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2 years ago

Find tan(30) (its a right triangle)

Mathematics

1 answer:

Travka [436]2 years ago

8 0

Use the 30-60-90 triangle.

Tan is opposite over adjacent.

$\frac{1}{ \sqrt{3} }$
Square roots cannot be on the bottom.

$\frac{1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} }$
The bottom cancel out the square root bar.

Your answer is:

$\frac{ \sqrt{3} }{3}$
(It's best to memorize the 30-60-90 and the 45-45-90 triangles during trigonometry. It helps a lot.)

Hope this helps!

:)

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The second term in a geometric sequence is 20. The fourth term in the same sequence is 45/4 or 11.25. What is the common ratio i

kati45 [8]

$\bf \begin{array}{ccll}
n&term&value\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
2&a_2&20\\
3&a_3&20r\\
4&a_4&20rr\\
&&20r^2\\\\
&&\frac{45}{4}
\end{array}\implies \stackrel{4^{th}~term}{20r^2=\cfrac{45}{4}}\implies r^2=\cfrac{45}{80}
\\\\\\
r^2=\stackrel{simplified}{\cfrac{9}{16}}\implies r=\sqrt{\cfrac{9}{16}}\implies r=\cfrac{\sqrt{9}}{\sqrt{16}}\implies r=\cfrac{3}{4}$

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3 years ago

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sergij07 [2.7K]

Answer:

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2 years ago

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8.0 ÷ 10 A) Sixty thousand B) Six thousand C) Six hundred D) sixdy

Mashutka [201]

The answer is 0.8. Non of the options are correct

6 0

3 years ago

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balandron [24]

Answer:

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2 years ago

Solve (x + 5)^(3/2)= (x - 1)^3

IRINA_888 [86]

Answer:

x = 4

Step-by-step explanation:

For an equation of this sort, my first step is to rewrite it so the solutions are the x-intercepts of the graph:

(x +5)^(3/2) -(x +1)^3 = 0

The graph is attached. The one real solution is x=4.

The solution method for something like this is necessarily ad hoc. Here, it appears that progress can be made by raising both sides of the equation to the 2/3 power:

((x +5)^(3/2))^(2/3) = ((x -1)^3)^(2/3)

x +5 = (x -1)^2

Now, you have an ordinary quadratic that can be solved using any of the usual methods.

x^2 -2x +1 = x +5 . . . . swap sides, expand the square

x^2 -3x -4 = 0 . . . . . . put in standard form

(x -4)(x +1) = 0 . . . . . . factor

The solutions to this are ...

x = 4, x = -1 . . . . . . . values of x that make the factors zero

To see if either of these solutions is extraneous, we can check them:

(4 +5)^(3/2) = (4 -1)^3 . . . . . substitute 4 for x

9^(3/2) = 3^3 . . . . . . . . . true

(-1 +5)^(3/2) = (-1 -1)^3 . . . . . substitute -1 for x

4^(3/2) = (-2)^3

8 = -8 . . . . . . . . . . . false; x = -1 is extraneous

The solution is x = 4.

_____

Additional comment

You can eliminate the x=-1 "solution" by considering the domains of the left- and right-side expressions. The 3/2 power is equivalent to the square root of the cube. That will generally only be defined for non-negative values (x ≥ -5). The cube on the right will only be positive for x > 1, so the practical domain of this equation is x ≥ 1.

5 0

2 years ago