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2 years ago

Write the equation of the line with the following characteristics through the origin and the point (2,2)

1 answer:

4 0

Y = X

Because the origin is 0,0 and the point is 2,2.

In order to get from 0,0 to 2,2 with a line, it must have equal increments of the Y as the X.

In y=mx+b form, you’d have y = 1x+0 which just simplified to what I already stated: y=x

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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

2 years ago

Angle EFG is 80°

Lana71 [14]

Answer:

X=80°

Step-by-step explanation:

Bc it’s in the same place as angle F

8 0

2 years ago

A cargo ship left port A and is headed across the ocean to shipping port B. After one month, the ship stopped at a refueling sta

Sergeu [11.5K]

Answer:

Step-by-step explanation:

Edge 2020

8 0

2 years ago

Read 2 more answers

As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship be

Vedmedyk [2.9K]

Answer:

0.63

Step-by-step explanation:

To get the relative frequency of students with red hair, we need to find the relative frequency of students with red hair from the students with gray eyes.

Since we already know that the total number of students with gray eyes is 35 and the number of red hair students with gray eye is 22

The formula we will use to calculate the relative frequency will be

The relative frequency of students with red hair = Total students of red hair with gray eyes divide by total number of gray eye students

22 ÷ 35 = 0.628 ≅ 0.63

6 1

2 years ago

Joint and Combined Variations

Crazy boy [7]

10 * 450 / 404 * 36 / 40 = 10.0247524752 liters

Source:
http://www.1728.org/combined.htm

3 0

2 years ago

Read 2 more answers