Answer:
-12/5
Step-by-step explanation:
-4 * 9 = -36 (numerator)
3 * 5 = 15 (denominator)
Take 3 out of both to simplify.
-36/3 = -12
15/3 = 5
Final Answer:
-12/5
Answer:
x=-1
Step-by-step explanation:
-3+75x<-75+3x
75x-3<-75+3x
75x-3<3x-7575x−3<3x−75
75x-3-3x<-75
72x-3<-75
72x<-75+3
72x<-72
x=-1
Answer:
24.76 mine
Step-by-step explanation:
The first thing is to calculate the area of the region, which we can calculate since we have the density and the population. The area would be the quotient between population and density:
260000/135 = 1925.93
The area would be 1925.93 square mine
We know that the area is given by:
A = pi * r ^ 2
we solve to r
r ^ 2 = A / pi
r ^ 2 = 1925.92 / 3.14
r ^ 2 = 613.3
r = 24.76
the radius is equal to 24.76 mine
Answer: There are no real number roots (the two roots are complex or imaginary)
The discriminant D = b^2 - 4ac tells us the nature of the roots for any quadratic in the form ax^2+bx+c = 0
There are three cases
- If D < 0, then there are no real number roots and the roots are complex numbers.
- If D = 0, then we have one real number root. The root is repeated twice so it's considered a double root. This root is rational if a,b,c are rational.
- If D > 0, then we get two different real number roots. Each root is rational if D is a perfect square and a,b,c are rational.
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.
