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2 years ago

3√6×2√3=...5√12+3√3=...

Mathematics

1 answer:

ikadub [295]2 years ago

6 0

Answer:

$3\sqrt{6}\times \:2\sqrt{3}=18\sqrt{2}$

$5\sqrt{12}+3\sqrt{3}=13\sqrt{3}$

Step-by-step explanation:

Given the expression

$3\sqrt{6}\:\times \:2\sqrt{3}$

$\mathrm{Factor\:integer\:}6=3\times \:2$

$=3\sqrt{3\times \:2}\times \:2\sqrt{3}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$

$=3\sqrt{3}\sqrt{2}\times \:2\sqrt{3}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{a}=a$

$=3\times \:2\times \:3\sqrt{2}$

$=18\sqrt{2}$

Thus,

$3\sqrt{6}\times \:2\sqrt{3}=18\sqrt{2}$

Given the expression

$5\sqrt{12}+3\sqrt{3}$

$\:=\:5\sqrt{\left(4\right)\left(3\right)}+3\sqrt{3}$

$=\:5\times 2\sqrt{\left(3\right)}+3\sqrt{3}$

$=10\sqrt{3}+3\sqrt{3}$

$\mathrm{Add\:similar\:elements:}\:10\sqrt{3}+3\sqrt{3}=13\sqrt{3}$

$=13\sqrt{3}$

Thus,

$5\sqrt{12}+3\sqrt{3}=13\sqrt{3}$

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The circumference of the ellipse approximate. Which equation is the result of solving the formula of the circumference for b?

Serhud [2]

Answer:

$b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}$

Step-by-step explanation:

Given - The circumference of the ellipse approximated by $C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }$ where 2a and 2b are the lengths of 2 the axes of the ellipse.

To find - Which equation is the result of solving the formula of the circumference for b ?

Solution -

$C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }\\\frac{C}{2\pi } = \sqrt{\frac{a^{2} + b^{2} }{2} }$

Squaring Both sides, we get

$[\frac{C}{2\pi }]^{2} = [\sqrt{\frac{a^{2} + b^{2} }{2} }]^{2} \\\frac{C^{2} }{(2\pi)^{2} } = {\frac{a^{2} + b^{2} }{2} }\\2\frac{C^{2} }{4(\pi)^{2} } = {{a^{2} + b^{2} }$

$\frac{C^{2} }{2(\pi )^{2} } = a^{2} + b^{2} \\\frac{C^{2} }{2(\pi )^{2} } - a^{2} = b^{2} \\\sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}} = b$

∴ we get

$b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}$

8 0

3 years ago

Plz Help Me With All Of The Problems Thx

love history [14]

Answer:

Step-by-step explanation:

17. A board 8 1/4 wanting to be cut out of the board are a number of pieces each piece 1 3/4 long

Convert both 8 1/4 and 1 3/4

8 1/4 = Multiply the denominator(4) by the whole number(8) to get 32 then add it to the numerator(1) to get 33, then put it over the original denominator to get 33/4. Do the same for the rest of the questions.

1 3/4 = 7/4

Divide 33/4 by 7/4 since we want to see how many times we can get 7/4 out of 33/4

33/4 ÷ 7/4

33/4 * 4/7, Changing the division sign to multiplication changes the fraction or number after it to the inverse of itself 7/4 = 4/7

132/28 - simplify by dividing the numerator and denominator by 4

33/7 - She will be able to cut 33/7 boards

Converting back to mixed fraction, divide the numerator by the denominator to give 4, write it as the whole number then write the remainder, 5, as the numerator and use the original denominator 7

= 4 5/7 boards

18. Total = 50

One serving = 1 1/3 = 4/3

50 ÷ 4/3

50 * 3/4

150/4 - simplify

75/2

= 37 1/2 servings

19. Saturday = 1 1/3 = 4/3

Sunday = 2 3/4 = 11/4

In a week, she watches 4/3 + 11/4 = 49/12 hrs

In 3 weeks, she watches 49/12 * 3 = 147/12- simplify = 49/4 hrs