If the discriminant b^2-4ac is 0, then you have TWO EQUAL, REAL ROOTS.
If you're given the x-intercepts, you can determine the factors of the polynomial as follows: Take -3, change the sign and write (x+3). Take 5, change the sign and write (x-5). Then the eq'n of the parabola is
f(x) = (x+3)(x-5) = x^2 - 2x -15, in which a=1, b = -2 and c= -15.
You can find the x-coordinate of the vertex, which is also the equation of the axis of symmetry, using
x= -b / (2a). Here, x = -(-2) / (2[1]), or x = 1
Find the y-coordinate by subbing 1 for x in the equation above:
y = (1)^2 - 2(1) - 15 = 1 - 2 - 15 = -16
The vertex is at (1, -16) and the equation of the axis of symm. is x = 1.
Answer: The numbers whose sum equals 12 and whose product and difference is largest is 6 and 6
Step-by-step explanation:
numbers whose sum is 12
Sum =12 Product Difference Product- Difference
11 +1 11 10 1
10 +2 20 8 12
9 +3 27 6 21
8 +4 32 4 28
7 +5 35 2 33
6+6 36 0 36
The numbers whose sum equals 12 and whose product and difference is largest is 6 and 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.
<span>Cross multiply:
2 * n = 5 * 12
Simplifying
2 * n = 5 * 12
Multiply 5 * 12
2n = 60
Solving
2n = 60
Solving for variable 'n'.
Move all terms containing n to the left, all other terms to the right.
Divide each side by '2'.
n = 30
Simplifying
n = 30</span>
Answer:
For statement 2, reason is Segment addition postulate.
Statement 3 and reason is
BD=AC+CD using substitution property of equality.
Statement 4 and reason is
AC+CD=BD using symmetric property of equality
Statement 5 is
BD= BC+CD
Statement 6 and reason is
AC+CD=BC+CD using transitive property of equality
Reason for 7 is
Subtraction property of equality.
Step-by-step explanation:
For statement 2, we use segment addition postulate to say AC= AE+EC.