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3 years ago

Three vertices of a square have coordinates (5, 1), (2, -2), and (-1, 1). What are the coordinates of the fourth vertex?

1 answer:

6 0

Plot the points
we notice that the square is tilted diagnaol

remember that the legnths of the diagonals of a square are equal

therefor the distance between the points (5,1) and (-1,1) is the same as the ohter diagonal (distance is 6)

the other point is probably that disance up or the y vairable
(2,-2)+6 on the y
-2+6=4
(2,4)
answer is (2,4)

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An horse gallops 200ft turns and trots 350ft turns again and travels 410ft

bija089 [108]

The area of the triangle formed by his path is 34971.98 ft sq to the nearest hundredth.

<h3>What is the Heron's formula?</h3>

The Heron's formula is given as;

√s(s-a)(s-b)(s-c)

where s is half the perimeter of the triangle

WE have been given that horse gallops 200ft, turns and trots 350ft, turns again and travels 410ft to return to the point he started from.

Perimeter of the triangle is given as = 200 + 350 + 410 = 960 ft

Semi perimeter = 960 ft/ 2 = 480 ft

Area = √s(s-a)(s-b)(s-c)

Area = √480 (480 -200)(480 -350)(480 -410)

Area = √480 (280)(130)(70)

Area = √480 (2548000)

Area = 34971.98

The area of the triangle formed by his path is 34971.98 ft sq to the nearest hundredth.

Learn more about the Heron's formula;

brainly.com/question/20934807

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The complete question is

A horse gallops 200ft, turns and trots 350ft, turns again and travels 410ft to return to the point he started from. What is the area of the triangle formed by his path? round to the nearest hundredth.

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1 year ago

If you were to randomly select a letter from the word below, what is the probability that letter would be a vowel?

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3 years ago

A right circular cylinder is inscribed in a sphere with diameter 4cm as shown. If the cylinder is open at both ends, find the la

SOVA2 [1]

Answer:

$8\pi\text{ square cm}$

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

$S=2\pi rh$

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

$4^2 = (2r)^2 + h^2$ ( see in the below diagram ),

$16 = 4r^2 + h^2$

$16 - 4r^2 = h^2$

$\implies h=\sqrt{16-4r^2}$

Thus, the surface area of the cylinder,

$S=2\pi r(\sqrt{16-4r^2})$

Differentiating with respect to r,

$\frac{dS}{dr}=2\pi(r\times \frac{1}{2\sqrt{16-4r^2}}\times -8r + \sqrt{16-4r^2})$

$=2\pi(\frac{-4r^2+16-4r^2}{\sqrt{16-4r^2}})$

$=2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})$

Again differentiating with respect to r,

$\frac{d^2S}{dt^2}=2\pi(\frac{\sqrt{16-4r^2}\times -16r + (-8r^2+16)\times \frac{1}{2\sqrt{16-4r^2}}\times -8r}{16-4r^2})$

For maximum or minimum,

$\frac{dS}{dt}=0$

$2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})=0$

$-8r^2 + 16 = 0$

$8r^2 = 16$

$r^2 = 2$

$\implies r = \sqrt{2}$

Since, for r = √2,

$\frac{d^2S}{dt^2}=negative$

Hence, the surface area is maximum if r = √2,

And, maximum surface area,

$S = 2\pi (\sqrt{2})(\sqrt{16-8})$

$=2\pi (\sqrt{2})(\sqrt{8})$

$=2\pi \sqrt{16}$

$=8\pi\text{ square cm}$

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3 years ago

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Answer:2 weeks

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