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3 years ago

Equilateral triangles are triangles .

Mathematics

2 answers:

Alexandra [31]3 years ago

4 0

Answer:

That is correct

Step-by-step explanation:

Schach [20]3 years ago

4 0

Answer:

ohmygosh

Step-by-step explanation:

I didn't know that...wow big brains

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The equation giving a family of ellipsoids is u = (x^2)/(a^2) + (y^2)/(b^2) + (z^2)/(c^2) . Find the unit vector normal to each

Fynjy0 [20]

Answer:

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Step-by-step explanation:

Given equation of ellipsoids,

$u\ =\ \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}$

The vector normal to the given equation of ellipsoid will be given by

$\vec{n}\ =\textrm{gradient of u}$

$=\bigtriangledown u$

$=\ (\dfrac{\partial{}}{\partial{x}}\hat{i}+ \dfrac{\partial{}}{\partial{y}}\hat{j}+ \dfrac{\partial{}}{\partial{z}}\hat{k})(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2})$

$=\ \dfrac{\partial{(\dfrac{x^2}{a^2})}}{\partial{x}}\hat{i}+\dfrac{\partial{(\dfrac{y^2}{b^2})}}{\partial{y}}\hat{j}+\dfrac{\partial{(\dfrac{z^2}{c^2})}}{\partial{z}}\hat{k}$

$=\ \dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}$

Hence, the unit normal vector can be given by,

$\hat{n}\ =\ \dfrac{\vec{n}}{\left|\vec{n}\right|}$

$=\ \dfrac{\dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}}{\sqrt{(\dfrac{2x}{a^2})^2+(\dfrac{2y}{b^2})^2+(\dfrac{2z}{c^2})^2}}$

$=\ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Hence, the unit vector normal to each point of the given ellipsoid surface is

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

3 0

3 years ago

The San Andreas fault separates the pacific plates from the North America plate. The pacific plate moved northward relative to t

lesantik [10]

Answer:

The time, t it will take LA and San Francisco to be next to each other is 8,245,614.04 years which is over 8 million years

Step-by-step explanation:

The given parameters are;

The speed with which the pacific plate moved northward relative to the North American plate = 5.7 cm/year = 5.7 × 10⁻⁵ km/year

The distance between current LA and San Francisco = 470 km

From the formula for speed, s, we have

Speed = Distance/Time

Therefore, Time, t = Distance/Speed

The time, t it will take LA and San Francisco to be next to each other is given as follows;

t = (Distance between LA and San Francisco)/(The speed with which the pacific plate)

t = (470 km)/(5.7 cm/year) = 470/(5.7 × 10⁽⁻⁵⁾) = 8245614.04 years

Therefore, the time, t it will take LA and San Francisco to be next to each other is 8245614.04 years.

6 0

3 years ago

I don't get this. can someone help me. I have a whole packet of this.

Harrizon [31]

For #2, ∠3 and ∠1 are supplementary. You know that the measure of ∠1 is 162°, so what is ∠3? 180-162=18.
m∠3=18° if ∠1=162°.
Hope this helped!

7 0

3 years ago

For each data set, find the mean, the first and third quartiles, and the interquartiles. Texts per day: 24, 53, 38, 12, 31, 19,

kolezko [41]

Mean = 29
Q1 = 19
Q2 = 26
Q3 = 38
IQR = Q3 - Q1 = 38 - 19 = 19

8 0

2 years ago

Find the number of terms and the degree of this polynomial. -9

Korvikt [17]

Answers:

Number of terms: 1
Degree: 9

===============================================

Explanation:

This is consider a monomial since we only have one term. Terms are separated by a plus sign, so something like 5x^2+10x has two terms.

The degree of a polynomial is the largest exponent when dealing with single variables. In the case of 9r^9, the largest exponent is 9, so the degree is 9. Going back to an example like 5x^2+10x, the largest exponent is 2 so this is the degree of this example.

8 0

3 years ago

Equilateral triangles are triangles . ​

Equilateral triangles are triangles .