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3 years ago

What is the area of the base of this right circular cone in terms of π?

Mathematics

2 answers:

Reptile [31]3 years ago

7 0

Step-by-step explanation: To find the area of the circle shown here, start with the formula for the area of a circle which is as followed.

Area = $\pi r^{2}$

Sloan [31]3 years ago

3 0

Answer:

25π

Step-by-step explanation:

A = πr²

π[5]² = 25π

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on a recent hike through riverbend park antoinette traveled 2/3 mile in 1/3 hour . Which unit rate describes antoinettes speed i

My name is Ann [436]

Answer:

Her speed is of 2 miles per hour.

Step-by-step explanation:

Velocity:

The velocity is given by the following formula:

$v = \frac{d}{t}$

In which v is the velocity, d is the distance and t is the time.

2/3 mile in 1/3 hour .

This means that $d = \frac{2}{3}, t = \frac{1}{3}$

Which unit rate describes antoinettes speed in miles per hour?

This is v. So

$v = \frac{d}{t} = \frac{\frac{2}{3}}{\frac{1}{3}} = \frac{2}{3}*\frac{3}{1} = 2$

Her speed is of 2 miles per hour.

5 0

3 years ago

Select the correct answer from each drop-down menu. Consider the following polynomials equations.

Zolol [24]

Answer:

Yes to all 3 questions.

Step-by-step explanation:

3x^2(x-1) + -3x^3+ 4x^2-2x+1

= 3x^3 - 3x^2 - 3x^3 + 4x^2 - 2x + 1

= x^2 - 2x + 1,

So A + B is a polynomial.

3x^2(x-1) - (-3x^3+ 4x^2-2x+1)

= 3x^3 - 3x^2 + 3x^3 - 4x^2 + 2x - 1

= 6x^3 - 7x^2 + 2x - 1.

So A - B is also a polynomial.

3x^2(x-1)( -3x^3+ 4x^2-2x+1)

= (3x^3 - 3x^2) ( -3x^3 + 4x^2 - 2x + 1)

= -9x^6 + 12x^5 - 6x^4 + 3x^3 + 9x^5 - 12x^4 + 6x^3 - 3x^2

= -9x^6 + 21x^5 - 18x^4 + 9x^3 - 3x^2.

So A * B is a polynomial.

5 0

3 years ago

Read 2 more answers

E temperature t of a metal sphere is inversely proportional to the distance from the centre of the sphere (the origin (0, 0, 0))

olasank [31]

(-x, -y, -z) the vector form (x, y, z) to the origin, in the direction of the greatest increase.

<h3>How to calculate temperature?</h3>

The quantity or amount of radiation contained in material or item, as measured by a temperature or sensed by touch and stated on a numerical scale.

The temperature T of a ball bearing is inverse to the length first from the origin, which we consider to be the center of the ball. The temperature at the exact location

(x, y, z) is a point on the sphere, the temperature at this point is given by

$T(x,y,z)= \dfrac{k}{(x^2 +y^2+z^2)^{1/2}}$

Where k is constant, then we have

T(1, 2, 2) = k/3 = 170

k = 510

$T(x,y,z)= \dfrac{510}{(x^2 +y^2+z^2)^{1/2}}$

Then we have

$\rm \triangledown T = \left ( -\dfrac{510x}{(x^2 +y^2+z^2)^{1/2}}, -\dfrac{510y}{(x^2 +y^2+z^2)^{1/2}}, \dfrac{510z}{(x^2 +y^2+z^2)^{1/2}} \right )\\\\\\\triangledown T (1, 2, 2) = -\dfrac{510}{27} (1, 2, 2) =-\dfrac{170}{9} (1, 2, 2)$

Then the direction will be from (1, 2, 2) to (4, 3, 5) will be (3, 1, 3)

So u = (3/√19, 1/√19, 3/√19)

Then we get

$\rm \triangledown T \cdot u = \dfrac{-170}{9}(1, 2, 2) \cdot \left (\dfrac{3}{\sqrt{19}}, \dfrac{1}{\sqrt{19}}, \dfrac{3}{\sqrt{19}} \right )\\\\\\\triangledown T \cdot u = - \dfrac{170}{9\sqrt{19}} (3 + 2 + 6)\\\\\\\triangledown T \cdot u = -\dfrac{1870}{9\sqrt{19}}$

The direction of the greatest inverse in the temperature is given by any vector parallel to and having the same direction $\triangledown$ T. (-x, -y, -z) the vector form (x, y, z) to the origin, in the direction of the greatest increase.