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Ludmilka [50]
3 years ago
7

An 8-inch dinner knife is sitting on a circular plate so that its ends are on the edge of the plate. If the minor arc that is in

tercepted by the knife measures 120 degrees, find the length of the diameter of the plate. Round your final answer to two decimal places.
Mathematics
1 answer:
ankoles [38]3 years ago
7 0

The diameter of the plate is 9.24 inches

Step-by-step explanation:

Let us consider the radius to be 'r'

Angle = 120°

Chord length = 8 inches

Chord length = 2rsin(θ/2)

8 = 2r sin(120/2)

8 = 2r sin60°

8/2 = r (√3/2)

4/(√3/2) = r

r = 8/√3

r = 8/1.73

r = 4.62 inches

Diameter of the plate = 2(4.62)

= 9.24 inches

The diameter of the plate is 9.24 inches

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E is the midpoint of DF, DE = 2x + 4, and EF = 3x + 1. Find DE, EF, and DF.
Agata [3.3K]
When there is a midpoint in a line segment, the two segments that are then produced have to be equal. So that means that because E is a midpoint of DF, DE=EF.
Set up the equation.
DE=EF
2x+4=3x+1
Then solve for x.
x=3
Then plug it back in the equation to find DE and EF.
DE=2x+4=2(3)+4=10
Because DE=EF then EF is also 10.
DF is made from the addition of DE and EF so DF is twice EF.
DF= 20

DE= 10, EF= 10, DF= 20

Hope this helps.
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3 years ago
What is the answer for question 7?
Norma-Jean [14]
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Thus, the tangent of 90° minus <span>θ also equals 5.</span>
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3 years ago
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kirill [66]

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13.28

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5 0
3 years ago
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Write an equation of a line that goes through the point (-9, 3), and is perpendicular to the line 3x + y = 5
Vlad [161]
To find the slope of the line, first find the slope of 3x + y = 5, and then its opposite reciprocal.

3x + y = 5
y = -3x + 5
the slope of 3x + y = 5 is -3.

the slope is -3, so the opposite reciprocal slope is 1/3.

the equation of any line is y = ax + b
to find this line, y = 3, x = -9, and the slope is 1/3.

3 = -9a + b
3 = -9 (1/3) + b
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3 0
3 years ago
PLEASE HELP WITH THIS WILL GET EXTRA POINTS
Aleks [24]

Answer:

Hight

1.2

2.4

3.6

4.8

5.9

6.4

7.3

8.6

Step-by-step explanation:

Formula used

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7-135

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C%

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