Answer:
The lines are parallel
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
Remember that
If two lines are parallel, then their slopes are the same
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
step 1
Find the slope JK
we have
substitute the values
step 2
Find the slope LM
we have
substitute the values
step 3
Compare the slopes
so
therefore
The lines are parallel
Answer:
V = 1538.6 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2h where r is the radius and h is the height
V = pi (7)^2 10
V = 3.14 (49)10
V = 1538.6 cm^3
Answer:
4th option
Step-by-step explanation:
-2a^2-a
Imagine you covered the outer part of the wheel with paint. Then you rolled the wheel one complete revolution. The paint on the wheel would transfer to the flat ground making a straight line. The length of this straight line is exactly equal to the distance around the circle (aka circumference)
Let's find the circumference
C = 2*pi*r
C = 2*pi*14
C = 28pi
The distance around the circle is exactly 28pi inches.
If we use pi = 3.14, which is an approximation of pi, then that approximates to 28*pi = 28*3.14 = 87.92
So one revolution corresponds to traveling 87.92 inches approximately
We want to travel 440 inches. The question is: how many revolutions do we need to go in order to achieve this goal?
Let k = number of revolutions needed to travel 440 inches
1 revolution = 87.92 inches traveled
k revolutions = k*87.92 inches traveled
Set the expressions k*87.92 and 440 equal to each other and solve
k*87.92 = 440
k*87.92/87.92 = 440/87.92
k = 5.0045495 ... this is approximate
So it takes about 5 revolutions to travel 440 inches. We'll need a bit over 5 to make sure we get to 440.
Final Answer: Choice B) 5 rotations
