Step-by-step explanation:
use the distance formula. calculate the distance between AB and then between CD showing AB = CD.
then use the distance formula on BC and AD, showing they are equal.
d=√((x_2-x_1)²+(y_2-y_1)²)
Answer:
To find the quotient, you must start by dividing 25 into 1,658.
Step-by-step explanation:
Answer:
y-3=-0/2(x+2)
Step-by-step explanation:
big brain
Answer:
-90 - (-144)
Step-by-step explanation:
Here you go!
Since we're depositing, you'll add the three numbers.
45 + 27 + 18 = $90
Cody deposits 90 dollars in total.
If you write checks, the numbers go down. So you'll add them, and then subtract that by the 90 dollars Cody deposits.
You'll end up with:
45 + 27 + 18 - (21 + 93)
This can simplify to..
90 - (21 + 93)
But wait! Let's add what's in the parenthesis!
93 + 21 = 144
90 - 144 = t
t = -54
Solving this equation will give you: -54
But the simple way is -90 - (-144)
Using integration, it is found that the area of the shaded region is of
units squared.
<h3>How is the area of a shaded region found?</h3>
- The area of shaded region, between two curves
and
, considering
, between x = a and x = b, is given by the following integral:
![A = \int_a^b f(x) - g(x) dx](https://tex.z-dn.net/?f=A%20%3D%20%5Cint_a%5Eb%20f%28x%29%20-%20g%28x%29%20dx)
In this problem, the curves are:
![f(x) = \sqrt[3]{x} = x^{\frac{1}{3}}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![g(x) = \frac{1}{x}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7Bx%7D)
The limits of integration are:
.
Hence:
![A = \int_1^{27} \left(x^{\frac{1}{3}} - \frac{1}{x}\right) dx](https://tex.z-dn.net/?f=A%20%3D%20%5Cint_1%5E%7B27%7D%20%5Cleft%28x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%20-%20%5Cfrac%7B1%7D%7Bx%7D%5Cright%29%20dx)
Applying the power properties of integration:
![A = 3x^{\frac{4}{3}} - \ln{x}|_{x = 1}^{x = 27}](https://tex.z-dn.net/?f=A%20%3D%203x%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%20-%20%5Cln%7Bx%7D%7C_%7Bx%20%3D%201%7D%5E%7Bx%20%3D%2027%7D)
Finally, applying the Fundamental Theorem of Calculus:
![A = 3(27)^{\frac{4}{3}} - \ln{27} - 3(1)^{\frac{4}{3}} + \ln{1}](https://tex.z-dn.net/?f=A%20%3D%203%2827%29%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%20-%20%5Cln%7B27%7D%20-%203%281%29%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%20%2B%20%5Cln%7B1%7D)
![A = 240 - \ln{27}](https://tex.z-dn.net/?f=A%20%3D%20240%20-%20%5Cln%7B27%7D)
The area of the shaded region is of
units squared.
To learn more about integration, you can take a look at brainly.com/question/20733870