An object is launched upwards from an initial height of 4 feet above ground, with an initial velocity of 48 feet per second. if the object's position at time x is given by f(x) = −16x2 + vt + s, where v is initial velocity and s is initial height, which equation can be used to find the maximum height of the object after x seconds?

The equation is used to find the maximum height.

The maximum height of the object is 40 feet at x=1.5.

Step-by-step explanation:

The vertex from of a parabola is

        ..... (1)

where, a is constant, (h,k) is vertex.

The object's position at time x is given by

where, v is initial velocity and s is initial height.

It is given that the initial height of the object is 4 feet and initial velocity is 48 feet per second.

Substitute v=48 and s=4 in the above function.

Rewrite the above equation in vertex form.

If an expression is , then we need to add in it to make it perfect square.

In the parenthesis b=3,

Add and subtract (1.5)^2 in the parenthesis.

           .... (2)

The equation is used to find the maximum height.

On comparing (1) and (2), we get

a=-16, h=1.5, k=40

Therefore, the maximum height of the object is 40 feet at x=1.5.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

step-by-step :