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3 years ago

The picture is the stated problem. Need help getting through this

Mathematics

1 answer:

In-s [12.5K]3 years ago

3 0

A A A A A A A A A A A A A A A A A A A A

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Rationalise:<br>(1) 4/(2+root3+root7)<br>(2) 4/(2root3+root5)

Temka [501]

$\frac{4}{2+\sqrt3+\sqrt7}\cdot\frac{2-(\sqrt3+\sqrt7)}{2-(\sqrt3+\sqrt7)}=\frac{8-4\sqrt3-4\sqrt7}{2^2-(\sqrt3+\sqrt7)^2}=\frac{8-4\sqrt3-4\sqrt7}{4-3-2\sqrt{3\cdot7}-7}\\\\=\frac{8-4\sqrt3-4\sqrt7}{-6-2\sqrt{21}}=\frac{-2(2\sqrt3+2\sqrt7-4)}{-2(3+\sqrt{21})}=\frac{2\sqrt3+2\sqrt7-4}{3+\sqrt{21}}\cdot\frac{3-\sqrt{21}}{3-\sqrt{21}}\\\\=\frac{6\sqrt3-2\sqrt{63}+6\sqrt7-2\sqrt{147}-12+4\sqrt{21}}{3^2-(\sqrt{21})^2}=\frac{6\sqrt3-2\sqrt{9\cdot7}+6\sqrt7-2\sqrt{49\cdot3}-12+4\sqrt{21}}{9-21}$

$=\frac{6\sqrt3-6\sqrt7+6\sqrt7-14\sqrt3-12+4\sqrt{21}}{-12}=\frac{-8\sqrt3+4\sqrt{21}-12}{-12}=\frac{-4(2\sqrt3-\sqrt{21}+3)}{-12}\\\\=\frac{2\sqrt3-\sqrt{21}+3}{3}$

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$\frac{4}{2\sqrt3+\sqrt5}\cdot\frac{2\sqrt3-\sqrt5}{2\sqrt3-\sqrt5}=\frac{8\sqrt3-4\sqrt5}{(2\sqrt3)^2-(\sqrt5)^2}=\frac{8\sqrt3-4\sqrt5}{4\cdot3-5}=\frac{8\sqrt3-4\sqrt5}{12-5}\\\\=\frac{8\sqrt3-4\sqrt5}{7}$

4 0

4 years ago

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Find the volume of the cylinder. Use 3.14 for u. Round to the nearest whole number.

Lynna [10]

Answer:

1530 cubic centimeters

8 0

3 years ago

Carry me in Rainbow six siege i need to reach plat put your xbox gamertag down below

Anuta_ua [19.1K]

Answer:

My username is

Step-by-step explanation:

IloveSatorisamam

4 0

3 years ago

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For each order pair ,determine whether is it a solution to 7x+4y=-23

trasher [3.6K]

Simplifying

7x + -4y = 23

Solving

7x + -4y = 23

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4y' to each side of the equation.

7x + -4y + 4y = 23 + 4y

Combine like terms: -4y + 4y = 0

7x + 0 = 23 + 4y

7x = 23 + 4y

Divide each side by '7'.

x = 3.285714286 + 0.5714285714y

Simplifying

x = 3.285714286 + 0.5714285714y

5 0

3 years ago

Please help I'm really confused

inessss [21]

Answer:

your answer should look like this.

Step-by-step explanation:

The horizontal line goes through y-intercept -1/2

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3 years ago