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3 years ago

Give your own example of an irrational number and explain why the number you chose is irrational

1 answer:

3 0

Definition
An irrational number is a number that cannot be expressed in as a fraction. It has decimal expression that does not terminate.

An example will be √2.

Reason:
(1) √2 cannot be expressed as a fraction form
(2) √2 has decimals that does not terminate

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Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).

Elan Coil [88]

Answer: $\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV$ = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = $\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]$ $\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]$

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

$a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0$

Then, replacing with point P and normal vector n:

$36(x-5) + 20(y-0) + 45(z-0) = 0$

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

$z = \frac{180-36x-20y}{45}$

When z = 0:

$y = 9 + \frac{-9x}{5}$

When z=0 and y=0:

x = 5

Then, triple integral is:

$\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx$

Calculating:

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$

$\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx$

$\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx$

$\frac{1}{45} [30375-60750+118462.5-39150]$

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$ = 1087.5

The volume of the tetrahedon is 1087.5 cubic units.

3 0

3 years ago

2* 7-t 8*y 9=9 Which is the equation?

GaryK [48]

Answer:

2+7_t×y+9 je pense que c la reponses

6 0

3 years ago

What is the length of the side of a square with an area of 64m^2?

Alika [10]

The answer is D.8m
you do this by finding the square root of 64.

3 0

3 years ago

the vertex of a quadratic function is (6,2) and the y-intercept of the function is (0,-70). the equation of the function in vert

VladimirAG [237]

Well, just solve the equation

-70 = $a(0-6)^2+2$
-70 = $a(-6)^2+2$
-70 - 2 = 36a
a = -72/36 = -2

5 0

3 years ago

Read 2 more answers

Find the sum and product of each of these pairs of num- bers. express your answers as a base 3 expansion.

alisha [4.7K]

Adding in base 3 is very much like adding in base 10, but instead of carrying digits when their sum exceeds 9, we have to watch for when the sum exceeds 2:

.   112
+ 210
- - - - -
.   322 -> 1022

.   12021
+    2122
- - - - - - -
.   14143 -> 14150 -> 14220 -> 21220

.   20001
+    1111
- - - - - - -
.   21112

.   120021
+      2002
- - - - - - - -
.    122023 -> 122030 -> 122100

5 0

3 years ago