When it hits the ground h = 0 so we have
-16t^2 + 36t + 4 = 0
t = 2.36 seconds to nearest hundredth.
Use the formula of arc length that is
s = rθ
where s = arc length, r = radius, θ = angle (unit must be in radian)
Given r = 5 in and θ = 48°( π /180°) = (4/15)* π = 0.2667 π,
s = 5 in (0.2667π) = 1.333 π in
y=mx+b is the equation of a line;
m=slope , b= y-intercept
You can find the slope with this following equation: (y(2)-y(1))/(x(2)-x(1))
In this case the points are (0,4) and (-2,-3). The first set being (0,4) and the second (-2,-3). This means (0,4) can be expressed as (x(1),y(1)) and (-2,-3) expressed as (x(2),y(2)). Plugging these numbers into the slope equation gives us: (-3-4)/(-2-0) = -7/-2 = 7/2.
m= 7/2 ; so we have : y= (7/2)x+b
We are give a set of points which it passes through, we can simply plug them in:
4 = (7/2)(0)+b (0 is the x and 4 is the y)
We get 4 = 0 +b .... 4=b
our final equation is : y=(7/2)x+4
Answer:it is only (x,y) -> (3x, 3y)
Step-by-step explanation: I just took the test and got it right,, hope it helped :)
Answer:
Step-by-step explanation:
y′′ + 4y′ − 21y = 0
The auxiliary equation is given by
m² + 4m - 21 = 0
We solve this using the quadratic formula. So
So, the solution of the equation is
where m₁ = 3 and m₂ = -7.
So,
Also,
Since y(1) = 1 and y'(1) = 0, we substitute them into the equations above. So,
Substituting A into (1) above, we have
Substituting B into A, we have
Substituting A and B into y, we have
So the solution to the differential equation is
