How many 5/6 are in three and 1/3

A rocket is launched from atop a 104-foot cliff with an initial velocity of 110 ft/s. A. Substitute the values into the vertical

miv72 [106K]

Answer:

7.68 s

Step-by-step explanation:

The vertical motion formula is:

$h_{t} = h_{0} + v_{0}t - \frac{gt^{2}}{2}$

<u>Where:</u>

h(t): is the final height = 0

h(0): is the height of the cliff = 104 foot

v(0): is the initial velocity = 110 ft/s

g: is the gravity = 9.8 m/s² = 32.15 ft/s²

Hence, from the vertical motion formula we can find the time that will take the rocket to hit the ground:

$0 = 104 + 110*t - \frac{32.15t^{2}}{2}$

$0 = 104 + t(110 - 16.08t)$

We have two solutions:

t₁= -0.84 s

t₂ = 7.68 s

We will take the positive value, thus the time that will take the rocket to hit the ground is 7.68 s.

I hope it helps you!

4 0

3 years ago

camila has a younger brother and an older brother. one is three years younger than her and the other is 5 years older than her

Stella [2.4K]

What’s the question?

8 0

3 years ago

Read 2 more answers

PLEASE HELP ME I WILL REWARD YOU BRAINLIEST: find the slope of the line through each pair of points <img src="https://tex.z-dn.n

son4ous [18]

Answer:

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Step-by-step explanation:

i googled it

6 0

3 years ago

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.