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3 years ago

Help! I am being timed. Thank you

Mathematics

1 answer:

natita [175]3 years ago

8 0

Answer:

Step-by-step explanation:

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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

How do you evaluate the expression to this problem 24 divided by (-4)+(-2) times (-5)

Tju [1.3M]

24/-30 would be the answer

8 0

3 years ago

Read 2 more answers

I need help please been getting all the answers wrong

vaieri [72.5K]

Answer:Question? :c

Step-by-step explanation:

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3 years ago

Read 2 more answers

A rug maker is using a patter that is a rectangle with a length of 96 inches and a width of 60 inches. the rug maker wants to in

dexar [7]

Recall that the formula for the perimeter of a rectangle is: 2Length+2Width
With this in mind, we have that the original design is 96×60, where 90 is length and 60 is width, so it would simply be:
2(96+l) + 2 (60+w) = New Perimeter
Or simplified, it'd be:
2l + 2w + 312 = New Perimeter

8 0

3 years ago

Antonia incorrectly solves the equation −2(14−54a)=6 . Her work is shown below.

bekas [8.4K]

Answer:

For the yes/no bit:

step 1: no

step 2: no

step 3: yes

step 4: yes

step 5: no

for the final answer bit: a = 2 3/5 (the last option)

Step-by-step explanation:

yes/no bit:

step 1 is wrong because she didn't multiply $-\frac{5}{4}a$ by -2

step 2 is wrong because she subtracted 1/2 instead of adding it

step 3 is correct because 6 - 1/2 = 11/2

step 4 is correct because she correctly multiplied both sides by 4

step 5 is wrong because she added 5 instead of dividing by -5.

for the final answer bit, I've attached an image below with my working out. hope this helps!

6 0

3 years ago