A projectile is fired straight upward with an initial velocity of 400 feet per second. The height of the projectile, h(t), if represented by the function h(t)=-16t^2+400t, where t is the time in seconds. How long does it take the projectile to reach the maximum height?
Answers
Taking into account the definition of maximum, minimum and vertex of a quadratic function, it takes 12.5 seconds for the projectile to reach maximum height.
A quadratic function is defined in the form:
y= f (x) = ax² + bx + c
Every quadratic function has a maximum or a minimum, which is the vertex of the parabola. If the parabola has an upward concavity, the vertex corresponds to a minimum of the function; whereas if the parabola has concavity downwards, the vertex will be a maximum.
That is, if the coefficient a is positive the parabola is concave and the vertex will be a minimum of the function, while if a is negative the parabola will be convex and the vertex is a maximum.
The maximum or minimum is reached in
The maximum or minimum value of y is obtained by evaluating the function at xv, this is, f (xv).
In this case, the function is:
h(t)= -16t² + 400t
where t is the time in seconds
Being a = -16 and b = 400, the value of a is negative, so the vertex will be the maximum.
You want to know the time it takes for the projectile to reach the maximum height, that is, the maximum in t. That is, you must calculate t using the expression:
So:
Solving:
t= 12.5 seconds
It takes 12.5 seconds for the projectile to reach maximum height.
Learn more about cuadratic function with this examples:
Answer:
You can find the answer by using the formula x=-b/2a
Step-by-step explanation:
Remember the maximum height will be at the vertex. The x value of the vertex is your time, so use x=-b/2a. Then if it had also asked what the height was, you would plug that answer into your equation to find the y value of the vertex. Pretty sure your teacher is just asking you to find the x though:)
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f (x), has (x-7) and (x+4i) as factors. F(X)=2x^5-13x^4+22x^3-187x^2-160x+336 what is the total number of real numbers of real zeros of f(X)
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Answers
(5)(3x-8y=24)
-15x+3y=-9
15x-40y=120
3y=-9
-40y=120
-37y=111
Divide both sides by -37
y=-3
To solve for x. Choose one equation from the given and plug what you get in Y.
I'll choose, -5x+y=-3
So, -5x+(-3)=-3
-5x=0
Divide both sides by -5
x=0/-5
Hope, this helps.
Answers
Answers
Answer:
Step-by-step explanation:
The problem tell us that is the inverse of
, where:
So, we need to find the inverse function of in order to find
Let's find the inverse function using the following steps:
1. Replace with
:
2. Solve the equation for :
3. Replace every with a
and replace every
with a
:
4. Finally, replace with
Therefore:
f(x)=y=4x+12
x=4y+12
==>4y=x-12
==>y=x/12- 3
g(x)=x/12 -3
Answers
It would look more like 1
------
-7 (as an exponent)
x
A)
2.4 in.
B)
4.8 in.
C)
2.4π in.
D)
4.8π in.
Answers
Answer:
D
Step-by-step explanation:
the circumference (C) of a circle is calculated as
C = πd ( d is the diameter )
here d = 4.8 in , then
C = π × 4.8 = 4.8π in
A.Two distinct lines are parallel if they are in the same plane and never intersect each other.
b.Two distinct lines are parallel if they point in the same direction.
c.Two distinct lines are parallel if one can be rotated to sit on top of the other.
Answers
Option (B) that is Two distinct lines are parallel if they are in the same plane and never intersect each other is correct.
What is a perpendicular line?
A Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
We know from the definition of the lines:
The line is a ray that goes infinitely from both sides.
In the perpendicular lines, they intersect at 90 degrees angles or right angles.
In the parallel lines, they never intersect and go parallel infinitely from both sides.
We have choices:
Choice A that is Two distinct lines are parallel if one can be rotated to sit on top of the other.
Choice B that is Two distinct lines are parallel if they are in the same plane and never intersect each other.
Choice C that is Two distinct lines are parallel if they point in the same direction.
The most precise and correct definition of parallel lines is two distinct lines are parallel if they are in the same plane and never intersect each other.
Thus, option (B) that is Two distinct lines are parallel if they are in the same plane and never intersect each other is correct.
Learn more about the perpendicular line here:
#SPJ2
Hope this helps! :)