Help! what is the right answer?

the initial vertical velocity of a rocket shot straight up is 42 meters per second. How long does it take for the rocket to retu

Snowcat [4.5K]

It takes 4.3 seconds for the rocket to return to earth.

The equation is:
$0=-9.8t^2+v_0t+h_0$
where -9.8m/sec² is the acceleration due to gravity, v₀ is the initial velocity, and h₀ is the initial height. We will go from the assumption that the rocket is launched from the ground, so h₀=0, and we are told that the initial velocity, v₀, is 42. This gives us:

$0=-9.8t^2+42t$

We will use the quadratic formula to solve this. The quadratic formula is:
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Plugging in our information we have:
$t=\frac{-42\pm \sqrt{42^2-4(-9.8)(0)}}{2(-9.8)}
\\
\\=\frac{-42\pm \sqrt{1764-0}}{-19.6}
\\
\\=\frac{-42\pm \sqrt{1764}}{-19.6}
\\
\\=\frac{-42\pm 42}{-19.6}=\frac{-42-42}{-19.6} \text{ or } \frac{-42+42}{-19.6}
\\
\\=\frac{-84}{-19.6}\text{ or }\frac{0}{-19.6}
\\
\\=4.3\text{ or }0$

x=0 is when the rocket is launched; x=4.3 is when the rocket lands.

8 0

4 years ago

Graph and solve the system <br><br> Y=-3x+3<br> Y=2x-7

guajiro [1.7K]

An equation of the form y=ax+b, where a and b are constants; y and x are variable, is called a linear equation.

They are called "linear" because if we draw all the solutions of such an equation, they form a line.

This also means that it is enough to:

1. find to solutions
2. plot them on the coordinate axis
3.join those 2 points

and all the solutions of the equation y=ax+b will be on that line.

Thus, to draw line y=-3x+3

let x=0, then y=3, so one solution is (0, 3)

let y=0, then x=1 so a second solution is (1, 0)

(remark we can pick x or y to be any value, then solve for the other)

to draw the second line y=2x-7

let x=0, then y=-7
let x=3, then y=-1

plot these points and join them as shown in the picture.

The solution of the system is the point where the lines intersect, which is
(2, -3)

8 0

3 years ago

Read 2 more answers

How do you solve this?

slavikrds [6]

Answer: To solve these types of questions what I always do is get a protractor if you have one and put it up against to where the dot is in the middle of the empty hole and then get a ruler or a pencil and make the line keep going to see what angle. In this case your answer is 65% I think.

4 0

3 years ago

Two math students were asked to write an exponential growth equation that had a starting value of 300 and a growth rate of 2%. P

Gemiola [76]

Answer:

Pierre is right

Step-by-step explanation:

The correct formula for Exponential growth rate is given as:

y = a( 1 + r) ^t

Where

y = Amount after time t

a = Initial amount

r = Growth rate

t = time

From the question

a = 300

r = 2% = 0.02

Hence, our exponential growth rate =

y = 300( 1 + 0.02)^t

y = 300( 1.02)^t

Therefore, Pierre is right

5 0

3 years ago

Simplify 6 to the 3rd

elixir [45]

Answer:

Isnt it 2?

Step-by-step explanation:

7 0

3 years ago

Help! what is the right answer?​

Help! what is the right answer?