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adoni [48]
2 years ago
8

Find the volume of the given solid region in the first octant bounded by the plane 9z+15y+15z=45 and the coordinate​ planes, usi

ng triple integrals.
Mathematics
1 answer:
dem82 [27]2 years ago
3 0

First,

9x+15y+15z=45\implies 3x+5y+5z=15

The volume is given by the integral (one of 6 possible combinations),

\displaystyle\int_0^5\int_0^{\frac{15-3x}5}\int_0^{\frac{15-3x-5y}5}\mathrm dz\,\mathrm dy\,\mathrm dx=\boxed{\frac{15}2}

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How do you figure out the answer?
svp [43]

we can divide the composite shape into on quadrilateral and triangle as shown in the diagram. since the line that joins the two shape is parallel to the base AB, the angle DEC is 85°.The angle CEA is 180°- angle DEC = 180-85=95. Angle BCE is sum of angle CEA, ABC and EAB subtracted from360°= 360°-(95+95+85)=85°. Angle DCE is 120°- ECB=35°. So, angle CDE = 180°-(35°+85°)= 60°. For reference see the diagram.

7 0
3 years ago
What the perimeter is ?
tigry1 [53]

Answer:

the perimeter is the total length of that plane figure

5 0
2 years ago
Paul bags of raisin bars in a pan shaped like a rectangle or prism the volume of the pan is 252 in.³ the length of the pants 12
e-lub [12.9K]

Answer:

The height of the pan is 2 inches.

Step-by-step explanation:

Given : Paul bags of raisin bars in a pan shaped like a rectangle or prism the volume of the pan is 252 in.³ the length of the pants 12 inches and it's with is 10\frac{1}{2} inches.

To find : What is the height of the pan ?

Solution :

The volume of a rectangle or prism is

V=l\times w\times h

Where, l=12 inches is the length

w=10\frac{1}{2} inches is the width

V=252 in.³ is the volume

h is the height

Substitute the value,

252=12\times 10\frac{1}{2}\times h

252=12\times \frac{21}{2}\times h

h=\frac{252\times 2}{12\times 21}

h=2

Therefore, the height of the pan is 2 inches.

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2 years ago
Simplify the expression. (15 + 8)[23 – (10 + 7)]
wariber [46]
(23)(23-17)
(23)(6)
138
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In the next olympics the united states can enter four athletes in the divivng competition. how many different teams of four dive
n200080 [17]
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