Answer:
381.51 in^3
Step-by-step explanation:
Volume of a sphere = 4/3 x pi x r^3
r = 9/2 = 4.5
4/3 x 3.14 x 4.5^3 = 381.51 in^3
The lines y = 2x - 1 and y = -2x + 3 intersect at exactly one point which means this system has exactly one solution. so the system is consistent and independent
the coordinates of the points of intersection of the graph of y=13−x with the axes
Given equation is y=13-x
x axis is x=0
y axis is y=0
Plug in the value of x =0 and find out y
y = 13 - x
y = 13 - 0 = 13
Plug in the value of y=0 and find out x
0 = 13 - x
x= 13
So coordinate axis
x= (13,0)
y= (0,13)
Base of the triangle is x=13
Height of the triangle is y= 13
Area of the triangle = 
=
= 84.5
Area of the triangle = 84.5
Answer:
We conclude that the function represents exponential growth.
Step-by-step explanation:
Given the function

As the function is of the form
and base 'b' > 1
We know that when the base 'b' of the exponential function > 1, meaning those numbers will get bigger, we call it exponential growth.
As b=8/5 is bigger than 1.
i.e. 8/5 > 1
Thus, we conclude that the function represents exponential growth.
Complete question
A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.
What is the rate of change of the distance between the bottom of the ladder and the wall at that instant(in meters per minute)
Answer:

Step-by-step explanation:
From the question we are told that
Slant height 
Change in Vertical height 
Horizontal length 
Generally in finding the distance form the top to the bottom of the wall it is mathematically given by




Generally solving for the differential equation is mathematically represented as






