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Rudiy27
3 years ago
5

I need helpp please help me!!!

Mathematics
1 answer:
icang [17]3 years ago
5 0

Answer:

SAS

Step-by-step explanation:

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Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant
Alex787 [66]

Find the intercepts for both planes.

Plane 1, <em>x</em> + <em>y</em> + 2<em>z</em> = 2:

y=z=0\implies x=2\implies (2,0,0)

x=z=0\implies y=2\implies(0,2,0)

x=y=0\implies 2z=2\implies z=1\implies(0,0,1)

Plane 2, 4<em>x</em> + 4<em>y</em> + <em>z</em> = 8:

y=z=0\implies4x=8\implies x=2\implies(2,0,0)

x=z=0\implies4y=8\impliesy=2\implies(0,2,0)

x=y=0\implies z=8\implies(0,0,8)

Both planes share the same <em>x</em>- and <em>y</em>-intercepts, but the second plane's <em>z</em>-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (<em>x</em>, <em>y</em>)-plane where <em>z</em> = 0, we see the bounded region projects down to the triangle in the first quadrant with legs <em>x</em> = 0, <em>y</em> = 0, and <em>x</em> + <em>y</em> = 2, or <em>y</em> = 2 - <em>x</em>.

So the volume of the region is

\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx

=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx

=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}

3 0
3 years ago
F(g(1)) if f(x)=5x g(x)=2x-3
RoseWind [281]

Answer:-5

Step-by-step explanation:

g(1)=2*1-3=2-3=-1

f(g(1))=5*-1=-5

7 0
3 years ago
Read 2 more answers
M3L3
eduard

The area of the David's pantry = 10 square feet.

The length of the pantry = 5 feet.

<h3>Define the term area of the rectangle?</h3>
  • The territory inhabited by a rectangle inside its 4 sides or limits is known as its area.
  • The area of such a rectangle is determined by its sides. Essentially, the formula calculating area is equivalent to the product of the rectangle's length and breadth.

For the given question.

  • David's kitchen is 60 square feet in size.
  • The kitchen is six times the size of the living room.

Thus,

Area of kitchen  = 6 x area of the pantry

60 = 6 x area of the pantry

area of the pantry = 60 / 6 = 10 square feet.

Area of the pantry = length x breadth

10 = length x 2

length = 10/2 = 5 feet.

Thus, the length of the pantry is found as the 5 feet.

To know more about the area of the rectangle, here

brainly.com/question/16239445

#SPJ4

6 0
1 year ago
100 POINTS AND MARKED AS BRAINLIEST IF YOU ANSWER THESE.
vazorg [7]

Answer:

Step-by-step explanation:1. Sure.  What you are looking for is a way to reduce both 24000 and 50 by the same factors until the 5 becomes a 1.  In which case whatever 24000 becomes is your answer.

When 50 is reduced to 1 that's the end point because we are saying 1 unit of whatever the 50 represents contains nnn units of that other number.  nnn is the answer.

So first of all we can reduce both numbers by a factor of 10 to get 2400 and 5.  Now we reduce both by a factor of 5 to get 480 and 1.  And there's your answer 480.  ANS.  2. A       all i know hope this helps luv

8 0
3 years ago
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In addition to his hourly rate, Mr. Smith is paid $2.20 for each watch he fixes. Write an expression for his income if he fixes
cricket20 [7]

Step-by-step explanation:

y = hourly income

r = number of watches fixed

equation: y = 2.20r + 9.5

5 0
3 years ago
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