y = -9
Ok so to write the equation of the line you will need the slope and y-intercept. Since we are given two-point we can easily find the slope by using this equation for slope formula:
So now that we have our equation we can just plug in the numbers:
After subtracting you should get:
0/8
Since zero is in the numerator and you can't divide zero by anything, the slope is 0. We still need the y-intercept for the equation however since the slope is 0 there is no need to put anything else.
Then to find the y-intercept all you have to do is plug in one of the coordinatines into the slope equation to solve, for example, using the point (5,-9):
B is the variable for the y-intercept. Also notice how I put 0 as our slope into the equation. Now all you have to do is solve for b. Which you would get b = -9. Since you have your slope and your y-intercept now you just write out your equatoin for the line which is:
y = 0x - 9
**Just write it as
y = -9
Answer:
They would need approximately 20 gallons of paint for the water tower, so yes, 25 gallons would be enough.
Step-by-step explanation:
In order to find out if there is enough paint for the surface area of the sphere, you need to first find the radius of the object so you can determine the measure of the entire surface area. Since they give us the volume, we can use that to solve for the radius using the volume formula: V = πr³ or 66840.28 = πr³. Using inverse operations, you can first multiply both sides of the equation by the reciprocal of 4/3 or 3/4, then divide by π, this gives you 15,965 = r³. In order to find 'r', take the cube root of both sides: ∛15965 = ∛r³ or r ≈ 25.
Now that you know radius = 25, you can use the formula for surface area: SA = 4πr² or 4π(25)² ≈ 7850 ft². Since one gallon of paint covers 400 square feet, we can take our total and divide by 400 to find the number of gallons: 7850 ÷ 400 ≈ 19.6. In total, we would need 19.6 gallons of paint for the water tower, so if there are 25 gallons available, there is enough.
Answer:
4.4
Step-by-step explanation:
The tenth place in this number is 4.<u>4</u>32, so that should be the last digit.
Now, we need to know wether to round up or down. That is determined by the digit that comes after it. <em>If that digit, here it is the hundredth, is 0-4, it rounds down, if it is 5-9, it rounds up</em>. Our next digit is <em>3</em>, which goes into the first category, <em>so the number rounds down</em>, so the tenth remains the same. That leaves us with 4.4.
Answer:
There is no diagram for me to look at i dont know how to answer this if this does not have the diagram thank you very much
Step-by-step explanation:
You find the eigenvalues of a matrix A by following these steps:
- Compute the matrix
, where I is the identity matrix (1s on the diagonal, 0s elsewhere) - Compute the determinant of A'
- Set the determinant of A' equal to zero and solve for lambda.
So, in this case, we have
![A = \left[\begin{array}{cc}1&-2\\-2&0\end{array}\right] \implies A'=\left[\begin{array}{cc}1&-2\\-2&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right]=\left[\begin{array}{cc}1-\lambda&-2\\-2&-\lambda\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C-2%260%5Cend%7Barray%7D%5Cright%5D%20%5Cimplies%20A%27%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C-2%260%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Clambda%260%5C%5C0%26%5Clambda%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1-%5Clambda%26-2%5C%5C-2%26-%5Clambda%5Cend%7Barray%7D%5Cright%5D)
The determinant of this matrix is
Finally, we have
So, the two eigenvalues are
