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2 years ago

HELPPPP :(((

Mathematics

2 answers:

sp2606 [1]2 years ago

4 0

Answer:

9.1

Step-by-step explanation:

mario62 [17]2 years ago

3 0

Answer:

9.13

Step-by-step explanation:

hope it helped

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2 tan 30° II 1 + tan- 300

shusha [124]

Question:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$

Answer:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= sin(60^{\circ})$

Step-by-step explanation:

Given

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$

Required

Simplify

In trigonometry:

$tan(30^{\circ}) = \frac{1}{\sqrt{3}}$

So, the expression becomes:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2 * \frac{1}{\sqrt{3}}}{1 + (\frac{1}{\sqrt{3}})^2}$

Simplify the denominator

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2 * \frac{1}{\sqrt{3}}}{1 + \frac{1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{1 + \frac{1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{ \frac{3+1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{ \frac{4}{3}}$

Express the fraction as:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2}{\sqrt 3} / \frac{4}{3}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2}{\sqrt 3} * \frac{3}{4}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{1}{\sqrt 3} * \frac{3}{2}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3}{2\sqrt 3}$

Rationalize

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3}{2\sqrt 3} * \frac{\sqrt{3}}{\sqrt{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3\sqrt{3}}{2* 3}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\sqrt{3}}{2}$

In trigonometry:

$sin(60^{\circ}) = \frac{\sqrt{3}}{2}$

Hence:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= sin(60^{\circ})$

3 0

3 years ago

Solve for X Tysm!! I need help ASAP

amm1812

X-4/3 <= 5

Multiply both sides by 3:

X-4 <= 15

Add 4 to both sides:

X <= 19

The answer is the third one.

6 0

3 years ago

HELPPPP PLSSSSS The side length of a cube can be found by taking the cube root of its volume. The side length of a square can be

emmainna [20.7K]

Answer: 3/2

Step-by-step explanation:

7 0

2 years ago

True or False If AM≅MB, then M must be the midpoint of AB

Juli2301 [7.4K]

Answer:

True

Step-by-step explanation:

is true bro yes is true

6 0

2 years ago

Titiknya 10 dan 8 ∫x-8)( x-9) (x-10) dx

Sav [38]

$\displaystyle\int_8^{10}(x-8)(x-9)(x-10)\,\mathrm dx$

Consider the substitution,

$y=x-9\implies\begin{cases}y-1=x-10\\y+1=x-8\\\mathrm dy=\mathrm dx\end{cases}$

so that the integral is equivalent to

$\displaystyle\int_{-1}^1y(y+1)(y-1)\,\mathrm dy$

Notice that

$f(y)=y(y+1)(y-1)\implies f(-y)=-y(-y+1)(-y-1)=-y(y-1)(y+1)=-f(y)$

which means $f(y)$ is odd, so

$\implies\displaystyle\int_{-1}^1f(y)\,\mathrm dy=0$

Perhaps more work than necessary, but it does make it easier to see that the original integrand exhibits some symmetry about $x=9$ .

6 0

3 years ago