Please help! Mathematics
1 answer:
Answer:
y = 2
Step-by-step explanation:
Kindly view the attached image to see the rules when looking for the horizontal asymptote.
In this situation we have 2x² / x²
The powers of both are equal to each other therefore the horizontal asymptote will be at the coefficient of the numerator divided by the coefficient of the denominator.
In other words the horizontal asymptote is at y = 2/1 or just 2
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The rate of change of the angle of elevation when the firework is 40 feet above the ground is 0.12 radians/second.
First we will draw a right angle triangle ΔABC, where ∠B = 90°
Lets, assume the height(AB) = h and base(BC)= x
If the angle of elevation, ∠ACB = α, then
tan(α) =
Taking inverse trigonometric function, α = tan⁻¹ () .............(1)
As we need to find the rate of change of the angle of elevation, so we will differentiate both sides of equation (1) with respect to time (t) :
Here, the firework is launched from point B at the rate of 10 feet/second and when it is 40 feet above the ground it reaches point A,
that means h = 40 feet and = 10 feet/second.
C is the observer's position which is 50 feet away from the point B, so x = 50 feet.
= 0.12 (Rounding up to two decimal places)
So, the rate of change of the angle of elevation is 0.12 radians/second.
Given,
Rate of free fall = 216 km/h
Solution,
km/h to m/s is converted as follows :
So, the rate of fall is 60 m/s.
If t = 20 s
Assume, initial velocity = 0
It will move under the action of gravity.
Using equation of motion,
Hence, this is all for the solution.
The other angles in the isosceles triangle with an angle of 100° will be 40°
Step-by-step explanation:
Lets define an isosceles triangle first.
"An isosceles triangle is a triangle with two equal sides and two equal angles.
Given that an angle of the triangle is 100°
We know that the sum of internal angles of a triangle is 180°
The sum of remaining two angles is:
=180°-100°
=80°
As the triangle is an isosceles triangle, the two angles will be equal.
So the angles will be:
The other angles in the isosceles triangle with an angle of 100° will be 40°
Keywords: Triangle, isosceles triangle
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