Answer:
45.27feet
Step-by-step explanation:
Given the height of the balloon (in feet) represented by the equation h=−16t2+28.7t+32.4, where t is the time (in seconds)
Note that the velocity of the balloon at maximum height is zero, hence;
v = dh/dt =0
-32t+28.7 = 0
-32t = -28.7
t = 28.7/32
t = 0.897secs
Get the maximum height
Recall that h=−16t²+28.7t+32.4
h = -16(0.897)²+28.7(0.897)+32.4
h= -12.87+25.74+32.4
h = 45.27feet
Hence the maximum height reached is 45.27feet
Answer:
P(X<=2) = 0.9736
Step-by-step explanation: Please find the attached file for the solution
Answer:
Option A) Circle.
Step-by-step explanation:
We are given the equation:
A general equation of the circle is of the form:
where (h,k) is the center of the circle and r is the radius of circle.
Comparing the two equations, we get,
Thus, the given equation is equation of a circle centered at (3,12) and of radius 5 units.
Answer:
g(-4) = -1
g(-1) = -1
g(1) = 3
Explanation:
If you are given a function that is defined by a system of equations associated with certain intervals of x, just find which interval makes x true, and then substitute x into the equation of that interval.
For example, given g(-4), this is an expression which is asking for the value of the equation when x = -4. So -4 is not ≥ 2, so ¼x - 1 will not be used. -4 is also not ≤ -1 and ≤ 2, so -(x - 1)² + 3 will not be used either. So in turn, we will just use -1 which is always -1 so g(-4) will just be -1, right because there is no x variable in -1 so it will always be the same.
Using the same idea as before g(-1) is g(x) when x = -1 so -1 will not be a solution because -1 is not less than -1 (< -1). -1 is not ≥ 2 either so we will be using the second equation because -1 is part of the interval -1≤x≤2 (it is a solution to this inequality), therefore -(x - 1)² + 3 will be used.
As x = -1, -(x - 1)² + 3 = -(-1 - 1)² + 3 = -(-2)² + 3 = -4 + 3 = -1.
It is a coincidence that g(-1) = -1.
Now for g(1), where g(x) has an input of 1 or the value of the function where x = 1, we will not use the first equation because x = 1 → x < -1 → 1 < -1 [this is false because 1 is never less than -1], so we will not use -1.
We will use -(x - 1)² + 3 again because 1 is not ≥ 2, 1≥2 [this is also false]. And -1 ≤ 1 < 2 [This is a true statement]. Therefore g(1) = -(1 - 1)² + 3 = -(0)² + 3 = 3
14 x² + 6 x - 7 x - 3 =
= ( 14 x² - 7 x ) + ( 6 x - 3 ) =
= 7 x ( 2 x - 1 ) + 3 ( 2 x - 1 ) =
= ( 2 x - 1 ) ( 7 x + 3 )
Answer:
1. GCF of the group ( 6 x - 3 ) is 3.
2. The common binomial factor is 2 x - 1.
3. The factored expression is: ( 2 x - 1 ) ( 7 x + 3 ).
