Answer:
Step-by-step explanation:
In any square with side length 
, the diagonal of the square is equal to 
. Since the side length of this square is 
, the diagonal is equal to 
.
Alternatively, you can form two 45-45-90 triangles with the diagonal of the square. The diagonal acts as the hypotenuse for the both these triangles, and the legs of both triangles are equal to the side length of the square. To find the length of the diagonal, use the Pythagorean Theorem, which states 
, where 
is the hypotenuse of the triangle, and 
and 
are the two legs of the triangle.
In this question, both legs are equal to , and we're solving for the diagonal, which is the hypotenuse in this case:
Answer:
Step-by-step explanation:
A hyperbola is a curve for which the difference of the distances |d₂ - d₁| of any point P from the foci is constant.
The definition leads to the equation
1. Calculate the value of a²
Assume the neighbours are at the foci A and B.
The explosion is farther from B than from A, so it occurred on the right branch of the hyperbola.
Then AB = 1 mi = 5280 ft
and the distance from the focus to the y-axis is
c = 2640
The vertices are (±a,0).
The speed of sound is 1100 ft/s, so B is 2200 ft further from the explosion.
The distance from A to the vertex V₁ is c - a. Then
AB = 2200 + 2(c - a) = 2200 -2(2640 - 2a) = 2200 +5280- 2a = 5280
2a = 2200
a = 1100
a² = 1 210 000
2. Calculate the value of b²
3. Write the equation for the hyperbola
Answer:
D
Step-by-step explanation:
her value is greater
2x+4x+30=90
6x+30=90
-30 -30
6x=60
/6 /6
x=10
A=2*10
A=20
