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2 years ago

What is the angle measure θ in degrees such that cos(θ) = 2/16? Round your answer to the nearest degree.

Mathematics

1 answer:

Marina86 [1]2 years ago

8 0

Answer: 83 degrees

Step-by-step explanation:

In order to find theta, you must take the arccosine of both sides. The arccosine eliminates the cosine, and extracts the argument. Therefore:

$cos(x)=\frac{2}{16} =\frac{1}{8}$

$arccos(cos(x))=arccos(\frac{1}{8} )=x$

Use a calculator the find the arccosine of 1/8. Its nearly impossible to find the exact answer without one:

$x=arccos(\frac{1}{8} )$

$x=83$

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In this fulcrum, for the weights to be balance, what do the distances d1 and d2 have to be if the overall length is 12 feet?

mel-nik [20]

For the fulcrum to balance, the product of weight and distance on both sides of the fulcrum must be the same.

Let d1= x. since total distance is 12, we can write d2 = 12 - x

for the fulcrum to balance:

60x = 50(12 - x)

60x = 600 - 50x

110x = 600

x = 5.45

Thus, d1= 5.45
and
d2= 12 - d1 = 12 - 5.45 = 6.55

d1 = 5.45
d2 = 6.55

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3 years ago

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A circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?

aivan3 [116]

Hello here is a solution :
 the radius of the circle is OA A(5;-12) and O (0;0)
OA= square root ((5-0)² + (-12-0)²)
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7 0

3 years ago

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Explain why a quadratic equation with a positive discriminant has two real solutions, a quadratic equation with a negative discr

Bad White [126]

Answer:

A quadratic equation can be written as:

a*x^2 + b*x + c = 0.

where a, b and c are real numbers.

The solutions of this equation can be found by the equation:

$x = \frac{-b +- \sqrt{b^2 - 4*a*c} }{2*a}$

Where the determinant is D = b^2 - 4*a*c.

Now, if D>0

we have the square root of a positive number, which will be equal to a real number.

√D = R

then the solutions are:

$x = \frac{-b +- R }{2*a}$

Where each sign of R is a different solution for the equation.

If D< 0, we have the square root of a negative number, then we have a complex component:

√D = i*R

$x = \frac{-b +- C*i }{2*a}$

We have two complex solutions.

If D = 0

√0 = 0

then:

$x = \frac{-b +- 0}{2*a} = \frac{-b}{2a}$

We have only one real solution (or two equal solutions, depending on how you see it)

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3 years ago

Bobby knows that the perimeter of the original rectangle is 120 meters. He also knows that the perimeter of the reduced rectangl

Whitepunk [10]

Answer:

24 meters is the width of the original rectangle.

Step-by-step explanation:

Given:

Bobby knows that the perimeter of the original rectangle is 120 meters. He also knows that the perimeter of the reduced rectangle is 30 meters and the reduced rectangle has a length of 9 meters.

Now, to get the width of original rectangle.

The reduced rectangle's perimeter = 30 meters.

The reduced rectangle's length = 9 meters.

Now, we find the width of reduced rectangle by using formula:

Let the width of reduced rectangle be $x.$