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2 years ago

Show that vertical opposite angles are equal

1 answer:

4 0

Vertical Angles: Theorem and Proof
Theorem: In a pair of intersecting lines the vertically opposite angles are equal. It can be seen that ray \overline{OA} stands on the line \overleftrightarrow{CD} and according to Linear Pair Axiom, if a ray stands on a line, then the adjacent angles form a linear pair of angles.

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Show that the maximum rate of change, with respect to radius, of the volume of a deflating balloon is four times the sphere's in

dmitriy555 [2]

Step-by-step explanation:

Let's say R is the initial radius of the sphere, and r is the radius at time t.

The volume of the sphere at time t is:

V = 4/3 π r³

Taking derivative with respect to radius:

dV/dr = 4π r²

This is a maximum when r is a maximum, which is when r = R.

(dV/dr)max = 4π R²

This is 4 times the sphere's initial great circle area, but not the great circle circumference. The problem statement contains an error.

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2 years ago

Which sequence follows the rule an =an–1 + 7?

Akimi4 [234]

Answer:

Step-by-step explanation:

using the rule : $a_{n}$ = $a_{n-1}$ + 7

sequence A with a₁ = 11

a₂ = a₁ + 7 = 11 + 7 = 18

a₃ = a₂ + 7 = 18 + 7 = 25

a₄ = a₃ + 7 = 25 + 7 = 32

sequence A is generated using the rule

sequence B with a₁ = 17

a₂ = a₁ + 7 = 17 + 7 = 24

a₃ = a₂ + 7 = 24 + 7 = 31

a₄ = a₃ + 7 = 31 + 7 = 38

sequence B is not generated using the rule

sequence C with a₁ = - 15

a₂ = - 15 + 7 = - 8

a₃ = a₂ + 7 = - 8 + 7 = - 1

a₄ = a₃ + 7 = - 1 + 7 = 6

sequence C is not generated using the rule

sequence D with a₁ = - 9

a₂ = a₁ + 7 = - 9 + 7 = - 2

a₃ = a₂ + 7 = - 2 + 7 = 5

a₄ = a₃ + 7 = 5 + 7 = 12

sequence D is not generated using the rule

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2 years ago

What is (5/9×(°F-32))

djyliett [7]

Answer:

32º

Step-by-step explanation:

Fº-32 ×5/9

5/9Fº-160/9

5/9Fº =160/9

(5Fº)9=9(160)

45Fº=1440

divide both sides by 45

Fº=32

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2 years ago

Hannah reads 3 pages every 8 minutes. Write an equation that shows the relationship between the number of pages she reads (p) an

PtichkaEL [24]

8/3p=m is the equation.

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2 years ago

Solve for B:<br><br> 1/5b=d+f

marshall27 [118]

Answer:

b=5d+5f

solve for b by simplifying both sides and then isolating the variable.

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1 year ago

Read 2 more answers

Show that vertical opposite angles are equal​

Show that vertical opposite angles are equal