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3 years ago

(sqrt(6))/(8+\sqrt(10))

Mathematics

1 answer:

valkas [14]3 years ago

5 0

Answer:

$\frac{4\sqrt{6}-\sqrt{15}}{27}$

Step-by-step explanation:

$\frac{\sqrt{6} }{8+\sqrt{10} } \\\\\mathrm{Multiply\:by\:the\:conjugate}\:\frac{8-\sqrt{10}}{8-\sqrt{10}}\\=\frac{\sqrt{6}\left(8-\sqrt{10}\right)}{\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)}\\\\\sqrt{6}\left(8-\sqrt{10}\right)=8\sqrt{6}-2\sqrt{15}\\\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)=54\\\\=\frac{8\sqrt{6}-2\sqrt{15}}{54}\\\\\mathrm{Factor}\:8\sqrt{6}-2\sqrt{15}:\quad 2\left(4\sqrt{6}-\sqrt{15}\right)\\\\=\frac{2\left(4\sqrt{6}-\sqrt{15}\right)}{54}\\$

$\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{4\sqrt{6}-\sqrt{15}}{27}$

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Step-by-step explanation:

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3 years ago

If two solids are similar and the ratio between the lengths of their edges is 2;7 what is the ratio of their volumes?

Art [367]

Answer:

8 : 343

Step-by-step explanation:

Given 2 similar figures

ratio of sides = a : b, then

ratio of volumes = a³ : b³

Here the ratio of edges = 2 : 7, hence

ratio of volumes = 2³ : 7³ = 8 : 343

3 0

3 years ago

PLZ CHECK MY ANSWER. Round your answer to the nearest tenth.

Umnica [9.8K]

Answer:

D. $70.34 cm^2$

Step-by-step explanation:

Area of sector of a circle is given as θ/360*πr²

Where,

r = radius = 12 cm

θ = 56°

Use 3.14 as π

Plug in the values into the formula and solve

$area = \frac{56}{360}*3.14*12^2$

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Area of the sector ABC = $70.34 cm^2$

The answer is D

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3 years ago

Complete the steps to demonstrate why you multiply by the reciprocal when dividing fractions. Find 1/4 ÷ 3/8. ..................

Nataliya [291]

To complete the steps to demonstrate why you multiply by the reciprocal when dividing fractions.

To find
$\frac{1}{4}\div\frac{3}8}$

Step 1:
Rewrite it as
$\frac{\frac{1}{4}}{\frac{3}{8}}$ .

Step 2:
Multiply the numerator and the denominator by the reciprocal of
$\frac{3}{8}$ .

 $\frac{\frac{1}{4}}{\frac{3}{8}}=\frac{\frac{1}{4}}{\frac{3}{8}}\times\frac{\frac{8}{3}}{\frac{8}{3}}$

Step 3:
Simplify the denominator
$\frac{\frac{1}{4}\times\frac{8}{3}}{1}$

Step 4:
Simplify the fraction
 $\frac{1}{4}\times\frac{8}{3}$ .

We complete the solution as follows:
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3 0

3 years ago