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2 years ago

Select the choice that translates the following verbal phrase correctly to algebra: (2 points)

1 answer:

6 0

This is just stuff you have to memorize, I can’t really explain much further than product always means multiplication. The “product of” means k*m

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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

PLEASE HELP ME ASAP!!!!! WILL GIVE BRAINLIEST!!! Solve the proof Thanks Y'all:))

jek_recluse [69]

Answer:

Below.

Step-by-step explanation:

Triangles ABC and CDE are congruent by 2 angles and the corrrespnding side (AAS).

Therefore AC = CE.

So C is the midpoint of AE.

6 0

2 years ago

Grant Valley School has hired a fleet of buses and vans to transport 96 students to a picnic. Each bus can seat 31 people, and e

77julia77 [94]

2 buses and 5 vans............

4 0

3 years ago

Read 2 more answers

John read the first 114 pages of a novel, which was 3 pages less than start fraction, 1/3 1, divided by, 3, end fraction of the

anyanavicka [17]

HERE IS YOUR ANSWER

114 = (1/3)p - 3
HOPED I HELPED AND SMASH THAT THANKS BUTTON AND ADD ME AS A FRIEND

3 0

3 years ago

A recipe calls for 3/4 cup of butter. Angie wants to triple the recipe, but she has only 1 5/8.

Alenkasestr [34]

So tripple of 3/4 is 3/4 times 3/1=9/4=2 and 1/4
she has 1 and 5/8
compare 1 and 5/8 and 2 and 1/4

convert 1/4 to 2/8

she has 1 and 5/8 but she needs 2 and 2/8
1=8/8
1 and 5/8 and needs 1 and 10/8
1 and 5/8+x=1 and 10/8
subtract 1
5/8+x=10/8
subtrarct 5/8
x=5/8
she must borrow 5/8 cups from neighbor

5 0

3 years ago