Answer:
B. There is one real, double root
Step-by-step explanation:
For ax² + bx + c = 0, the discriminant is b² − 4ac.
If the discriminant is positive and a perfect square, there are two real, rational roots.
If the discriminant is positive and not a perfect square, there are two real, irrational roots.
If the discriminant is 0, there is one real, double root.
If the discriminant is negative, there are two complex roots.
Here, a = 64, b = -16, and c = 1.
b² − 4ac
= (-16)² − 4(64)(1)
= 0
The discriminant is 0. Therefore, there is one real, double root
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.
__
<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:

Step-by-step explanation:
<h3>Equation of the blue line:</h3>
since the line is horizontal and passes <u>-</u><u>2</u> the equation of the blue line should be

<h3>Equation of the red line:</h3>
remember The form of equation of a line

where m is slope of the line and b is the y-intercept we can clearly see that the red line crosses y-axis at (0,-3) therefore b=-3
to figure out m we can consider the following formula:

from the graph we acquire ∆y=1 and ∆x=2
thus substitute:

so we have figured out m and b
therefore our equation of blue line is

our given options are in standard form so
move -3 to left hand side and change its sign:

cross multiplication:

move 6 to right hand side and x to left hand side and change its sign

multiply both sides by -1:

hence, our system of linear equation is

The answer is
D: 160π cm^3
Answer:
79 degrees
Step-by-step explanation:
PQU is a straight line, so
. This is also the sum of the four smaller angles. We can subtract 34+37+30 from 180 to get that 
(if right pls give brainliest :) )