Answer:
Step-by-step explanation:
41,000
If the polygons are similar then the sides are in proportion.
Therefore we have the equations:
When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
The question is an illustration of bearing (i.e. angles) and distance (i.e. lengths)
The distance between both lighthouses is 5783.96 m
I've added an attachment that represents the scenario.
From the attachment, we have:
Convert to degrees
Convert to degrees
So, the measure of angle S is:
---- Sum of angles in a triangle
The required distance is distance AB
This is calculated using the following sine formula:
Where:
So, we have:
Make AB the subject
Hence, the distance between both lighthouses is 5783.96 m
Read more about bearing and distance at:
brainly.com/question/19017345
Answer:
12 =x
20.78460969=y
Step-by-step explanation:
sin theta = opposite side / hypotenuse
sin 60 = y /24
Multiply each side by 24
24 sin 60 = y/24*24
24 sin 60 =y
20.78460969=y
cos theta = adjacent side / hypotenuse
cos 60 = x /24
Multiply each side by 24
24*cos 60 = x/24*24
24 cos 60=x
12 =x
