MATHEMATICS MIDDLE SCHOOL

A ball is thrown vertically upward from the ground with an initial velocity of 122 ft/sec. Use the quadratic functionh(t) = -16t2 + 122t +0 to find how long it will take for the ball to reach its maximum height, and then find the
maximum height. Round your answers to the nearest tenth.

Answers

Answer 1

Answer:

Answer:

232.6 metres after 3.8 seconds.

Step-by-step explanation:

h(t) = -16t² + 122t

a = -16 b = 122 c = 0

Substitute into the quadratic formula

(Ignore the Â)

$x = \frac{-b±\sqrt{b^(2)-4ac}}{2a}$

$x = \frac{-122±\sqrt{122^(2)-4(-16)(0)}}{2(-16)}$

$x = (-122±122)/(-32)$

Split the equation at the ±

$x = (-122+122)/(-32)$ $x = (-122-122)/(-32)$

$x = (0)/(-32)$ $x = (-244)/(-32)$

$x = 0$ $x = (61)/(8)$

The two x-intercepts at 0 and 61/8. The midpoint of the x-intercepts is the axis of symmetry, which is the x-coordinate of the vertex.

Midpoint = [0 + (61/8)] / 2

Midpoint = 61/16 <= This is the time for maximum height

t = 61/16

t = 3.8125 => Round to t = 3.8

To find the maximum height, substitute t=61/16 into the equation

h(t) = -16t² + 122t

h(61/16) = -16(61/16)² + 122(61/16)

h(61/16) = 232.5625 => Round to h = 232.6

Therefore, the ball will reach the maximum height of 232.6 metres after 3.8 seconds.

Zero complex roots or two complex roots.

Step-by-step explanation:

First of all, we have to know that complex roots can happen only in pairs, because they are based on the square root of a negative number.

On the other hand, a third degree polynomial can only have 3 roots as solution, because the degree of the polynomial specifies how many roots would have.

So, if we only can have 3 roots, and complex roots can only happen in pairs, then f(x) would have zero complex roots or two complex roots only, those are the unique scenarios.

the answer would be 0 or 2

What is the difference between a prime number and a complex number?

Answers

"Prime"and "complex"are not opposites. If a number is a prime, then it has
exactly two factors ... ' 1 ' anditself. If it has any more factors, then it's not
a prime number, it's a"COMPOSITE" number.

(If a number is not a 'complex' number, then it's a REAL number.)

A Prime number is a number is a number which cannot be divided by any numbers except for itself and one to give an integer

A Complex Number is any number containing Real and Imaginary parts ( $Imaginary= √(-1)=i$