Evaluate the triple integral ∭Tx2dV, where T is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,3,0), and (0,0,3).
bixtya [17]
Answer:
the integral I=81
Step-by-step explanation:
for the integral I
where T is the solid tetrahedron , then
the integral is equal to 81
x - mean
z-score = ------------------
std. dev.
Here we have:
45 - 61.2
z-score = ------------------ = -0.757
21.4
The area is:
A = x * y
The perimeter is:
P = 2x + 2y = 100
We clear y:
2y = 100-2x
y = 50-x
We write the area in terms of x:
A (x) = x * (50-x)
Rewriting:
A (x) = 50x-x ^ 2
Deriving:
A '(x) = 50-2x
We equal zero and clear x:
50-2x = 0
x = 50/2
x = 25
Then, the other dimension is given by:
y = 50-x
y = 50-25
y = 25
Therefore, the largest area is:
A = (25) * (25)
A = 625 feet ^ 2
Answer:
the largest area you can enclose using the materials you have is:
A = 625 feet ^ 2
Answer:
x = -1 and x = 5
Step-by-step explanation:
<em>What are the solutions of the equation (x – 3)² + 2(x – 3) -8 = 0? Use u substitution to solve.</em>
<em />
(x – 3)² + 2(x – 3) -8 = 0 -------------------------------------------------------(1)
To solve this problem, we will follow the steps below;
let u = x-3
we will replace x-3 by u in the given equation:
(x – 3)² + 2(x – 3) -8 = 0
u² + 2u -8 = 0 ----------------------------------------------------------- --------------(2)
We will now solve the above quadratic equation
find two numbers such that its product gives -8 and its sum gives 2
The two numbers are 4 and -2
That is; 4×-2 = -8 and 4+(-2) = 2
we will replace 2u by (4u -2u) in equation (2)
u² + 2u -8 = 0
u² + 4u - 2u -8 = 0
u(u+4) -2(u+4) = 0
(u+4)(u-2) = 0
Either u + 4 = 0
u = -4
or
u-2 = 0
u = 2
Either u = -4 or u = 2
But u = x-3
x = u +3
when u = -4
x = u + 3
x = -4 + 3
x=-1
when u = 2
x = u + 3
x = 2 + 3
x=5
Therefore, x = -1 and x =5
x
Answer:
Step-by-step explanation:
The equation of line in the form .
y = mx + c
Where m is the slope and c is the y- intercept .
As given
The lines y=3x-1 and y=ax+2 are perpendicular .
Here 3 is slope for equation of line y=3x-1 and a is slope for equation of line
y=ax+2 .
Now by using properties of the perpendicular lines property .
When two lines are perpendicular than slope of one line is negative reciprocal of the other line .
Thus
Therefore
