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Paul [167]
2 years ago
11

The circle below has center P, and its radius is 6in. Given that =m∠QPR170°, find the length of the major arc QSR.

Mathematics
1 answer:
kenny6666 [7]2 years ago
7 0

The length of the major arc QSR is 39.77 inches

<h3>How to find the length of the major arc QSR?</h3>

The given parameters are:

m∠QPR = 170 degree

Radius, r = 6 inches

The length of the major arc QSR is calculated as:

Arc length = (360 - Angle/360) * 2πr

Substitute the known values in the above equation

Arc length = (360 - 170/360) * 2 * 3.14 * 6

Evaluate the difference

Arc length = (190/180) * 2 * 3.14 * 6

Evaluate the product

Arc length = 39.77

Hence, the length of the major arc QSR is 39.77 inches

Read more about arc lengths at:

brainly.com/question/2005046

#SPJ1

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Let T be the plane-2x-2y+z =-13. Find the shortest distance d from the point Po=(-5,-5,-3) to T, and the point Q in T that is cl
GaryK [48]

Answer:

d=10u

Q(5/3,5/3,-19/3)

Step-by-step explanation:

The shortest distance between the plane and Po is also the distance between Po and Q. To find that distance and the point Q you need the perpendicular line x to the plane that intersects Po, this line will have the direction of the normal of the plane n=(-2,-2,1), then r will have the next parametric equations:

x=-5-2\lambda\\y=-5-2\lambda\\z=-3+\lambda

To find Q, the intersection between r and the plane T, substitute the parametric equations of r in T

-2x-2y+z =-13\\-2(-5-2\lambda)-2(-5-2\lambda)+(-3+\lambda) =-13\\10+4\lambda+10+4\lambda-3+\lambda=-13\\9\lambda+17=-13\\9\lambda=-13-17\\\lambda=-30/9=-10/3

Substitute the value of \lambda in the parametric equations:

x=-5-2(-10/3)=-5+20/3=5/3\\y=-5-2(-10/3)=5/3\\z=-3+(-10/3)=-19/3\\

Those values are the coordinates of Q

Q(5/3,5/3,-19/3)

The distance from Po to the plane

d=\left| {\to} \atop {PoQ}} \right|=\sqrt{(\frac{5}{3}-(-5))^2+(\frac{5}{3}-(-5))^2+(\frac{-19}{3}-(-3))^2} \\d=\sqrt{(\frac{5}{3}+5))^2+(\frac{5}{3}+5)^2+(\frac{-19}{3}+3)^2} \\d=\sqrt{(\frac{20}{3})^2+(\frac{20}{3})^2+(\frac{-10}{3})^2}\\d=\sqrt{\frac{400}{9}+\frac{400}{9}+\frac{100}{9}}\\d=\sqrt{\frac{900}{9}}=\sqrt{100}\\d=10u

7 0
3 years ago
Help ASAP!!!<br> Please and thank you so much
PilotLPTM [1.2K]
Rectangle on the left = 3 × 4 = 12

Rectangle in the middle = 3 × 2 = 6

Rectangle on the right = 4 × 3 = 12

Add:

12 + 6 + 12 = 30

Answer = 30

Hope this helped☺☺
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3 years ago
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Anita plans to give her husband 3 shirts for his birthday. She narrows the search to 3 shirts from a selection of 17 shirts at D
Lunna [17]

Using the combination formula, it is found that she can select the shirts in 775,200 ways.

The order in which the shirt are chosen is not important, hence, the <em>combination formula</em> is used to solve this question.

Combination formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by:

C_{n,x} = \frac{n!}{x!(n-x)!}

In this problem:

  • 3 shirts from a set of 17.
  • Then, 3 shirts from a set of 20.
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T = C_{17,3} \times C_{20,3} = \frac{17!}{3!14!} \times \frac{20!}{3!17!} = 680 \times 1140 = 775200

She can select the shirts in 775,200 ways.

To learn more about the combination formula, you can check brainly.com/question/25821700

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Andreyy89

Answer:

x < -8

Step-by-step explanation:

-x - 10 > 14 + 2x

Subtract 2x from both sides;

-3x - 10 > 14

Add 10 to both sides;

-3x > 24

Divide both sides by -3

The sign switches when divide by a negative number.

x < -8

6 0
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