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3 years ago

Which Greek mathematician wrote the most definitive text on geometry, one that is still referred to today?

2 answers:

5 0

This mathematician is named Pythagoras. He was the mathematician who discovered in what relation are the sides, angles, and length of the sides of a triangle. Today this idea is still being used in mathematics and represents one of the foundations in geometry that we use all around.

KiRa [710]3 years ago

4 0

Answer: Euclid

Step-by-step explanation:

Euclid, the Greek mathematician wrote the most definitive text on geometry, is still referred to today. Euclid was considered as the “Father of Geometry”, and was known to be a great mathematician

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1 millimeter on the map represents 1 meter on the ground. What is the ratio

qwelly [4]

1mm:1m

since its just one to one, thats the ratio

3 0

3 years ago

99 POINT QUESTION, PLUS BRAINLIEST!!!

sattari [20]

We know, that the <span>area of the surface generated by revolving the curve y about the x-axis is given by:

$\boxed{A=2\pi\cdot\int\limits_a^by\sqrt{1+\left(y'\right)^2}\, dx}$

In this case a = 0, b = 15, $y=\dfrac{x^3}{15}$ and:

$y'=\left(\dfrac{x^3}{15}\right)'=\dfrac{3x^2}{15}=\boxed{\dfrac{x^2}{5}}$

So there will be:

$A=2\pi\cdot\int\limits_0^{15}\dfrac{x^3}{15}\cdot\sqrt{1+\left(\dfrac{x^2}{5}\right)^2}\, dx=\dfrac{2\pi}{15}\cdot\int\limits_0^{15}x^3\cdot\sqrt{1+\dfrac{x^4}{25}}\,\, dx=\left(\star\right)\\\\-------------------------------\\\\
\int x^3\cdot\sqrt{1+\dfrac{x^4}{25}}\,\,dx=\int\sqrt{1+\dfrac{x^4}{25}}\cdot x^3\,dx=\left|\begin{array}{c}t=1+\dfrac{x^4}{25}\\\\dt=\dfrac{4x^3}{25}\,dx\\\\\dfrac{25}{4}\,dt=x^3\,dx\end{array}\right|=\\\\\\$

$=\int\sqrt{t}\cdot\dfrac{25}{4}\,dt=\dfrac{25}{4}\int\sqrt{t}\,dt=\dfrac{25}{4}\int t^\frac{1}{2}\,dt=\dfrac{25}{4}\cdot\dfrac{t^{\frac{1}{2}+1}}{\frac{1}{2}+1}= \dfrac{25}{4}\cdot\dfrac{t^{\frac{3}{2}}}{\frac{3}{2}}=\\\\\\=\dfrac{25\cdot2}{4\cdot3}\,t^\frac{3}{2}=\boxed{\dfrac{25}{6}\,\left(1+\dfrac{x^4}{25}\right)^\frac{3}{2}}\\\\-------------------------------\\\\$

$\left(\star\right)=\dfrac{2\pi}{15}\cdot\int\limits_0^{15}x^3\cdot\sqrt{1+\dfrac{x^4}{25}}\,\, dx=\dfrac{2\pi}{15}\cdot\dfrac{25}{6}\cdot\left[\left(1+\dfrac{x^4}{25}\right)^\frac{3}{2}\right]_0^{15}=\\\\\\=
\dfrac{5\pi}{9}\left[\left(1+\dfrac{15^4}{25}\right)^\frac{3}{2}-\left(1+\dfrac{0^4}{25}\right)^\frac{3}{2}\right]=\dfrac{5\pi}{9}\left[2026^\frac{3}{2}-1^\frac{3}{2}\right]=\\\\\\=
\boxed{\dfrac{5\Big(2026^\frac{3}{2}-1\Big)}{9}\pi}$

Answer C.
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3 0

3 years ago

To test for the significance of a regression model involving 3 independent variables and 51 observations, the numerator and deno

LenKa [72]

Answer:

numerator degree of freedom = 3

Denominator degree of freedom = 47

Step-by-step explanation:

The numerator degree of freedom is given by :

p - 1 ; where p = number of predictors ;

p = number of independent variables + 1

Number of independent variables = 3

p = 3 + 1 = 4

Numerator degree of freedom = p - 1 = 4 - 1 = 3

The denominator degree of freedom = n - p ; where n = number of observations

Number of observations, n = 51

Denominator degree of freedom = n - p = 51 - 4 = 47

6 0

2 years ago

The sum of 6 consecutive even numbers is 126

tatyana61 [14]

Start at 16 and count up by 2 until 26.

5 0

2 years ago

What is volume and how is it measured?

USPshnik [31]

Volume is the amount of space that a substance or object occupies, or that is enclosed within a container. It is measured in <span>Volumetric units. </span>

6 0

3 years ago

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