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zvonat [6]
2 years ago
9

Find the area of the triangle defined by the given system?

Mathematics
1 answer:
just olya [345]2 years ago
6 0
Look at my pfp it tells you the answer
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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by
11111nata11111 [884]

Answer:

The dimension of the open rectangular box is 8.216\times 4.216\times 1.392.

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is V=l\times b\times h

V=(11-2x)\times (7-2x)\times x

V=4x^3-36x^2+77x

Derivate w.r.t x,

V'(x)=4(3x^2)-2(36x)+77

V'(x)=12x^2-72x+77

The critical point when V'(x)=0

12x^2-72x+77=0

Solve by quadratic formula,

x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}

x=4.607,1.392

Derivate again w.r.t x,

V''(x)=24x-72

Now, V''(4.607)=24(4.607)-72=38.568>0 (+ve)

V''(1.392)=24(1.392)-72=-38.592 (-ve)

So, there is maximum at x=1.392.

The length of the box is l=11-2x

l=11-2(1.392)=8.216

The breadth of the box is b=7-2x

b=7-2(1.392)=4.216

The height of the box is h=1.392.

The dimension of the open rectangular box is 8.216\times 4.216\times 1.392.

The volume of the box is V=l\times b\times h

V=8.216\times 4.216\times 1.392

V=48.217\ in.^3

The volume of the box is 8.217 cubic inches.

5 0
3 years ago
What expression is not equal to 1/4 of 52?
dmitriy555 [2]
1/4 of 52 = 13.
you didn't list the options....


3 0
3 years ago
A box has dimensions of 17 inches long, 1.3 feet wide, and 8 inches high. What is the volume of the box? The formula for the vol
s344n2d4d5 [400]
I hope this helps you



Volume =17×1,3×8


Volume =176,8
6 0
2 years ago
The measure of angle 1 is 39 degrees. What is the measure of the angle adjacent to angle<br> 1?
Bogdan [553]

Answer:

51

Step-by-step explanation:

90-39 = 51

6 0
3 years ago
Doughnuts at one shop cost £2.20 each. Doughnuts at a second shop cost 25% more. What is the difference in the cost of doughnuts
Zanzabum

Answer:

0.55

Step-by-step explanation:

diference= 25/100*2.20=0.55

3 0
2 years ago
Read 2 more answers
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