Consider the three functions below. f(x) = Negative StartFraction 6 Over 11 EndFraction (eleven-halves) Superscript x g(x) = Sta
2 answers:
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Check the picture below.
now, bear in mind that, there are 60minutes in 1 degree, so 23' is just 23/60 degrees or about 0.38 degrees.
and 29' is just 29/60 degrees or about 0.48 degrees.
so 16°23' is about 16.38°, and 49°29' is about 49.48°
make sure your calculator is in Degree mode.
now, bear in mind that, there are 60minutes in 1 degree, so 23' is just 23/60 degrees or about 0.38 degrees.
and 29' is just 29/60 degrees or about 0.48 degrees.
so 16°23' is about 16.38°, and 49°29' is about 49.48°
make sure your calculator is in Degree mode.
The resultant velocity of the plane is the sum of the two velocity vectors which are perpendicular to each other. See the attached figure.
The magnitude of the resultant velocity is
.
The approximate value of the actual velocity of the plane is . Correct choice is (D).
Answer:
Step-by-step explanation:
Lets call x,y the numbers we obtain from the calculator. x and y are independent random variables of uniform[0,1] distribution.
Lets note that, since both x and y are between 0 and 1, then 1 is the biggest side of the triangle.
Lets first make a geometric interpretation. If the triangle were to be rectangle, then the side of lenght 1 should be its hypotenuse, and therefore x and y should satisfy this property:
x²+y² = 1
Remember that in this case we are supposing the triangle to be rectangle. But the exercise asks us to obtain an obtuse triangle. For that we will need to increase the angle obtained by the sides of lenght x and y. We can do that by 'expanding' the triangle, but if we do that preserving the values of x and y, then the side of lenght 1 should increase its lenght, which we dont want to. Thus, if we expand the triangle then we should also reduce the value of x and/or y so that the side of lenght 1 could preserve its lenght. With this intuition we could deduce that
x²+y² < 1
Now lets do a more mathematical approach. According to the Cosine theorem, a triangle of three sides of lenght a,b,c satisfies
a² = b²+c² - 2bc* cos(α), where α is the angle between the sides of lenght b and c.
Aplying this formula to our triangle, we have that
, where
is the angle between the sides of lenght x and y.
Since the triangle is obtuse, then , and for those values
is negative , hence we also obtain
1 > x² + y²
Thus, we need to calculate P(x²+y² <1). This probability can be calculated throught integration. We need to use polar coordinates.
(x, y) = (r*cosФ,r*senФ)
Where r is between 0 and 1, and Ф is between 0 and (that way, the numbers are positive).
The jacobian matrix has determinant r, therefore,
As a conclusion, the probability of obtaining an obtuse triangle is .
The right answer is Option B:
Step-by-step explanation:
Given,
Current value of car = $5500
This is 55% of the original value.
Let,
p be the original price of car.
Therefore,
55% of p = 5500
Dividing both sides by p
The equation can be used to find the price Mrs. Merson paid for the car.
The right answer is Option B:
Keywords: percentage, division
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