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2 years ago

The figure shows a circle circumscribed around a triangle.

Mathematics

1 answer:

e-lub [12.9K]2 years ago

4 0

Option B is right perpendicular bisectors of the sides of the triangle

<h3>What circumcircle?</h3>

If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle. We have in a triangle there are some properties inherent.

One is the perpendicular bisectors of all sides are concurrent. These three concur at a point called the circumcentre of the triangle.

When we draw a perpendicular bisector for a side AB, we get that all points on the perpendicular bisector are equidistant from A and B.

When we take the point of intersection of the perpendicular bisector of AB and BC, we have the intersecting point S(say) is equidistant from A and B and also from B and C

In short, this is equidistant from all 3 vertices and hence is the centre of the circumcircle of triangle ABC

Therefore Option B is right perpendicular bisectors of the sides of the triangle.

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An arch is in the shape of a parabola. It has a span of 100 feet and a maximum height of 25 ft.

faltersainse [42]

Answer:

$y=-\frac{1}{100}(x-50)^2+25$

the height of the arch 10 feet from the center is 24 feet

Step-by-step explanation:

An arch is in the shape of a parabola. It has a span of 100 feet, the vertex lies at the center 50 and the maximum height of 25 ft.

Vertex at (50,25)

vertex form of the equation is

$y=a(x-h)^2+k$ , (h,k) is the center

$y=a(x-50)^2+25$

the parabola starts at (0,0) that is (x,y)

$0=a(0-50)^2+25$

subtract 25 from both sides

$-25=a(-50)^2$

$-25=a(2500)$

divide both sides by 2500

$a=-\frac{1}{100}$

$y=-\frac{1}{100}(x-50)^2+25$

the height of the arch 10 feet from the center.

center is at 50, 10 feet from the center so x=40 and x=60

$y=-\frac{1}{100}(40-50)^2+25$

y=24

the height of the arch 10 feet from the center is 24 feet

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3 years ago

Solve 7 ÷ one half = ___. Question 1 options: 14 15 24 40

Norma-Jean [14]

Answer:

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Step-by-step explanation:

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2 years ago

Use trig identities to transform the left side of the equation to the right side.

Taya2010 [7]

Answer and explanation

(1+sinθ)(1-sinθ)=cos²θ

We are to prove that the left hand side is equal to the right hand side.

(1+sinθ)(1-sinθ) = 1(1-sinθ) + sinθ(1-sinθ)

= 1 - sinθ + sinθ - sin²θ

= 1 - sin²θ

From the trigonometric identity sin²θ + cos²θ = 1,

1 - sin²θ = cos²θ

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3 years ago

One mile is approximately kilometres

allsm [11]

Answer:

1 mile ~ 1.60934 kilometers

Step-by-step explanation:

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2 years ago

Read 2 more answers

A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at

vitfil [10]

Complete question

A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.

What is the rate of change of the distance between the bottom of the ladder and the wall at that instant(in meters per minute)

Answer:

$\frac{dx}{dt}=11.94m/min$