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3 years ago

Find the value of each variable

Mathematics

1 answer:

ohaa [14]3 years ago

6 0

9514 1404 393

Answer:

11. x = 13, y = 13√2

12. x = 8, y = 4√3

13. x = 14√3, y = 7√3

14. x = y = 11√2

15. x = 12√2, y = 12, z = 12√3

Step-by-step explanation:

The ratios of side lengths in the "special" triangles are (shortest to longest)

1 : 1 : √2 . . . . . isosceles right triangle

1 : √3 : 2 . . . . 30°-60°-90° triangle

These ratios make answering these questions much easier.

11. 13 : x : y = 1 : 1 : √2

x = 13, y = 13√2

12. 4 : y : x = 1 : √3 : 2

x = 8, y = 4√3

13. y : 21 : x = 1 : √3 : 2

y = 21/√3 = 7√3

x = 14√3

14. x : y : 22 = 1 : 1 : √2

x = 22/√2 = 11√2

x = y = 11√2

15. Let 'a' represent the altitude. Then we have ...

a : z : 24 = 1 : √3 : 2

a = 12, z = 12√3

and ...

a : y : x = 1 : 1 : √2

y = 12, x = 12√2

_____

Additional comment

It is worth remembering that 1/√n = (√n)/n. This is useful when you have to divide by √2 or √3 in the above problems.

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Answer: Choice B (i)

Step-by-step explanation:

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2 years ago

Given: R=2m

mr_godi [17]

Answer:

$V = \frac{2L\sqrt{3}}{3} \pi}$

$A = 4\pi + \sqrt{3L^{2} + 16}$

Step-by-step explanation:

Figure of cone is missing. See attachment

Given

Radius, R = 2m

Let L = KL=LM=KM

Required:

Volume, V and Surface Area, A

Calculating Volume

Volume is calculated using the following formula

$V = \frac{1}{3} \pi R^{2} H$

Where R is the radius of the cone and H is the height

First, we need to determine the height of the cone

The height is represented by length OL

It is given that KL=LM=KM in triangle KLM

This means that this triangle is an equilateral triangle

where OM = OK = $\frac{1}{2} KL$

OK = $\frac{1}{2}L$

Applying pythagoras theorem in triangle LOM,

|LM|² = |OL|² + |OM|²

By substitution

L² = H² + ( $\frac{1}{2}L$ )²

H² = L² - $\frac{1}{4}L$ ²

H² = L² (1 - $\frac{1}{4}$ )

H² = L² $\frac{3}{4}$

H² = $\frac{3L^{2} }{4}$

Take square root of bot sides

$H = \sqrt{\frac{3L^{2} }{4}}$

$H = \frac{L\sqrt{3}}{2}$

Recall that $V = \frac{1}{3} \pi R^{2} H$

$V = \frac{1}{3} \pi 2^{2} * \frac{L\sqrt{3}}{2}$

$V = \frac{1}{3} \pi * 4} * \frac{L\sqrt{3}}{2}$

$V = \frac{1}{3} \pi} * {2L\sqrt{3}}$

$V = \frac{2L\sqrt{3}}{3} \pi}$

in terms of $\pi$ an d L where L = KL = LM = KM

Calculating Surface Area

Surface Area is calculated using the following formula

$H = \frac{L\sqrt{3}}{4}$

$A=\pi r(r+\sqrt{h^{2} +r^{2} } )$

$A=\pi * 2(2+\sqrt{((\frac{L\sqrt{3}}{2})^{2} +2^{2} } )$ )

$A=\pi * 2(2+\sqrt{{\frac{3L^{2}}{4} } + 4 }$ )

$A=\pi * 2(2+\sqrt{{\frac{3L^{2}+16}{4} } })$

$A=2\pi(2+\sqrt{{\frac{3L^{2}+16}{4} } })$

$A = 2\pi (2 + \frac{\sqrt{3L^{2} + 16}}{\sqrt{4}} )$

$A = 2\pi (2 + \frac{\sqrt{3L^{2} + 16}}{2} )$

$A = 2\pi (2 + {\frac{1}{2} \sqrt{3L^{2} + 16})$

$A = 4\pi + \sqrt{3L^{2} + 16}$

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2 years ago

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Vesnalui [34]

I’m pretty sure the answer is 6. Have a wonderful day!

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2 years ago

Make w the subject of Y-aw=2w-1

Luda [366]

So you're gonna take add 1 to both sides and add aw to both sides also
y+1=2w+aw
then you factorize the w
y+1=w(2+a)
divide 2+a in both sides
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3 years ago

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11111nata11111 [884]

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