10. The y-intercept uses which letter? M Z B Y
2 answers:
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Roots with imaginary parts always occur in conjugate pairs. Three of the four roots are known and they are all real, which means the fourth root must also be real.
Because we know 3 and -1 (multiplicity 2) are both roots, the last root is such that we can write
There are a few ways we can go about finding , but the easiest way would be to consider only the constant term in the expansion of the right hand side. We don't have to actually compute the expansion, because we know by properties of multiplication that the constant term will be
.
Meanwhile, on the left hand side, we see the constant term is supposed to be 9, which means we have
so the missing root is 3.
Other things we could have tried that spring to mind:
- three rounds of division, dividing the quartic polynomial by , then by
twice, and noting that the remainder upon each division should be 0
- rational root theorem
<u>Given</u>:
A ball is kicked 4 feet above the ground with an initial vertical velocity of 55 feet per second.
The function represents the height h(in feet) of the ball after t seconds.
We need to determine the time of the ball at which it is 30 feet above the ground.
<u>Time:</u>
To determine the time that it takes for the ball to reach a height of 30 feet above the ground, let us substitute h(t) = 30, we get;
Adding both sides of the equation by 16t², we get;
Subtracting both sides of the equation by 55t, we have;
Let us solve the quadratic equation using the quadratic formula, we get;
The value of t is t = 0.6 because this denotes the time taken by the ball to reach a height of 30 feet from the ground.
Therefore, the time taken by the ball to reach a height of 30 feet above the ground is 0.6 seconds.
Answer:
a = 26°
b = 48°
c = 26°
d = 106°
