First set up a proportion of 8/12 then set up another proportion of x/96 cross multiply to get 12x = 768
Divide by 12 to get your answer of 64
Given:
The expression is
To find:
The simplified form of the given expression.
Solution:
We have,
It can be written as
Taking LCM, we get
Cancel out the common factors.
Therefore, the simplified form of the given expression is .
Answer:
• you have correctly identified the radius as 157 miles
• 77,398 square miles is the coverage area
Step-by-step explanation:
The area of a circle is given by the formula ...
A = π·r^2
Filling in your numbers and doing the arithmetic, we get ...
A = 3.14·(157 mi)^2 = 77,397.86 mi^2
The area is approximately 77,398 square miles.
Answer:
Step-by-step explanation:
We are dealing with the "american" measure of feet, so the pull of gravity that we need is -16t^2. The quadratic that models this, in standard form, is
where v0 is the initial vertical velocity (64) and h0 is the initial height (4). Filling that standard position function in with our stuff gives us:
We are asked how long it will take for the object to reach its max height, then of course we are asked what the max height is (of course!). I am going to use calculus here since it's the easiest way to go. The first derivative of the position function is the velocity function.
v(t) = -32t + 64
You should know at this point from either algebra 2 or physics or calculus that an object has no velocity at its max height because it has to stop in the air in order to turn around and head back down. So we will set the velocity function equal to 0 and solve for how long it takes to reach that max height.
0 = -32(t - 2) so
t = 2 seconds, which answers the first question. If it takes 2 seconds to reach its max height, we can sub in 2 for t in the position function to find the object's position at 2 seconds. This will be the max height.
so
s(2) = 68 feet. The max height is 68 feet, which answers the seconds question.
As far as the range goes, the position function is an upside down parabola with a max height of 68. So the range, if I'm understanding what is being asked, is y | y ≤ 68
Answer:
B. 0
Step-by-step explanation:
Given the expression
Un = 5n + (-1)ⁿ/n²
Limit of the sequence is taken by tending the value of n to infinity
Note that lim (aⁿ) as n tends to infinity is zero for values of a<1
Find the remaining solution in the attachment.
Limit of the sequence 5n + (-1)ⁿ/n² as n tends to infinity is 0