The three perpendicular bisectors of a triangle intersect at the _______.

1 answer:

7 0

The three perpendicular bisectors of a triangle intersect at the A) Circumcenter

Explanation :
A circle which passes through all three vertices of a triangle also "Circumscribed circle".

The circumcircle always passes through all three vertices of a triangle. Its center is at the point where all the perpendicular bisectors of the triangle's sides meet. This center is called the circumcenter.

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Use calculus to find the volume of the following solid S:

Troyanec [42]

S casts a "shadow" on the x-y plane given by the set

$S' = \left\{(x,y) ~:~ -1 \le x \le 1 \text{ and } x^2 \le y \le 1\right\}$

Each cross section is a square whose side length is determined by the vertical distance between y = 1 and y = x², which is |1 - x²|. But since -1 ≤ x ≤ 1, this distance simplifies to 1 - x².

The volume of an infinitesimally thin section is then (1 - x²)² ∆x (where ∆x represents its thickness), and so the volume of S is

$\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = \int_{-1}^1 (1 - 2x^2 + x^4) \, dx$

The integrand is even, so this integral is equal to twice the integral over [0, 1] :

$\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = 2 \int_0^1 (1 - 2x^2 + x^4) \, dx = 2 \left(1 - \frac23 + \frac15\right) = \boxed{\frac{16}{15}}$

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2 years ago

The question is provided on the image

Artemon [7]

Answer:

Use scale factor

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Three integers x, y and z satisfy 34x+5ly=6z. If y and z are primes, find the

pickupchik [31]

X= -3/2y+3/17z
y=-2/3x+2/17z
z=-17/3x+17/2y

6 0

3 years ago

Can someone please help me?? I don’t understand what the order is? And or the symmetry

Vika [28.1K]

It is probably a rectangle so u see the answer would make s eve but in your mind does it

3 0

3 years ago

Find the base of the triangle !Area = 48 sq.mHeight = 12 mplease hurry! Thank you!

Shtirlitz [24]

It is given that,

$\begin{gathered} Area\text{ = 48 m}^{2\text{ }} \\ Height\text{ = 12 m} \\ Base\text{ = x} \end{gathered}$

Area of the triangle is calculated as,

$\begin{gathered} Area\text{ = }\frac{1}{2}\text{ }\times\text{ Base }\times\text{ Height} \\ 48\text{ = }\frac{1}{2}\text{ }\times\text{ x }\times\text{ 12} \\ x\text{ = }\frac{48\times2}{12} \\ x\text{ = 8 m } \end{gathered}$

Thus the base of the given right angled triangle is 8 m.

4 0

1 year ago