Hm. Have you ever dispensed water from a hose unto a cone? I know I haven’t, but math can give us a good idea of what it would be like — or at least, how long it would take.
We are told that the hose spills 1413 cm^3 of water every minute. We are also told the cone has a height of 150 cm and a radius of 60 cm. So far, so good.
First things first, we need to find out how much water can fit in the cone. That means volume. The volume of a cone is
π • r^2 • (h/3)
Let’s go ahead and plug in (remember we use 3.14 for π)
(3.14) • (60)^2 • (150/3)
The volume of the cone is 565,200 cm^3
Wait, I’m lost. What were we supposed to do again? Oh, right. We needed to find how long it would take for the hose to fill in the cone. Well, if we know the hose dispenses 1413 cm^3 per minute, and there is a total of 565,200 cm^3 the cone can take, we can divide the volume of the cone by the amount the hose dispenses per minute to get the number of minutes it’d take to fill it.
565200/1413
400 minutes. Wow, ok. I wouldn’t want to wait that long. That’s like watching 3 movies!
Step-by-step explanation:
The equation of a exponential function is
where a is the y value of the y intercept, b is the constant rate of change.
Here the y intercept is (0,4), the y value of the y intercept is 4.
So a=4
The graph passes through point (1,2) so
Plug in 1 for x, 2 for h(x)
Anything to the first power is itself so
Isolate b.
So our function is
The inverse of the matrix ![\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D11%26-5%5C%5C3%26-1%5Cend%7Barray%7D%5Cright%5D)
is the matrix ![\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B-1%7D%7B4%7D%20%26%5Cfrac%7B5%7D%7B4%7D%20%5C%5C%5C%5C%5Cfrac%7B-3%7D%7B4%7D%20%26%5Cfrac%7B11%7D%7B4%7D%20%5Cend%7Barray%7D%5Cright%5D)
.
The inverse of a matrix A is calculated by the formula:
A' = (1/|A|)(Adj A),
where A' represents the inverse of matrix A,
|A| represents the determinant value of matrix A, and
Adj A represents the Adjoin matrix of matrix A.
So, to calculate the inverse of the matrix , we will first calculate its Adj.
Adj = ![\left[\begin{array}{cc}-1&-3\\5&11\end{array}\right] ^{T}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%26-3%5C%5C5%2611%5Cend%7Barray%7D%5Cright%5D%20%5E%7BT%7D)
= ![\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%265%5C%5C-3%2611%5Cend%7Barray%7D%5Cright%5D)
.
Now, we calculate |A| = 11*(-1) - (-5)*3 = -11 + 15 = 4.
Therefore A' = (1/|A|)(Adj A),
or, A' = ![(1/4)*\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right]](https://tex.z-dn.net/?f=%281%2F4%29%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%265%5C%5C-3%2611%5Cend%7Barray%7D%5Cright%5D)
,
or, A' = .
Therefore, the inverse of the matrix is the matrix .
Learn more about the inverse of a matrix at
brainly.com/question/16862241
#SPJ10
Answer:
21
Step-by-step explanation:
the answer to everything is 21
