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3 years ago

What does -16i equal?

Mathematics

1 answer:

Alisiya [41]3 years ago

3 0

16i equals an amount to no other as it is majestic and formal. 16i equals nothing else than life it's self...

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Which of these values represents the longest period of time?

laiz [17]

The answer is D. 6 days

A. 60 hours is 3600 minutes
B. 60,000 milliseconds is 0.016 minutes
C. 6,000 minutes
D. 6 days is 8640 minutes

8 0

2 years ago

Rationalise the denominator of:<br>1/(√3 + √5 - √2)

Paul [167]

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} }$

can be re-arranged as

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} - \sqrt{2} + \sqrt{5} }$

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} }$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} } \times \dfrac{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }$

We know,

$\rm :\longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}$

So, using this, we get

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ {( \sqrt{3} - \sqrt{2} )}^{2} - {( \sqrt{5}) }^{2} }$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{3 + 2 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{5 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{ - ( - \sqrt{3} + \sqrt{2} + \sqrt{5}) }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}}$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}} \times \dfrac{ \sqrt{6} }{ \sqrt{6} }$

$\rm \: = \: \dfrac{- \sqrt{18} + \sqrt{12} + \sqrt{30}}{2 \times 6}$

$\rm \: = \: \dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}$

$\rm \: = \: \dfrac{- 3\sqrt{2} + 2 \sqrt{3} + \sqrt{30}}{12}$

Hence,

$\boxed{\tt{ \rm \dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} } =\dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}}}$

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<h3><u>More Identities to </u><u>know:</u></h3>

$\purple{\boxed{\tt{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}}}}$

$\purple{\boxed{\tt{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}}}$

$\purple{\boxed{\tt{ {(x + y)}^{3} = {x}^{3} + 3xy(x + y) + {y}^{3}}}}$

$\purple{\boxed{\tt{ {(x - y)}^{3} = {x}^{3} - 3xy(x - y) - {y}^{3}}}}$

$\pink{\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}}$

$\pink{\boxed{\tt{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}}}$

6 0

2 years ago

Please help me!! I will give brainliest to best answer

Ksju [112]

Answer:- 2

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

What’s the greatest hundred you can multiply by 17 to get close to but not go over 821

Julli [10]

Answer:

Step-by-step explanation:

821 rounded down to 800

17 rounded up to 20

820/20 =41

20x41=820

17 x 41 = 697

17 x 51 = 867

Midpoints

697+867/2 = 782

41 +51/2 = 46

46 x 17 = 782

47 x 17 = 799

48 x 17 =816

49 x 17 =833

50 x 17 =850

So, the highest number is 48.

The closest we can get is 48 x 17=816 & without going over 821.

8 0

2 years ago

Find x in the given figures.

marin [14]

Answer:

$\large\boxed{X=\sqrt{12}\ in=2\sqrt3\ in}$

Step-by-step explanation:

ΔADC and ΔCBD are similar. Therefore the corresponding sides are in proportion:

$\dfrac{AD}{CD}=\dfrac{CD}{DB}$

We have

AD = 2, CD = X, DB = 6.

Substitute:

$\dfrac{2}{X}=\dfrac{X}{6}$ <em>cross multiply</em>

$X^2=(2)(6)\\\\X^2=12\to X+\sqrt{12}$

$\sqrt{12}=\sqrt{4\cdot3}=\sqrt4\cdot\sqrt3=2\sqrt3$

4 0

3 years ago