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2 years ago

8

Using a reciprocal for

ac{3}{4}" align="absmiddle" class="latex-formula"> what is $8\frac{1}{5}$ ÷ $3\frac{3}{4}$

1 answer:

Soloha48 [4]2 years ago

8 0

Answer:

123/4

Step-by-step explanation:

3 3/4=15/4

Reciprocal of 15/4=-4/15

8 1/5 / 3 3/4

=41/5 / 15/4

= 123/4

I didn’t get the first part of the question that well but this is the answer for the question

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Viktor [21]

Answer:

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3 years ago

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 sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the

bonufazy [111]

X = first number
x - 8 = 2nd number
5x = 3rd number

x + x - 8 + 5x = 69
7x - 8 = 69 <=== this is the equation u would use

7x - 8 = 69
7x = 69 + 8
7x = 77
x = 11

1st number = 11
2nd number : x - 8 = 11 - 8 = 3
3rd number : 5x = 5(11) = 55

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3 years ago

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You are a volunteer at a physical therapy clinic. a set of stairs you use to help patients is shown with it's dimensions. What i

vazorg [7]

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3 years ago

The setup fee for a photo book is $35. The papwe is an additional charge of $0.80 per page. What is the greatest number of pages

N76 [4]

Answer:

18 pages

Step-by-step explanation:

18 pages would cost $14.40 and the you add $35 for the setup fee. This makes the total $49.4 and no more pages can be added because it would cost too much.

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3 years ago