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yarga [219]
3 years ago
5

Convert 45° from degrees to radians.

Mathematics
2 answers:
Vadim26 [7]3 years ago
8 0

Answer:

\displaystyle \frac{π}{4}

Step-by-step explanation:

\displaystyle [45°][\frac{π}{180°}] = \frac{45}{180}π = \frac{π}{4}

<em>Degrees to Radians</em>

\displaystyle \frac{π}{180°}

<em>Radians to Degrees</em>

\displaystyle \frac{180°}{π}

I am joyous to assist you anytime.

leonid [27]3 years ago
6 0
<h2>pi divided by four</h2>

Step-by-step explanation:

Let the angle in degrees be a

Let the angle in radians be r

If a is the angle in degrees and r is the angle in radians,

a\times \frac{\pi }{180}=r

It is given that the a=45

r=\frac{\pi}{180}\times a= \frac{\pi}{180}\times 45=\frac{\pi}{4}

So,r=\frac{\pi}{4}

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If x = (√2 + 1)^-1/3 then the value of x^3 + 1/x^3 is​
Shtirlitz [24]

Step-by-step explanation:

<u>Given</u><u>:</u> x = {√(2) + 1}^(-1/3)

<u>Asked</u><u>:</u> x³+(1/x³) = ?

<u>Solution</u><u>:</u>

We have, x = {√(2) + 1}^(-1/3)

⇛x = [1/{√(2) + 1}^(1/3)]

[since, (a⁻ⁿ = 1/aⁿ)]

Cubing on both sides, then

⇛(x)³ = [1{/√(2) + 1}^(1/3)]³

⇛(x)³ = [(1)³/{√(2) + 1}^(1/3 *3)]

⇛(x)³ = [(1)³/{√(2) + 1}^(1*3/3)]

⇛(x)³ = [(1)³/{√(2) + 1}^(3/3)]

⇛(x * x * x) = [(1*1*1)/{√(2) + 1)^1]

⇛x³ = [1/{√(2) + 1}]

Here, we see that on RHS, the denominator is √(2)+1. We know that the rationalising factor of √(a)+b = √(a)-b. Therefore, the rationalising factor of √(2)+1 = √(2) - 1. On rationalising the denominator them

⇛x³ = [1/{√(2) + 1}] * [{√(2) - 1}/{√(2) - 1}]

⇛x³ = [1{√(2) + 1}/{√(2) + 1}{√(2) - 1}]

Multiply the numerator with number outside of the bracket with numbers on the bracket.

⇛x³ = [{√(2) + 1}/{√(2) + 1}{√(2) - 1}]

Now, Comparing the denominator on RHS with (a+b)(a-b), we get

  • a = √2
  • b = 1

Using identity (a+b)(a-b) = a² - b², we get

⇛x³ = [{√(2) - 1}/{√(2)² - (1)²}]

⇛x³ = [{√(2) - 1}/{√(2*2) - (1*1)}]

⇛x³ = [{√(2) - 1}/(2-1)]

⇛x³ = [{√(2) - 1}/1]

Therefore, x³ = √(2) - 1 → → →Eqn(1)

Now, 1/x³ = [1/{√(2) - 1]

⇛1/x³ = [1/{√(2) - 1] * [{√(2) + 1}/{√(2) + 1}]

⇛1/x³ = [1{√(2) + 1}/{√(2) - 1}{√(2) + 1}]

⇛1/x³ = {√(2) + 1}/[{√(2) - 1}{√(2) + 1}]

⇛1/x³ = [{√(2) + 1}/{√(2)² - (1)²}]

⇛1/x³ = [{√(2) + 1}/{√(2*2) - (1*1)}]

⇛1/x³ = [{√(2) + 1}/(2-1)]

⇛1/x³ = [{√(2) + 1}/1]

Therefore, 1/x³ = √(2) + 1 → → →Eqn(2)

On adding equation (1) and equation (2), we get

x³ + (1/x³) = √(2) -1 + √(2) + 1

Cancel out -1 and 1 on RHS.

⇛x³ + (1/x³) = √(2) + √(2)

⇛x³ + (1/x³) = 2

Therefore, x³ + (1/x³) = 2

<u>Answer</u><u>:</u> Hence, the required value of x³ + (1/x³) is 2.

Please let me know if you have any other questions.

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2 years ago
Please answer the questions down below. <br> Savvas Realize 10-1 Interactive Additional Practice.
masha68 [24]
9. If they come in packages of 8 he needs 12 1/2

If they come in packages of 12 he needs 8 1/3

10. Equation: $9.25 - $4.50 - 3.50 = m

Answer: $1.25
4 0
2 years ago
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How man 1/3 cups make 3/4 cups
Sati [7]

Answer:

it would take 2.25 1/3 cups if you are looking for an exact answer, or if you are looking for the minimum amount of 1/3 cups necessary to make 3/4 it would be 3.

Step-by-step explanation:

You can solve this by cross multiplying 1/3 and 3/4

You will get 9/4 which simplifies to 2 1/4 or 2.25

8 0
2 years ago
What is the value of x?<br><br> Enter your answer, as a decimal, in the box.
Katarina [22]

Answer:

x=50.6cm

Step-by-step explanation:

Triangle MAB is similar to triangle MNP

Since the triangles are similar, the corresponding ratios are in the same proportion.

Therefore we can write the relation;

\frac{|MB|}{|MP|}=\frac{|MA|}{|MN|}


\frac{x}{72.6}=\frac{46.2-14}{46.2}


This implies that;

\frac{x}{72.6}=\frac{32.2}{46.2}


We multiply both sides by 72.6 to get


\frac{x}{72.6}\times 72.6=\frac{32.2}{46.2}\times72.6


\Rightarrow x=50.6


Hence the value of x is 50.6 cm



8 0
3 years ago
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The hour hand on a clock is 4 cm long, and the minute hand is 10 cm long. What is the exact distance between the tips of the han
Allushta [10]

Answer:

2 sqrt(19)

Step-by-step explanation:

We know that the angle between the two hands

360 /12 *2 = 60 degrees

We divide by 12 because there are 12 number and multiply by 2 because there are 2 number between 10 and 12

This is a triangle where we know 2 sides and the angle between them.

We can use the law of cosines to determine the third side

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Where C is the angle between sides a and b

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c^2 = 4^2 + 10^2 -2*4*10 cos60

c^2 =16+100 - 80cos 60

c^2 = 76

Take the square root of each side

sqrt(c^2) = sqrt(76)

c = sqrt(76)

c =sqrt(4) sqrt(19)

c =2 sqrt(19)


4 0
3 years ago
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