Answer:
(-10, 10) and (0,10).
Step-by-step explanation:
For a point to be a solution to the system of inequalities, you will need to see which of the points falls into the shaded area.
When we test out each of the points, we can see that only:
(-10, 10) and (0,10) fall into the blue-shaded area.
We have:
Thus:
Adding
gives:
Factoring gives:
Thus, we have:
or
.
Note that because
, there will be no solutions
of the form
for positive integer
and solution
. So we find the basic values of
giving
.
For
with positive
,
(this can be seen easily from the unit circle. But
, a contradiction. So we examine the case in which
.
In this case,
. So this is the only solution to this equation.
Substituting this back in, we have
, as desired. So this is a valid solution.
Thus,
.
I'm pretty sure it's an infinite number of lines
Answer:
The surface area of the cylinder is 326.56yd²
Step-by-step explanation:
To solve this problem we have to calculate the circle area and the lateral area
To calculate the area of the circle we use the following formula
a = area
r = radius = 4yd
π = 3.14
a = π * r²
we replace with the known values
a = π * (4yd)²
a = π * 16yd²
a = 50.24yd²
The area of the circle is 50.24yd²
To calculate the lateral area of the cylinder we use the following formula
a = area
h = heighti = 9yd
r = radius = 4yd
π = 3.14
a = 2 * π * r * h
we replace with the known values
a = 2 * 3.14 * 4yd * 9yd
a = 6.28 * 36yd²
a = 226.08yd²
The lateral area of the cylinder is 226.08yd²
Now we add the lateral area of the cylinder with 2 times the area of the circle and obtain the area of the cylinder
226.08yd² + (2 * 50.24yd² ) = 326.56yd²
The surface area of the cylinder is 326.56yd²
Answer:
The number of days the number will be greater than 60 is 45.
Step-by-step explanation:
Since there are 80 total numbers and a number of the day can be repeated, then there is the same chance each day of picking one of the numbers. There are 20 numbers greater than 60 between 1 and 80. So, the chances of picking a number greater than 60 each day is 20/80, or 1/4 (25%). This probability is the same each day and we would take the total number of school days (180) multiplied by this probability to get our predicted number of days the number would be greater than 60 during the school year. 180 x .25 = 45.