Answer:
A linear formula for S as a function of D is S=17D+1534
Step-by-step explanation:
We are supposed to find a linear formula for S as a function of D.
Equation of line : y = mx+c
We are given that At the surface, the speed of sound is 1534 meters per second.
c = 1534
We are given that for each increase in depth by 1 km, the speed increases by 17 m/s
So, Slope = m = 17
Substitute the values in equation
y=17x+1534
x denotes depth
y denotes speed
We are given that Use D for depth and S for the speed of sound
So, S=17D+1534
Hence a linear formula for S as a function of D is S=17D+1534
It’s the second one because 0.5 is like 50% then 3/4 is like 75 and then the other is simply 80%
The best way to approach this problem is to find out how much fell in week. As you know what two weeks is, you simply have to halve this, giving you that one week is 5 inches of rain. One you have this, you can multiply this by 4 (as this will give you 4 weeks, or 28 days), and this gives you 20 inches in 28 days. You should then find the odd three days. If you divide 5 by 7, this will give you the rain fall in one day. 5/7= 0.8 inches per day. You then have top multiply this by 3 (as you've got three odd days), and this gives you 2.4. You then have to add together 2.4 and 20, giving you 22.4
Therefore, if the rain continued to fall at the same rate for 31 days, it would receive 22.4 inches of rain.
Hope this helps :)
Answer:
![W=\{\left[\begin{array}{ccc}a+2b\\b\\-3a\end{array}\right]: a,b\in\mathbb{R} \}](https://tex.z-dn.net/?f=W%3D%5C%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%2B2b%5C%5Cb%5C%5C-3a%5Cend%7Barray%7D%5Cright%5D%3A%20a%2Cb%5Cin%5Cmathbb%7BR%7D%20%5C%7D)
Observe that if the vector ![x=\left[\begin{array}{ccc}x\\y\\z\end{array}\right]](https://tex.z-dn.net/?f=x%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D)
is in W then it satisfies:
![\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{c}a+2b\\b\\-3a\end{array}\right]=a\left[\begin{array}{c}1\\0\\-3\end{array}\right]+b\left[\begin{array}{c}2\\1\\0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Da%2B2b%5C%5Cb%5C%5C-3a%5Cend%7Barray%7D%5Cright%5D%3Da%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C0%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%2Bb%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C1%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
This means that each vector in W can be expressed as a linear combination of the vectors ![\left[\begin{array}{c}1\\0\\-3\end{array}\right], \left[\begin{array}{c}2\\1\\0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C0%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%2C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C1%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
Also we can see that those vectors are linear independent. Then the set
![\{\left[\begin{array}{c}1\\0\\-3\end{array}\right], \left[\begin{array}{c}2\\1\\0\end{array}\right]\}](https://tex.z-dn.net/?f=%5C%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C0%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%2C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C1%5C%5C0%5Cend%7Barray%7D%5Cright%5D%5C%7D)
is a basis for W and the dimension of W is 2.
Answer:1:1000
Step-by-step explanation:
It’s 1:1000 because compared to the other one the height of the model would be 9.3 centimeters if 1:1000 was the scale of the model
