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3 years ago

Points N and R both lie on circle O. Line segment RQ is tangent to the circle at point R.

Mathematics

2 answers:

ANEK [815]3 years ago

4 0

Answer:

Perimeter ΔRON = 18.66 units

Step-by-step explanation:

Complete Question has these information given as well:

Circle with center O
RN = QN
RQ = $5\sqrt{3}$
ON = 5 units
RQ is tangent

Now, we draw an image according to the information given. THe image drawn is attached.

Looking at the figure, we can say the perimeter of triangle RON would be:

RON = OR + ON + RN

We know according to tangent theorem, QN = QR

RN is equal to that as well and RN = $5\sqrt{3}$

Now,

OR and ON is the radius, which is "5"

Perimeter of RON = 5 + 5 + $5\sqrt{3}$ = 10 + $5\sqrt{3}$ = 18.66 units

Perimeter ΔRON = 18.66 units

LUCKY_DIMON [66]3 years ago

4 0

Answer:

18.7 units

Step-by-step explanation:

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Find the slope of the tangent line to the given polar curve at the point specified by the value of θ

MariettaO [177]

The given curve has equation

r(θ) = 9 + 8 cos(θ)

and its derivative is

dr/dθ = -8 sin(θ)

When θ = π/3, we have r (π/3) = 13, and dr/dθ (π/3) = -4√3.

Differentiate these with respect to θ :

dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)

dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)

In polar coordinates, we have

y(θ) = r(θ) sin(θ)

x(θ) = r(θ) cos(θ)

and when θ = π/3, we have y (π/3) = 13√3/2 and x (π/3) = 13/2.

The slope of the tangent line to the curve is dy/dx. By the chain rule,

dy/dx = dy/dθ • dθ/dx = (dy/dθ) / (dx/dθ)

dy/dx = (dr/dθ sin(θ) + r(θ) cos(θ)) / (dr/dθ cos(θ) - r(θ) sin(θ))

When θ = π/3, the slope is

dy/dx = (-4√3 sin(π/3) + 13 cos(π/3)) / (-4√3 cos(π/3) - 13 sin(π/3))

dy/dx = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))

dy/dx = - 1/(17√3)

So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is

y - 13√3/2 = -1/(17√3) (x - 13/2)

y = -(x - 338)/(17√3)

4 0

2 years ago

5.5 times a number is fourteen

Anni [7]

Answer:

x = 2.55 (rounded)

x = 2. 5454545455 (exact)

Step-by-step explanation:

We can change this sentence, into a mathematical expression and solve:

5.5 · x = 14

x = 14 / 5.5

x = 2.5454545

x = 2.55 (rounded)

Hope this helps!!

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3 years ago

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Marat540 [252]

Answer:

3.5

Step-by-step explanation:

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13. 27 - 21 =

Verdich [7]

13. 6

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2 years ago

Find the second, fifth, and ninth terms of the sequence. an = -7 + (n - 1) 4

castortr0y [4]

Answer:

- 3, 9, 25

Step-by-step explanation:

To find the required terms of the sequence substitute n = 2, 5, 9 into the given rule, that is

$a_{2}$ = - 7 + (2 - 1)4 = - 7 + (1 × 4) = - 7 + 4 = - 3

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5 0

3 years ago