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2 years ago

The circle below has center P, and its radius is 3 m. Given that m 2 QPR=170°, find the length of the minor arc OR.

Mathematics

1 answer:

QveST [7]2 years ago

4 0

Any smooth curve connecting two points is called an arc. The length of the arc m∠QPR is 2.8334π m.

<h3>What is the Length of an Arc?</h3>

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

$\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}$

where

θ is the angle, that which arc creates at the centre of the circle in degree.

Given the radius of the circle is 3m, while the angle made by the arc at the centre of the circle is 170°. Therefore,

The length of an arc = 2πr×(θ/360°) = 2π × 3 ×(170/360°) = 2.8334π m

Hence, the length of the arc m∠QPR is 2.8334π m.

Learn more about Length of an Arc:

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What is the sum of the first 20 terms of the arithmetic sequence shown? \displaystyle \frac{1}{3} 3 1 , \displaystyle \frac{2}

Murrr4er [49]

Answer:

Step-by-step explanation:

$a_1$ = First term = $\dfrac{1}{3}$

$d$ = Common difference = $\dfrac{2}{3}-\dfrac{1}{3}=\dfrac{1}{3}$

$n$ = Number of terms = 20

Sum of arithmetic progression is given by

$S=\dfrac{n}{2}[2a_1+(n-1)d]\\\Rightarrow S=\dfrac{20}{2}\times (2\times \dfrac{1}{3}+(20-1)\dfrac{1}{3})\\\Rightarrow S=70$

The sum of the first 20 terms of the arithmetic sequence is 70.

5 0

3 years ago

If tan 0 = -2.5, then cot 0 =<br> = ?

trapecia [35]

The answer shld be 0.99

4 0

3 years ago

Assume that in january 2013, the average house price in a particular area was $289,400. in january 2000, the average price was $

PtichkaEL [24]

The problem is an arithmetic sequence with:
a₁ = 206,300
an = 208,400

n = 2013 - 2000
n = 13

To find the annual increase, use this following formula
an = a₁ + d(n - 1)
d represents the annual increase

Input the numbers
an = a₁ + d(n - 1)
289,400 = 206,300 + d(13 - 1)
289,400 = 206,300 + 12d
289,400 - 206,300 = 13d
83,100 = 12d
12d = 83,100
d = 83,100/12
d = 6,925

The annual increase is $6925

7 0

3 years ago

El triángulo ABC es equilátero y L, M y N son los puntos medios de BC, AB y CA respectivamente. Si MN = 3, ¿cuál es el valor de

Flauer [41]

The value of <u>ML = 3</u>, using the mid-point theorem of triangles.

According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."

In the question, we are given that triangle ABC is an equilateral triangle, and L, M, and N are the midpoints of BC, AB, and CA respectively.

Thus, by the midpoint theorem, we can say that:

MN || BC, and MN = (1/2)BC,
ML || AC, and ML = (1/2)AC, and
NL || AB, and NL = (1/2)AB.

Assuming AB = BC = AC = x units, we get:

MN = (1/2)BC = x/2,
ML = (1/2)AC = x/2, and
NL = (1/2)AB = x/2.

Thus, the triangle LMN is an equilateral triangle.

Thus, MN = ML = NL.

Given MN = 3, we can write the value of ML = 3.

Thus, the value of <u>ML = 3</u>, using the mid-point theorem of triangles.

Learn more about the mid-point theorem of triangle at

brainly.com/question/9635025

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The given question is in Spanish. The question in English is:

"Triangle ABC is equilateral and L, M, and N are the midpoints of BC, AB, and CA respectively. If MN = 3, what is the value of ML?"

4 0

2 years ago

Which function is a horizontal compression of its parent function f(x)=x^7 by a factor of 4

evablogger [386]

Answer:

$r(x)=(4x)^7$

Step-by-step explanation:

For a horizontal compression, we multiply whole numbers greater than 1 in front of $x$ of the given function.
For horizontal expansion, we multiply by the reciprocal of the number for horizontal compression, in front of $x$ of the function.

For example,

If we wanted to <u>horizontally compress</u> $y=x^2$ , we would multiply by 4 to get $y=(4x)^2$ , and

if we wante to <u>horizontally expand</u> $y=x^2$ , we would multiply by $\frac{1}{4}$ to get $y=(\frac{1}{4}x)^2$

Since this question asks for horizontal compression, we multiply the $x$ of the function by 4. So the function we need is $f(x)=(4x)^7$ . The second choice is correct.

8 0

3 years ago