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2 years ago

Two mixed numbers that have a sum of 3

Mathematics

1 answer:

hram777 [196]2 years ago

6 0

1 1/2 + 1 1/2 & 1 3/4 + 1 1/4

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t

Tresset [83]

Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = $xyz$

with subject to $x+2y+3z=9$

So, let $z=\dfrac{9-x-2y}{3}$

So, Volume becomes,

$V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}$

Partially derivative wrt x and y we get that

$9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9$

By solving these two equations, we get that

$x=3,y=\dfrac{3}{2}$

So, $z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1$

So, Volume of largest rectangular box would be

$xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5$

Hence, the volume of largest rectangular box is 4.5 units.

4 0

3 years ago

Find the volume of a trough 5 meters long whose ends are equilateral triangles, each of whose

yawa3891 [41]

Answer:

$V=5\sqrt{3}\ m^3$

Step-by-step explanation:

we know that

The volume of a trough is equal to

$V=BL$

where

B is the area of equilateral triangle

L is the length of a trough

step 1

Find the area of equilateral triangle B

The area of a equilateral triangle applying the law of sines is equal to

$B=\frac{1}{2} b^{2} sin(60\°)$

where

$b=2\ m$

$sin(60\°)=\frac{\sqrt{3}}{2}$

substitute

$B=\frac{1}{2}(2)^{2} (\frac{\sqrt{3}}{2})$

$B=\sqrt{3}\ m^{2}$

step 2

Find the volume of a trough

$V=BL$

we have

$B=\sqrt{3}\ m^{2}$

$L=5\ m$

substitute

$V=(\sqrt{3})(5)$

$V=5\sqrt{3}\ m^3$

3 0

3 years ago

Find a b if a = (4,3) and b =(4,5).<br> a. 31<br> C. (16,15)<br> b. (8,8)<br> d.-1

liq [111]

Your answer will be c

8 0

3 years ago

Read 2 more answers

Find the slope of the line containing the points (1, 2) and (6, 12).

Sholpan [36]

Answer:6

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

2 − 4 x 6 Select the expression that represents the following statement: multiply the difference of 5 and 2 by 7, and then add 6

otez555 [7]

Hey there!

2 - 4 * 6

= 2 - 24

= -22

Option A.
7 * (5 - 2) + 6

= 7 * 3 + 6

= 21 + 6

= 27

Option A. is incorrect

Option B.
5 + 2 * 7 + 6

= 5 + 14 + 6

= 19 + 6

= 25

Option B. is also incorrect

Option C.
7 * (5 + 2) - 6
= 7 * 7 - 6

= 49 - 6

= 43

Option C. is also incorrect

Option D.

6 - 2 + (7 * 5)

= 6 - 2 + 35

= 4 + 35

= 39

Thus, it seems like NONE of the ABOVE is correct

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

7 0

2 years ago