Which of these points represent 1/5 on the number line shown below?
1 answer:
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Answer:
As per the statement:
The path that the object takes as it falls to the ground can be modeled by:
h =-16t^2 + 80t + 300
where
h is the height of the objects and
t is the time (in seconds)
At t = 0 , h = 300 ft
When the objects hit the ground, h = 0
then;
-16t^2+80t+300=0
For a quadratic equation: ax^2+bx+c=0 ......[1]
the solution for the equation is given by:
On comparing the given equation with [1] we have;
a = -16 ,b = 80 and c = 300
then;
Simplify:
= -2.5 sec and
= 7.5 sec
Time can't be in negative;
therefore, the time it took the object to hit the ground is 7.5 sec
Answer:
b = 15.75
Step-by-step explanation:
Lets find the interception points of the curves
36 x² = 25
x² = 25/36 = 0.69444
|x| = √(25/36) = 5/6
thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).
The area of the bounded region is given by the integral
The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.
125/18 = b^{1.5}/9
b = (62.5²)^{1/3} = 15.75