Answer:
Step-by-step explanation:
y = k*x This is the formula for a direct variation.
- y = 20
- x = 4 Substitute these values into the direct variation
20 = 4 * k Divide by 4
20/4 = 4k/4
k = 5
Answer: the constant of variation is 5
9514 1404 393
Answer:
y < -1/4x -1
Step-by-step explanation:
The boundary line appears to go through the points (-4, 0) and (0, -1). This tells you it has a "rise" of -1 for a "run" of 4. The slope is ...
m = rise/run = -1/4
The y-intercept (b) is the point where the y-axis is crossed. The slope-intercept equation of the boundary line is ...
y = mx + b
y = -1/4x -1
__
The boundary line is dashed, so is not included in the solution set. The shading is below the line, so all y-values less than (but not equal to) the boundary line are in the solution set:
y < -1/4x -1
Answer:
A
Step-by-step explanation:
Calculate the slope m using the slope formula
m = ![\frac{y_{2}-y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D-y_%7B1%7D%20%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%20%7D)
with (x₁, y₁ ) = (- 3, 4 ) and (x₂, y₂ ) = (2, - 1 )
m =
=
=
= - 1 → A
The answer to this question is 48.
Answer:
![y'' =12x^2 -72=0](https://tex.z-dn.net/?f=%20y%27%27%20%3D12x%5E2%20-72%3D0)
And solving we got:
![x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}](https://tex.z-dn.net/?f=%20x%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B72%7D%7B12%7D%7D%20%3D%5Cpm%20%5Csqrt%7B6%7D)
We can find the sings of the second derivate on the following intervals:
Concave up
inflection point
Concave down
inflection point
Concave up
Step-by-step explanation:
For this case we have the following function:
![y= x^4 -36x^2](https://tex.z-dn.net/?f=%20y%3D%20x%5E4%20-36x%5E2)
We can find the first derivate and we got:
![y' = 4x^3 -72x](https://tex.z-dn.net/?f=%20y%27%20%3D%204x%5E3%20-72x)
In order to find the concavity we can find the second derivate and we got:
![y'' = 12x^2 -72](https://tex.z-dn.net/?f=%20y%27%27%20%3D%2012x%5E2%20-72)
We can set up this derivate equal to 0 and we got:
![y'' =12x^2 -72=0](https://tex.z-dn.net/?f=%20y%27%27%20%3D12x%5E2%20-72%3D0)
And solving we got:
![x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}](https://tex.z-dn.net/?f=%20x%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B72%7D%7B12%7D%7D%20%3D%5Cpm%20%5Csqrt%7B6%7D)
We can find the sings of the second derivate on the following intervals:
Concave up
inflection point
Concave down
inflection point
Concave up