Our matrix C is the encoder. Let X be our secret message and let B be our encoded message. Therefore the relationship between the 3 can be represented as:
CX = B
So we want to solve for X (our secret message). So using matrix algebra:
X = C^-1*B
where C^-1 is the inverse of C.
C^-1 = | 3 -2 |
|4 -3 |
So we take C^-1 and multiply it by matrix B to get X. Matrix B is already given to us. So just multiply those two. I used a calculator to get:
X = | 20 8 5 3 15 12 15 |
| 18 9 19 2 12 21 5 |
And since A = 1, B = 2, C = 3, etc....
We decode our message and it says:
X = | T H E C O L O |
| R I S B L U E |
So the answer is: The color is blue (D)
Check the picture below, so pretty much reaches its maximum height at the vertex, now let's take a peek at the equation above hmmmm
![~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ h(t)=-16(t ~~ - ~~ \stackrel{h}{5})^2~~ + ~~\stackrel{k}{116}~\hfill \underset{maximum~height}{\stackrel{vertex}{(5~~,~~\underset{\uparrow }{116})}}](https://tex.z-dn.net/?f=~~~~~~%5Ctextit%7Bvertical%20parabola%20vertex%20form%7D%20%5C%5C%5C%5C%20y%3Da%28x-%20h%29%5E2%2B%20k%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22a%22~is~negative%7D%7Bop%20ens~%5Ccap%7D%5Cqquad%20%5Cstackrel%7B%22a%22~is~positive%7D%7Bop%20ens~%5Ccup%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20h%28t%29%3D-16%28t%20~~%20-%20~~%20%5Cstackrel%7Bh%7D%7B5%7D%29%5E2~~%20%2B%20~~%5Cstackrel%7Bk%7D%7B116%7D~%5Chfill%20%5Cunderset%7Bmaximum~height%7D%7B%5Cstackrel%7Bvertex%7D%7B%285~~%2C~~%5Cunderset%7B%5Cuparrow%20%7D%7B116%7D%29%7D%7D)
Answer:
Step-by-step explanation:
a) What point would be the Center of the circle C (above)? C
b) What line segment would be the Radius? BC
c) What line segment would be the Diameter? AD
d) What line Color is representing the Circumference? Dark Blue/Black?
e) What number represents the ratio of Circumference/Diameter? π
f) if the radius is 5 meters, what is the distance of the circumference?
5π ≈ 15.707... m
Answer:
20 g/cm³
Step-by-step explanation:
Utilise the formula Density = Mass ÷ Volume where mass is measured in grams and volume is litres. First we have to substitute the value into the formula and then simplify it to work out the density of the object so
Density = Mass ÷ Volume
→ Substitute the values into the formula
Density = 350 ÷ 17.5
→ Simplify
Density = 20
Answer:
5 10 15 20 25 30 this one is the largest interquartile range
