Answer:
see explanation
Step-by-step explanation:
a
The tangent and the radius at the point of contact form a right angle
Using Pythagoras' identity on the right triangle formed.
Let x be the distance from the centre to P, then
x² = 4² + 10² = 16 + 100 = 116 ( take the square root of both sides )
x = 
≈ 10.77 cm (to 2 dec. places )
b
let the required angle be Θ, then
Using the sine or cosine ratio in the right triangle.
cosΘ = 
= 
Θ = 
( ) ≈ 21.8°
Answer:
C - f(t) = 4(t − 1)^2 + 2; the minimum height of the roller coaster is 2 meters from the ground.
Step-by-step explanation:
Here we're asked to rewrite the given equation f(t) = 4t^2 − 8t + 6 in the form f(t) = a(t - h)^2 + k (which is known as the "vertex form of the equation of a parabola.") Here (h, k) is the vertex and a is a scale factor.
Let's begin by factoring 4 out of all three terms:
f(t) = 4 [ t^2 - 2t + 6/4 ]
Next, we must "complete the square" of t^2 - 2t + 6/4; in other words, we must re-write this expression in the form (t - h)^2 + k.
(To be continued)
Well assuming that this would be a typical triangle, and not a right angle one, knowing that the sum of all sides adds up to 180 degrees, simply add all of the expressions and one value and make it equal to 180, and then solve for x.
(6x-1) + (X+14) + 20 = 180
6x - 1 + X + 14 = 160
7x - 1 + 14 = 160
7x + 13 = 160
7x = 147
X = 21.
Now solve for the angles by plugging in X.
A = 6x - 1 = 6(21) - 1 = 125 degrees
C = X + 14 = (21) + 14 = 35 degrees.
I believe these are the solutions.
The answer is : a^2=1 x 2^n-1
To check if it’s correct
a^2= 1 x 2^2-1
a^2 = 1x 2
a^2 = 2
Hope this helps!
Answer:
8 inches.
Step-by-step explanation:
In the first bounce, the height that the ball reaches was 125 inches.
If the ball always bounces back to 
of the height, then after 2nd bounce it will reach 
inches height.
Again, after 3rd bounce, it will reach 
inches height.
And, after 4th bounce, it will reach 
inches height. (Answer)
