∈ ℝ | −3 ≤ x ≤ 0}, which represents the closed interval from -3 to 0, including both endpoints. Set b is defined as {x ∈ ℝ | −1 < x < 2}, representing an open interval from -1 to 2, excluding both endpoints.

To find the union of a and b, we combine the elements that satisfy either the conditions of set a or the conditions of set b. In this case, the union of a and b (a ∪ b) consists of all real numbers that fall within the ranges −3 ≤ x ≤ 0 or −1 < x < 2.

Combining these intervals, we obtain the interval −3 ≤ x < 2. This means that a ∪ b includes all real numbers from -3 up to (but not including) 2, covering the interval −3 ≤ x < 2.

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Answer:

isnt like 40 the answer (im sorry if im wrong 3rd grader)

Step-by-step explanation:

The break-even point is the level of output at which total revenue (TR) equals total cost (TC). In this case, with TR(x) = 20x and TC(x) = 120 + 10x, we need to find the value of x where TR(x) = TC(x).

To find the break-even point, we set TR(x) equal to TC(x) and solve for x.
TR(x) = TC(x) can be expressed as:
20x = 120 + 10x
Simplifying the equation, we combine like terms:
20x - 10x = 120
10x = 120
To isolate x, we divide both sides of the equation by 10:
x = 12
Therefore, the break-even point occurs when x is equal to 12. At this level of output, the total revenue is equal to the total cost.

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Answer:

First, we need to define a zero in the vertical position.

Let's define the zero as the ocean's surface.

"A scuba diver dove 63 feet below the ocean's surface."

Then the scuba's position at this moment was:

P = -63ft

"He then ascended 27 feet to under an underwater cave."

The new position will be:

P = -63ft + 27ft = -36ft

And here is the entrance of the underwater cave.

Then we can conclude that the depth of the entrance of the underwater cave is 36ft deep, or that the entrance is 36ft below the ocean's surface.

Answer:

24.549 pounds

Step-by-step explanation:

The power series expansion for 1/z around z = 1 + i is given by:

1/z = (1 - i)/(2 + 2i) + (z - (1 + i))/(2 + 2i)^2 + (z - (1 + i))^2/(2 + 2i)^3 + ...

To find the power series expansion for 1/z around z = 1 + i, we can use the geometric series expansion formula. The formula states that for a function f(z), the power series expansion around a point z = a is given by:

f(z) = f(a) + f'(a)(z - a) + f''(a)(z - a)^2/2! + f'''(a)(z - a)^3/3! + ...

In this case, we have f(z) = 1/z and a = 1 + i. Taking the derivatives of 1/z and evaluating them at z = 1 + i, we can substitute them into the formula to obtain the power series expansion.

The expansion starts with the term (1 - i)/(2 + 2i), which represents the constant term. The subsequent terms involve higher powers of (z - (1 + i)), divided by powers of (2 + 2i). Each term in the expansion corresponds to the derivative of 1/z evaluated at z = 1 + i, multiplied by the appropriate power of (z - (1 + i)).

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Answer:

A

Step-by-step explanation: