What is x equal to <br> 2/3x+4=1/6x-5

A dog is on a 5 ft leash staked to the ground. If he can rotate around the stake, forming a circle, what is the area of the gras

Zanzabum

Answer:

78.5 ft²

Step-by-step explanation:

In this situation, the dog's 5 ft leash is the radius of the circle that he forms.

So, the radius is 5.

Use the area formula, A = $\pi$ r². Plug in 5 as r, and 3.14 as $\pi$

A = $\pi$ r²

A = (3.14)(5²)

A = (3.14)(25)

A = 78.5

So, the area of the grass he can cover is 78.5 ft²

7 0

2 years ago

GEOMETRY HELP ASAP!!!!!!!!!!!!!!!!!!!

vovangra [49]

Area of equilateral triangle = a^2/4 * √3 so side of triangle = a

but if area of equilateral triangle = area of square multiplied by √3 then area of square = a^2 / 4 so side of square = a/2

the ratio length of side triangle to length side of square = a: a/2 that means the side of triangle is doubled the side of square

answer
a) 2:1

6 0

3 years ago

Sin theta+costheta/sintheta -costheta+sintheta-costheta/sintheta+costheta=2sec2/tan2 theta -1

sleet_krkn [62]

$\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}$

From Left side:

$\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)$

$\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}$

NOTE: sin²θ + cos²θ = 1

$\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}$

$\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}$

$\dfrac{2sec^2\theta}{tan^2\theta-1}$

Left side = Right side <em>so proof is complete</em>

8 0

3 years ago

Read 2 more answers

Drag and drop an answer to each box to correctly complete the explanation for deriving the formula for the volume of a sphere

denis-greek [22]

The answers that would fill in the blanks are

2r
a circle
an annulus
1/3πr³
4/3πr³

<h3>What is the Cavalier's principle?</h3>

This principle states that if two solids are of equal altitude then the sections that the planes would make would have to be parallel and also be at the same distances from their bases which are equal such that the volumes of the solids would be equal.

Now we have to fill in the blanks with the solution.

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius r and height<u> 2r</u> minus the volume of two cones, each with a radius and height of r. A cross section of the sphere is a <u>circle</u> base of cylinder, is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is an <u>annulus_ </u>.The volume of the cylinder with radius r and height 2r is 2πr³, and the volume of each cone with radius r and height r is 1/3πr³. So the volume of the cylinder minus the two cones is 4/3πr³. Therefore, the volume of the sphere is by Cavalieri's principle

Read more on Cavalieri's principle here

brainly.com/question/22431955

#SPJ1

5 0

10 months ago

What Does It Mean to Be A Responsible Food Citizen?

Lelu [443]

Answer:

the meaning of it means the practice of engaging in food-related behaviors that support, rather than threaten, the development of a democratic, socially and economically just, and environmentally sustainable food system.

Step-by-step explanation:

3 0

3 years ago

What is x equal to 2/3x+4=1/6x-5