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aliya0001 [1]
2 years ago
14

6.7.35

Mathematics
1 answer:
valentinak56 [21]2 years ago
6 0

Answer:

Step-by-step explanation:

This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!

The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.

If:

s(t)=-16t^2+112t+360, then the velocity function, the first derivative is:

v(t) = -32t + 112 and solve for t:

-112 = -32t so

t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.

Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:

s(3.5)=-16(3.5)^2+112(3.5)+360 and

s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.

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a missile is launched from the ground. its height, h(x), can be represented by a quadratic function in terms of time, x, in seco
fomenos

Answer:

The height of the missile in the air  after 11 seconds is 330 feet.

Step-by-step explanation:

The standard form for the quadratic function f(x)= ax^2 + bx + c, which is the function of the parabola model.

We are given two points.

(1, 130) and (2, 240)

Here the first coordinate represents the x (time) and the second coordinate represents h(x), which is height.

Now plug these two coordinates and find the two equations.

(1, 130), the equation is

130 = a.(1)^2 + b(1) + c, where "c" is the initial height. Which is equal to zero.

Therefore, we get

130 = a + b + 0

a + b = 130 -------(1)

Now let's form the second equation using the coordinate (2, 240)

240 = a(2)^2 + b(2) + 0

240 = 4a + 2b -------------(2)

Now let's solve the equations (1) and (2) and find the value of "a" and "b"

a + b = 130 can be written as a = 130 - b

Here we can use the substitution method.

Now plug in a = 130 - b in the second equation, we get

240 = 4(130 - b) + 2b

240 = 520 - 4b + 2b

240 = 520 - 2b

2b = 520 - 240

2b = 280

Dividing both sides by 2, we get

b = 140

Now plug in b = 140 in a = 130 -b and find the value of a

a = 130 - 140

a = -10

Now we got a = -10 and b = 140.

We plug in a = -10 and b = 140 in the general form, we gety

h(x) = -10x^2 + 140x + c

Where c is the initial height, which is equal to 0.

h(x) = -10x^2 + 140x

Now plug in x = 11 seconds and find the height.

h(11) = -10(11)^2 + 140 (11)

= -10 (121) + 1540

= - 1210 + 1540

h(11) = 330 feet,

Therefore, the height of the missile in the air  after 11 seconds is 330 feet.

6 0
3 years ago
Write the quadratic equation whose roots are six and -2 and who’s leading coefficient is 3 use the letter X to represent the var
Artist 52 [7]

Answer:

3X^{2} - 12X - 36 = 0

Step-by-step explanation:

6 and - 2 are the only two solutions to the required quadratic equation.

So, if the variable is represented by X then (X - 6) and (X + 2) will be the only two factors of the polynomial function.

Therefore, the equation is  

(X - 6)(X + 2) = 0

⇒ X^{2} - 4X - 12 = 0

If the leading coefficient of the equation is 3 then we can write the equation as 3X^{2} - 12X - 36 = 0 (Answer)

6 0
3 years ago
If DE=6x what is the perimeter of the triangle in terms of x? <br><br> A 6<br> B 18 <br> C 18x
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HELP
Darya [45]

Answer:

lo que opinaria sería modo serio pero en realidad no pero bueno lo que creo que sería bien sería pieseses pero eso tiene cosa que ver con la metoforsosis o como se llame

8 0
3 years ago
What is the missing value , 2/3 and n/12
gavmur [86]
N=8
If you set 2/3 equal to n/12 then you multiple 3 by 4 to get 12. So you have to multiple 2 by 4 to get N.
8 0
2 years ago
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