WILL GIVE BRAINLIST

A potato gun is a device made out of plastic pipe that launches a potato using compressed air. They can be great fun, and even e

snow_tiger [21]

Answer:

The potato is 224 feet in the air after 2.75 second on the way up and after 5 seconds on the way back down.

Step-by-step explanation:

Given : A potato launched by a particular potato gun has a height described by $h ( t ) =-16 t^2+124 t+4$ .

To find : When is the potato 224 feet in the air?

Solution :

When the potato is 224 feet in the air i.e. $h(t)=224$

Substitute in the equation $h ( t ) =-16 t^2+124 t+4$ ,

$224=-16 t^2+124 t+4$

$16t^2-124 t+220=0$

$4t^2-31t+55=0$

Applying quadratic formula, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, a=4, b=-31 and c=55

$t=\frac{-(-31)\pm\sqrt{(-31)^2-4(4)(55)}}{2(4)}$

$t=\frac{31\pm\sqrt{81}}{8}$

$t=\frac{31\pm9}{8}$

$t=\frac{31+9}{8},\frac{31-9}{8}$

$t=5,2.75$

The potato is 224 feet in the air after 2.75 second on the way up and after 5 seconds on the way back down.

5 0

3 years ago

How would I make an equation into an inverse of itself?

gavmur [86]

To make an equation an inverse, you would raise it to the -1 power. For example:

3^-1 = 1/3
1/3^-1=3

:)

5 0

3 years ago

The solution of the equation 16 m + 16 = 32 is<br><br><br>1<br><br>3<br><br>6<br><br>12

blsea [12.9K]

16(1)=16
16(1)+16
16+16=32

7 0

3 years ago

Read 2 more answers

17. Santino loves to rock different colored polo shirts every day. He recently wore the following colors:

qaws [65]

Answer:

The mode for the colors that Santino wore recently is Blue.

Step-by-step explanation:

The mode of a data set is the term or observation that presents most of the time.

The frequency table of different colored polo shirts worn by Santino is:

Color Frequency

Yellow 2

Blue 3

Green 1

Pink 1

Brown 1

Orange 1

Chartreuse 1

Black 1

Puce 1

The color Blue has the highest frequency, i.e. 3.

So, the mode for the colors that Santino wore recently is Blue.

3 0

3 years ago

Write the polynomial f(x)=x^4-10x^3+25x^2-40x+84. In factored form

Verizon [17]

<h2>Steps:</h2>

So firstly, to factor this we need to first find the potential roots of this polynomial. To find it, the equation is $\pm \frac{p}{q}$ , with p = the factors of the constant and q = the factors of the leading coefficient. In this case:

$\textsf{leading coefficient = 1, constant = 84}\\\\p=1,2,3,4,6,7,12,14,21,28,42,84\\q=1\\\\\pm \frac{1,2,3,4,6,7,12,14,21,28,42,84}{1}\\\\\textsf{Potential roots =}\pm 1, \pm 2,\pm 3,\pm 4,\pm 6, \pm 7,\pm 12,\pm 14,\pm 21,\pm 28,\pm 42,\pm 84$

Next, plug in the potential roots into x of the equation until one of them ends with a result of 0:

$f(1)=(1)^4-10(1)^3+25(1)^2-40(1)+84\\f(1)=1-10+25-40+84\\f(1)=60\ \textsf{Not a root}\\\\f(2)=2^4-10(2)^3+25(2)^2-40(2)+84\\f(2)=16-10*8+25*4-80+84\\f(2)=16-80+100-80+84\\f(2)=80\ \textsf{Not a root}\\\\f(3)=3^4-10(3)^3+25(3)^2-40(3)+84\\f(3)=81-10*27+25*9-120+84\\f(3)=81-270+225-120+84\\f(3)=0\ \textsf{Is a root}$

Since we know that 3 is a root, this means that one of the factors is (x - 3). Now that we know one of the roots, we are going to use synthetic division to divide the polynomial. To set it up, place the root of the divisor, in this case 3 from x - 3, on the left side and the coefficients of the original polynomial on the right side as such:

3 | 1 - 10 + 25 - 40 + 84
_________________

Firstly, drop the 1:

3 | 1 - 10 + 25 - 40 + 84
↓
_________________
1

Next, multiply 3 and 1, then add the product with -10:

3 | 1 - 10 + 25 - 40 + 84
↓ + 3
_________________
1 - 7

Next, multiply 3 and -7, then add the product with 25:

3 | 1 - 10 + 25 - 40 + 84
↓ + 3 - 21
_________________
1 - 7 + 4

Next, multiply 3 and 4, then add the product with -40:

3 | 1 - 10 + 25 - 40 + 84
↓ + 3 - 21 + 12
_________________
1 - 7 + 4 - 28

Lastly, multiply -28 and 3, then add the product with 84:

3 | 1 - 10 + 25 - 40 + 84
↓ + 3 - 21 + 12 - 84
_________________
1 - 7 + 4 - 28 + 0

Now our synthetic division is complete. Now since the degree of the original polynomial is 4, this means our quotient has a degree of 3 and follows the format $ax^3+bx^2+cx+d$ . In this case, our quotient is $x^3-7x^2+4x-28$ .

So right now, our equation looks like this:

$f(x)=(x-3)(x^3-7x^2+4x-28)$

However, our second factor can be further simplified. For the second factor, I will be factoring by grouping. So factor x³ - 7x² and 4x - 28 separately. Make sure that they have the same quantity inside the parentheses:

$f(x)=(x-3)(x^2(x-7)+4(x-7))$

Now it can be rewritten as:

$f(x)=(x-3)(x^2+4)(x-7)$

<h2>Answer:</h2>

Since the polynomial cannot be further simplified, your answer is:

$f(x)=(x-3)(x^2+4)(x-7)$

6 0

3 years ago