How many inches are in 8.5 feet (show work please thank you you)

A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) =- 5<img src="https://tex.z-dn.net/?f=t%5E%7

DanielleElmas [232]

Answer:

Part A)

No

Part B)

About 2.9362 seconds.

Step-by-step explanation:

The equation $\displaystyle h(t)=-5t^2+14t+2$ models the height h in meters of the ball t seconds after its launch.

Part A)

To determine whether or not the ball reaches a height of 14 meters, we can find the vertex of our function.

Remember that the vertex marks the maximum value of the quadratic (since our quadratic curves down).

If our vertex is greater than 14, then, at some time t, the ball will definitely reach a height of 14 meters.

However, if our vertex is less than 14, then the ball doesn’t reach a height of 14 meters since it can’t go higher than the vertex.

So, let’s find our vertex. The formula for vertex is given by:

$\displaystyle (-\frac{b}{2a},h(-\frac{b}{2a}))$

Our quadratic is:

$\displaystyle h(t)=-5t^2+14t+2$

Hence: a=-5, b=14, and c=2.

Therefore, the x-coordinate of our vertex is:

$\displaystyle x=-\frac{14}{2(-5)}=\frac{14}{10}=\frac{7}{5}$

To find the y-coordinate and the maximum height, we will substitute this value back in for x and evaluate. Hence:

$\displaystyle h(\frac{7}{5})=-5(\frac{7}{5})^2+14(\frac{7}{5})+2$

Evaluate:

$\displaystyle \begin{aligned} h(\frac{7}{2})&=-5(\frac{49}{25})+\frac{98}{5}+2 \\ &=\frac{-245}{25}+\frac{98}{5}+2\\ &=\frac{-245}{25}+\frac{490}{25}+\frac{50}{25}\\&=\frac{-245+490+50}{25}\\&=\frac{295}{25}=\frac{59}{5}=11.8\end{aligned}$

So, our maximum value is 11.8 meters.

Therefore, the ball doesn’t reach a height of 14 meters.

Part B)

To find out how long the ball is in the air, we can simply solve for our t when h=0.

When the ball stops being in the air, this will be the point at which it is at the ground. So, h=0. Therefore:

$0=-5t^2+14t+2$

A quick check of factors will reveal that is it not factorable. Hence, we can use the quadratic formula:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Again, a=-5, b=14, and c=2. Substitute appropriately:

$\displaystyle x=\frac{-(14)\pm\sqrt{(14)^2-4(-5)(2)}}{2(-5)}$

Evaluate:

$\displaystyle x=\frac{-14\pm\sqrt{236}}{-10}$

We can factor the square root:

$\sqrt{236}=\sqrt{4}\cdot\sqrt{59}=2\sqrt{59}$

Hence:

$\displaystyle x=\frac{-14\pm2\sqrt{59}}{-10}$

Divide everything by -2:

$\displaystyle x=\frac{7\pm\sqrt{59}}{5}$

Hence, our two solutions are:

$\displaystyle x=\frac{7+\sqrt{59}}{5}\approx2.9362\text{ or } x=\frac{7-\sqrt{59}}{5}\approx-0.1362$

Since our variable indicates time, we can reject the negative solution since time cannot be negative.

Hence, our zero is approximately 2.9362.

Therefore, the ball is in the air for approximately 2.9362 seconds.

5 0

3 years ago

Read 2 more answers

If (9 to the 2nd power)p = 9 to the 8th power , what is the value of p?

Novay_Z [31]

$(9^2)^p=9^8\\\\9^{2p}=9^8\\\\2p=8\\\\p=4$

3 0

3 years ago

Read 2 more answers

PLEASE HELP!!!

Marizza181 [45]

The function would be f(x)=11,500-.16xPlug in 4 for x

8 0

3 years ago

What is the difference between decimal and binary numbering systems give examples of when you would use each?

vaieri [72.5K]

The difference between decimal and binary system are-

The base-10 system, often known as the decimal system, is the oldest and most widely used system of numbers.
The binary number system, often known as base 2, is used by computers.

<h3>What is decimal system?</h3>

Our daily use of numbers is based on a decimal number system, which uses 10 digits. A number system in mathematics is thought of as the use of digits or symbols to represent numbers.

The binary number system, the decimal number system, the octal number system, and the hexadecimal number system are the four primary varieties of the number system.
Given that it was challenging to multiply & divide big numbers by hand in earlier civilizations, this decimal system system is sometimes called as the Hindu-Arabic and Arabic number system.

<h3>What is binary system?</h3>

The base-2 number system is the binary system. That implies that it solely use the digits 0 and 1. The 1 one location is moved to its left into the 2s place when adding one to one, and a 0 is placed in the ones place, yielding the number 10. In such a base-10 system, 10 thus = 10. 10 = 2 in the base-2 system.

The place values in a base-2 system begin with ones and progress to twos, fours, then eights as one move to its left.
This is due to the base-2 system's foundation in powers of two.
A bit is the term for each binary digit.

Therefore, a binary number system only employs two different digits(0 and 1), whereas decimal number system includes ten different digits (ranging from 0 to 9).

To know more about decimal system, here

brainly.com/question/16913175

#SPJ4

6 0

2 years ago

When f(x) = 2x 2 + 3, find f(-3).<br> -15<br> 21<br> 39

notsponge [240]

Answer:

21

Step-by-step explanation:

f(x) = 2x^2 + 3

f(-3) = 2(-3)^2 + 3

f(-3) = 2(9) + 3

f(-3) = 18 + 3

f(-3) = 21

6 0

3 years ago