Answer:
The triangle ABC is an isosceles right triangle
Step-by-step explanation:
we have
The coordinates of triangle ABC are
A (0, 2), B (2, 5), and C (−1, 7)
we know that
An isosceles triangle has two equal sides and two equal internal angles
The formula to calculate the distance between two points is equal to

step 1
Find the distance AB
substitute in the formula



step 2
Find the distance BC
substitute in the formula



step 3
Find the distance AC
substitute in the formula



step 4
Compare the length sides




therefore
Is an isosceles triangle
Applying the Pythagoras Theorem

substitute


-----> is true
therefore
Is an isosceles right triangle
Answer:
$7803.72
Step-by-step explanation:
We have been given that a silo is in the shape of a cone. The silo is 8 meters tall and it's base has a diameter of 3 meters. Soybeans cost $414 per cubic meter. We are asked to find the total cost to fill the silo with soybeans.
First of all, we will find the volume of silo using volume of cone formula.
, where,
r = radius
h = Height
We know that radius is half the diameter, so radius of silo would be
.





Now we will multiply total volume by $414 to find total cost.\



Therefore, it will cost $7803.72 to fill the silo with soybeans.
Given:
A circle with diameter 9 cm.
To find:
The area of the circle.
Solution:
The area of a circle is:
...(i)
Where r is the radius.
We know that, the diameter of a circle is twice than its radius.
The diameter of the given circle is 9 cm.


Substituting
in (i), we get




Therefore, the area of the given circle is 63.6.
Answer: B and D
Step-by-step explanation:
First, solve the terms inside of the parenthesis. As a general rule, whenever you multiply two terms that have the same base, you can add their exponents.
Applying this rule, the base in the problem is 6, and the exponents are 3 and -4. The sum of 3 and -4 leaves -1. Therefore, this is one of our solutions:

When you have an exponential term raised to another exponent, you can simply multiply the exponents. In the previous solution given above, multiply -1 and -3 to get 3. Therefore our second solution is:

Given a complex number in the form:
![z= \rho [\cos \theta + i \sin \theta]](https://tex.z-dn.net/?f=z%3D%20%5Crho%20%5B%5Ccos%20%5Ctheta%20%2B%20i%20%5Csin%20%5Ctheta%5D)
The nth-power of this number,

, can be calculated as follows:
- the modulus of

is equal to the nth-power of the modulus of z, while the angle of

is equal to n multiplied the angle of z, so:
![z^n = \rho^n [\cos n\theta + i \sin n\theta ]](https://tex.z-dn.net/?f=z%5En%20%3D%20%5Crho%5En%20%5B%5Ccos%20n%5Ctheta%20%2B%20i%20%5Csin%20n%5Ctheta%20%5D)
In our case, n=3, so

is equal to
![z^3 = \rho^3 [\cos 3 \theta + i \sin 3 \theta ] = (5^3) [\cos (3 \cdot 330^{\circ}) + i \sin (3 \cdot 330^{\circ}) ]](https://tex.z-dn.net/?f=z%5E3%20%3D%20%5Crho%5E3%20%5B%5Ccos%203%20%5Ctheta%20%2B%20i%20%5Csin%203%20%5Ctheta%20%5D%20%3D%20%285%5E3%29%20%5B%5Ccos%20%283%20%5Ccdot%20330%5E%7B%5Ccirc%7D%29%20%2B%20i%20%5Csin%20%283%20%5Ccdot%20330%5E%7B%5Ccirc%7D%29%20%5D)
(1)
And since

and both sine and cosine are periodic in

, (1) becomes