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3 years ago

Find all solutions to the equation. sin x = square root of three divided by two.

Mathematics

2 answers:

Dafna1 [17]3 years ago

8 0

Answer:

x=60+k.360 or x =120+k.360

Step-by-step explanation:

$sin x = \frac{ \sqrt{3} }{2 \\ ?}$
$ref \: angle = 60 \\ x = 120+ k.360 \\ x = 60 + k360$
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ddd [48]3 years ago

5 0

Answer:

x = 60°

Step-by-step explanation:

Special Angles :

sin = opposite divided by hypotenuse

opposite of angle 60° is square root of three

hypotenuse is two

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Help ASAP show work please thanksss!!!!

Llana [10]

Answer:

$\displaystyle log_\frac{1}{2}(64)=-6$

Step-by-step explanation:

<u>Properties of Logarithms</u>

We'll recall below the basic properties of logarithms:

$log_b(1) = 0$

Logarithm of the base:

$log_b(b) = 1$

Product rule:

$log_b(xy) = log_b(x) + log_b(y)$

Division rule:

$\displaystyle log_b(\frac{x}{y}) = log_b(x) - log_b(y)$

Power rule:

$log_b(x^n) = n\cdot log_b(x)$

Change of base:

$\displaystyle log_b(x) = \frac{ log_a(x)}{log_a(b)}$

Simplifying logarithms often requires the application of one or more of the above properties.

Simplify

$\displaystyle log_\frac{1}{2}(64)$

Factoring $64=2^6$ .

$\displaystyle log_\frac{1}{2}(64)=\displaystyle log_\frac{1}{2}(2^6)$

Applying the power rule:

$\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}(2)$

Since

$\displaystyle 2=(1/2)^{-1}$

$\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}((1/2)^{-1})$

Applying the power rule:

$\displaystyle log_\frac{1}{2}(64)=-6\cdot log_\frac{1}{2}(\frac{1}{2})$

Applying the logarithm of the base:

$\mathbf{\displaystyle log_\frac{1}{2}(64)=-6}$

5 0

3 years ago

A square pool has a side length of x feet.A uniform border around pool is 1 footwide.The total area of the pool and the border o

lions [1.4K]

The total area of pool and border = 361 square feet.

Length of square pool = x

Length of square pool plus border = (x + 1 +1 ) = x + 2

There is 1 foot length on each side on the x length.

The other length of the square pool and border = (x + 2)

Area = (x+2)(x+2)

   (x + 2)(x +2) = 361.    Let A = x +2

A*A = 361
    A² = 361    Take square root of both sides
   A = √361
   A = 19

A = x + 2 = 19
   x = 19 - 2
   x = 17

Area of square pool = x*x = 17*17 = 289

Area of the pool = 289 square feet.

8 0

3 years ago

In rhombus MNPQ, diagonals MP and NQ intersect at point K. If m_MQP = 56', then which of the

Murrr4er [49]

the answer is 90 degrees

3 0

3 years ago

The diameter of a round coin is 27.9 millimeters. What is the approximate area of one face of the coin?

Paladinen [302]

Answers is C

Step by step solution is attached