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2 years ago

Is -49 a rational number? please explain

1 answer:

7 0

Yes, because a rational number is any number that can be expressed as a fraction a/b where a/b are both integers, but cannot be zero.

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Use a half-angle identity to find the exact value

Tatiana [17]

Given:

$\cos 15^{\circ}$

To find:

The exact value of cos 15°.

Solution:

$$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}$

Using half-angle identity:

$$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}$

$$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}$

Using the trigonometric identity: $\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}$

$$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}$

Let us first solve the fraction in the numerator.

$$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}$

Using fraction rule: $\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}$

$$=\sqrt{\frac {2+\sqrt{3}}{4}}$

Apply radical rule: $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

$$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}$

Using $\sqrt{4} =2$ :

$$=\frac{\sqrt{2+\sqrt{3}}}{2}$

$$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}$

5 0

3 years ago

An equilateral triangle and a square both have perimeters of 48 inches. what is the ratio of the length of the side of the trian

labwork [276]

A square with a perimeter of 48 inches would have 12 in sides, while a triangle of the same perimeter would have 16 in sides. The ratio would be 16/12 which simplified to 4/3.

8 0

2 years ago

∠A and ∠ B ∠B are vertical angles. If m ∠ A = ( 3 x − 21 ) ∘ ∠A=(3x−21) ∘ and m ∠ B = ( 2 x − 13 ) ∘ ∠B=(2x−13) ∘ , then find th

Sav [38]

Answer:

x=8

Step-by-step explanation:

start by setting angle a equal to angle b

next add 21 to the opposite side

then subtract 2x from the opposite side

finally you're left with x=8

3 0

3 years ago

X - x equals ?............

Paul [167]

Answer:

Step-by-step explanation:

if x stade for any number like 5 then it will be 5-5=0

hope this helps you out need more help ask me

4 0

3 years ago

Find the missing length and round to the nearest tenth if necessary

cricket20 [7]

C= 6.7

A^2 + B^2 = C^2
6^2 + 3^2 = C^2
36+9 = 45
Square root 45 = 6.7

6 0

2 years ago

Read 2 more answers