Answer:
6
Step-by-step explanation:
(x^10)^3/5
=x^(10×3/5)
=x^6
Answer:
a. see attached
b. H(t) = 12 -10cos(πt/10)
c. H(16) ≈ 8.91 m
Step-by-step explanation:
<h3>a.</h3>
The cosine function has its extreme (positive) value when its argument is 0, so we like to use that function for circular motion problems that have an extreme value at t=0. The midline of the function needs to be adjusted upward from 0 to a value that is 2 m more than the 10 m radius. The amplitude of the function will be the 10 m radius. The period of the function is 20 seconds, so the cosine function will be scaled so that one full period is completed at t=20. That is, the argument of the cosine will be 2π(t/20) = πt/10.
The function describing the height will be ...
H(t) = 12 -10cos(πt/10)
The graph of it is attached.
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<h3>b. </h3>
See part a.
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<h3>c.</h3>
The wheel will reach the top of its travel after 1/2 of its period, or t=10. Then 6 seconds later is t=16.
H(16) = 12 -10cos(π(16/10) = 12 -10cos(1.6π) ≈ 12 -10(0.309017) ≈ 8.90983
The height of the rider 6 seconds after passing the top will be about 8.91 m.
Answer:
about $10859.47 if you're talking total but about $5859.47 if you're talking about how much more than the initial value
Step-by-step explanation:
Answer:
Lacrosse = 62 students
Swimming = 62 students
Soccer = 124 students
Football = 186 students
Step-by-step explanation:
Based on the information, we can draw some equations
<em>1.</em> Lacrosse = Swimming
<em>2.</em> Soccer = 2 * Lacrosse
<em>3.</em> Football = 3 * Swimming
<em>4.</em> Football + Soccer + Swimming + Lacrosse = 434
Lets solve for once sport at a time, I will start with Football.
I will put equation 1, 2 and 3 into equation 4
3Sw + 2L + L + L = 434
We can now again put equation 1 into the new equation 4
3L + 2L + L + L = 434
Simplify
7L = 434
L = 434 ÷ 7
L = 62 students
Since L = Sw, 62 students did swimming also
We can put L into equation 2 to solve for So
So = 2 * 62
So = 124 students
And now we can put Sw into equation 3 to solve for F
F = 3 * 62
F = 186 students
Given:
The graph of a system of inequalities.
To find:
The ordered pair which is a solution to the graphed inequality.
Solution:
The boundary lines are:


From the given graph it is clear that only point (3,1) lies in the shaded region.
Points (2,-1) and (4,0) lie on the boundary line
but the boundary line is dotted. It means the points on the line are not in the solution set.
point (0,-1) does not belong to the shaded region.
Therefore, the correct option is A.