A line segment has one endpoint on a circle and one endpoint at the center of the circle. What is the segment called?

A. Diameter

B. Radius

C. Chord

D. Arc

Answer:

d

Step-by-step explanation:

Final answer:

In mathematics, 'squaring the circle' means to create a square with the same area as a given circle, though it is impossible to achieve precisely due to the nature of π. When fitting a circle in a square, the side of the square is twice the radius of the circle, and the circle's area is approximately three-quarters that of the square.

Explanation:

To "square a circle" in mathematical terms traditionally means to create a square with the same area as a given circle, using only a finite number of steps with compass and straightedge. This problem is known to be impossible to solve exactly due to the transcendental nature of π (pi). However, when we discuss fitting a circle within a square, we often refer to having the diameter of the circle, which is twice the radius (2r), fit exactly across the side length of the square (a).

The area of the circle is πr², and when the circle fits within a square the area of the square is a². Since a = 2r, the area of the square can be expressed as 4r². From this, we can approximate that a circle's area would be less than the area of the square but more than half, possibly around three-quarters, thus approximately 3r².

Perimeter-wise, a circle within a square would have a circumference less than the perimeter of the square but significantly longer than a straight line passing through the center of the square. This understanding allows for practical estimations without requiring exact precision, which can be particularly useful in everyday contexts where an approximation suffices.

Answer:

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Answer:

C

Step-by-step explanation:

Answer:

The circumference is [tex]23.236\ in[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=3.7\ in[/tex]

substitute

[tex]C=2(3.14)(3.7)=23.236\ in[/tex]

To represent the situation, the function can be written as f(t) = 35000 × (1 + 0.04)^t, where t represents the number of years into the future.

To write a function in terms of t that represents the situation, we can start with the initial salary of $35,000 and then calculate the annual increase using the 4% growth rate.

We need to multiply the current salary by (1 + 0.04) to get the new salary for each year. The function can be written as:

f(t) = 35000 × (1 + 0.04)^t

Here, t represents the number of years into the future from the initial starting point.

For example, if you want to find the salary after 3 years, you can plug in t = 3 into the function.

A function that represents your annual salary starting at $35,000 and increasing by 4% each year,
[tex]S(t) = 35000 * (1 + 0.04)^t[/tex], where t is the number of years.

To create a function that represents your annual salary starting at $35,000 and increasing by 4% each year,
we use the formula for exponential growth,
[tex]final amount = initial amount * (1 + growth rate)^t^i^m^e.[/tex]
Given that your initial salary is $35,000 and the growth rate is 4% (or 0.04),
let's define the function S(t) where S represents your salary and t represents the number of years:

   [tex]S(t) = 35000 * (1 + 0.04)^t[/tex]
the initial salary=$35,000.

Convert the percentage increase to a decimal,
4% becomes 0.04.

Set up the function using the formula for exponential growth,
which is initial amount multiplied by [tex](1 + growth rate) ^t[/tex]

Thus, for any year t, the function [tex]S(t) = 35000 * (1 + 0.04)^t[/tex] calculates your annual salary.

In right triangle the leg is geometrical mean of its projection on the hypotenuse and the hypotenuse. Thus,

[tex] AB^2=BD\cdot BC [/tex].

Substitude BC=16, BD=9, then

[tex] AB^2=9\cdot 16,\\ AB^2=144,\\ AB=12 [/tex].

Answer: AB=12

The area of triangle ABC, given that it is similar to triangle DEF with an area of 90, cannot be estimated without the ratio of corresponding sides. Areas of similar triangles are proportional to the square of the ratio of their corresponding sides.

To estimate the area of triangle ABC given that triangle ABC is similar to triangle DEF, and the area of triangle DEF is 90, we first need to understand that the areas of similar triangles are proportional to the square of the ratio of their corresponding sides. However, without knowing the specific ratio of the corresponding sides of triangles ABC and DEF, we cannot calculate the exact area of triangle ABC.

For example, if we knew that every side of triangle ABC was twice as long as the corresponding sides of triangle DEF, the area of triangle ABC would be 4 times the area of triangle DEF, because the area is proportional to the square of the side lengths (2 squared is 4). In this case, if the area of DEF is 90, then the area of ABC would be 90 × 4 = 360.

Without the ratio of the sides, we can't directly calculate the area of triangle ABC from the area of triangle DEF. The relationship between similar triangles and their areas illustrates an important geometric principle, but requires specific information about the ratio of corresponding linear dimensions to make an estimation.

The perimeter of Mark's deck in real life is calculated by converting the layout measurements to actual measurements using the scale factor and then applying the perimeter formula. The perimeter is found to be 160 meters.

To calculate the perimeter of Mark's deck, which is represented on a layout where the scale is 1 centimeter = 10 meters, we use the perimeter formula for a rectangle: Perimeter (P) = 2 * (length + width). Since both the length and width of Mark's deck are provided as 4 centimeters each, and each centimeter corresponds to 10 meters in reality, we first convert the measurements from centimeters to meters by multiplying them by the scale factor.

Length in meters = 4 cm * 10 meters/cm = 40 meters
Width in meters = 4 cm * 10 meters/cm = 40 meters

Now, calculate the perimeter:

P = 2 * (40 meters + 40 meters)
P = 2 * 80 meters
P = 160 meters

The real-life perimeter of Mark's deck is 160 meters.

A person who makes faces all day is often described as expressive or animated, and may be humorously termed a 'mugger' or 'face-puller'. Facial expressions are crucial for conveying emotion in human interaction and can be particularly striking in literature and dramatic performances.

The question 'What do you call a person who makes faces all day long?' is asking about a term or description for someone who frequently changes their facial expressions. While there is no specific term that describes this behavior in a clinical or professional sense, in a colloquial context, you might call such a person expressive, animated, or if the expressions are humorous or exaggerated, a 'mugger' or 'face-puller'. In literature and drama, characters known for their expressive faces can bring a story to life or provide comic relief.

Facial expressions are an integral part of human communication. They can underscore the emotional state of a person, such as the sense of pride on the face of a monomaniacal king, the devotion seen in a religious fanatic, or the terror described in the imagery of wallpaper patterns appearing to have expressive eyes. Whether in social interactions, literature, or public speaking, the alignment of facial expressions with spoken words is important for conveying meaning and emotion.

Answer:

198

Step-by-step explanation:

Of means multiply and 22% as a decimal is 0.22, so multiply 0.22 by 900.

900*0.22=198

Answer:

5 to the power of 8

Step-by-step explanation:

To find the perimeter of the quarter circle, the radius is first calculated using the area, and then the perimeter formula for a circle is applied, adjusting the final calculation to include the straight edges of the quarter circle.

The student has provided the area of a quarter circle and is seeking to find its perimeter. The area of the full circle can be found by multiplying the quarter circle area by 4, yielding an area of 3.14 square kilometers (since the area of a quarter circle is 0.785 square kilometers). Using the formula for the area of a circle, A = πr², we can solve for the radius (r).

Let's calculate the radius of the circle:

Now, the perimeter (or circumference) of the full circle is given by the formula P = 2πr. For a quarter circle, the perimeter includes the arc of the quarter circle and the two radii.

The perimeter of the quarter circle is thus:

But since we know the measurements are to a certain precision, we must adjust our answer accordingly:

The final perimeter of the quarter circle, rounded to an appropriate number of significant figures based on the original measurement given, is approximately 3.57 km.