Answer:
The answer is 596 square feet
Step-by-step explanation:
Recall the following formulas for area:
Rectangle of lenght l and width w:
Triangle of base b and height h:
In our case, since we have a pyramid with rectangular base, so we have 5 sides: the rectangular base and 4 triangles, that are grouped in two pairs of identicall triangles. Let us call the triangles T1 and T2. Then the total surface area is given by
surface area = Area of the base + 2*Area of T1 + 2* Area of T2
The base is a rectangle of lenght 16 and width 12, so the area is 16*12 = 192.
T1 is a triangle of base 16 and height 14, so it has area 16*14/2 = 112.
T2 is a triangle of base 12 and height 15, so it has area 15*12/2 = 90.
So the total area is
Area = 192+2*112+2*90 = 596.
Answer:
See proof below
Step-by-step explanation:
Let . If w=-z, then r=0 and r is real. Suppose that w≠-z, that is, r≠0.
Remember this useful identity: if x is a complex number then where
is the conjugate of x.
Now, using the properties of the conjugate (the conjugate of the sum(product) of two numbers is the sum(product) of the conjugates):
=
Thus . From this,
. A complex number is real if and only if it is equal to its conjugate, therefore r is real.
Answer:
Step-by-step explanation:
Answer:
(x-4)^2 + (y-2)^2 = 3^2
or
(x-4)^2 + (y-2)^2 = 9 (simplified if needed)
Step-by-step explanation:
-Equation of a circle is:
where the center is (h, k) and the radius is
.
-Place the center and the point onto that equation:
-Then, you solve:
-So, the result is:
or
(simplified if needed)