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:
14
Step-by-step explanation:
you have opposite but need to find hypotenuse so you use SOH (sine=opposite/hypotenuse)
so sin(30)= 7/a
7/sin(30)=14
Hope its right
Answer:
343
Step-by-step explanation:
There are quarters(25¢), loonies ($1), and toonies ($2)
And total number of coins is 9
If loonies ($1), and toonies ($2) are one, then quarters(25¢) is 7
If quarters(25¢), and toonies ($2) are one, then loonies ($1)is 7
If loonies ($1), and quarters(25¢) are one, then toonies ($2) is 7
So possible number number of combination for an item that cost between $10 and $12 is
= 1^3 * 1^3 * 7^3
= 343
hope this helps, stay safe :)
Answer:
-52 / 5
Step-by-step explanation:
3 9/10 * -8 / 3 = 39 / 10 * -8 / 3 = -52 / 5