Answer:
Please check the explanation.
Step-by-step explanation:
Let us consider

To find the area under the curve
between
and
, all we need is to integrate
between the limits of
and
.
For example, the area between the curve y = x² - 4 and the x-axis on an interval [2, -2] can be calculated as:

=


solving


![=\left[\frac{x^{2+1}}{2+1}\right]^2_{-2}](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cfrac%7Bx%5E%7B2%2B1%7D%7D%7B2%2B1%7D%5Cright%5D%5E2_%7B-2%7D)
![=\left[\frac{x^3}{3}\right]^2_{-2}](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%5Cright%5D%5E2_%7B-2%7D)
computing the boundaries

Thus,

similarly solving


![=\left[4x\right]^2_{-2}](https://tex.z-dn.net/?f=%3D%5Cleft%5B4x%5Cright%5D%5E2_%7B-2%7D)
computing the boundaries

Thus,

Therefore, the expression becomes



square units
Thus, the area under a curve is -10.67 square units
The area is negative because it is below the x-axis. Please check the attached figure.
Answer:
Slope
0.33
Step-by-step explanation:
Answer:
Step-by-step explanation:
Hi Millie.
First we can realize that the number of cubes of each type does not matter, only the ratios between them. We see that if there are x yellow cubes, there are 3x blue cubes. And therefore, there are 5*3x green cubes, or 15x green cubes. This means that the cubes are in a 1:3:15 ratio, or that for every 1 yellow cube, there are 3 blue and 15 green cubes.
Now we can find the probability of picking a yellow cube. Since there are 18 non-yellow cubes for every yellow cube, this means that there is a 1/19 possibility of picking a yellow cube.
Answer:
9
Step-by-step explanation:
Solution
Here,
(a^3)^6=(a^2)^x
or, a^18=a^2x
or, 18=2x
or, x=18/2
x=9