The answer is <span>10 units
</span>
The diameter of the cylinder (d) is the twice of its radius (r): d = 2r
The volume (V) of the cylinder with radius r and height h is:
V = π r² h
We have:
d = 2r
r = ?
h = 7
π = 3.14
V = 175π
175π = π * r² * 7
175 = r² * 7
r² = 175/7
r² = 25
r = √25
r = 5
d = 2r
d = 2 * 5
d = 10
A recursive sequence is a sequence of numbers whose values are determined by the numbers that come before them in the sequence.
We’re given a sequence whose (n + 1)-th term f(n + 1) depends on the value of the n-th term f(n), specified by the recursive rule
f(n + 1) = -4 f(n) + 3
We’re also given the 1st term in the sequence, f(1) = 1. Using this value and the recursive rule, we can find the next term f(2). (Just replace n with 1.)
f(1 + 1) = -4 f(1) + 3
f(2) = -4 • 1 + 3
f(2) = -1
We do the same thing to find the next term f(3) :
f(2 + 1) = -4 f(2) + 3
f(3) = -4 • (-1) + 3
f(3) = 7
One more time to find the next term f(4) :
f(3 + 1) = -4 f(3) + 3
f(4) = -4 • 7 + 3
f(4) = -25
Answer: x = $7, y = $6
Step-by-step explanation:
Let x be the cost of an adult ticket
Let y be the cost of a children's ticket
Translate these sentences to algebra:
At the circus, three adult tickets and five child tickets cost $51: 3x + 5y = 51
Five adult tickets and two child tickets cost $47: 5x + 2y = 47
Now we have two equations. Let's use substitution to solve.
3x + 5y = 51
3x = 51 - 5y
.: x = 17 - 5y/3
Now substitute this value of x into the second equation to find the numerical value of y:
5(17 - 5y/3) + 2y = 47
85 - 25y/3 + 2y = 47
-19y/3 = -38
-19y = -114
.: y = 6
Now find x:
x = 17 - 5y/3
x = 17 - 10
.: x = 7
So an adult ticket costs $7, and a child ticket costs $6 :)
The slope form equation is: y=mx+b so once you plug in the numbers available through the diagram you get.
y=3x+4
Step-by-step explanation:
Given
Lin walks half a mile at a constant rate i.e. Lin velocity is constant. So, in the graph, it will be a straight line through the origin.
Lin is still for five minutes and after she began sprinting for the slip up to halfway i.e. Lin is accelerating or velocity is increasing for the halfway and later she started walking for the rest of the way.
