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Varvara68 [4.7K]
3 years ago
7

Explain what is meant by a 100% decrease.

Mathematics
1 answer:
dsp733 years ago
7 0
So lets say u have 100$ and it decreases by 100% u would have no money left
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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
Someone please tell me how to work out this type of problem i completely forgot
fenix001 [56]

Answer:

Plug the x-values into the equation to get the y values. This will give you coordinates that you can graph a line with.

Step-by-step explanation:

For x = -5:  y = -3 - 2 * (-5) = 7, so the coordinates are (-5, 7)

For x = -2:  y = -3 - 2 * (-2) = 1, so the coordinates are (-2, 1)

(Etc.)

Then, plot these coordinates and draw a line through them to complete the graph.  

8 0
2 years ago
What is the length of the line segment shown on this coordinate grid?PLEASE HELP :-)
tigry1 [53]
 The line is 4 units in length.
5 0
2 years ago
Find the point on the line 2x+4y−3=0 which is closest to the point (2,0)
Finger [1]
L1: 2x+4y-3=0 ..........(1)
P: (2,0)
The point on the line L1 closest to the given point P is at the intersection of L1 with L2, which is the perpendicular passing through P. 

Slope of L1=-2/4=-1/2
Slope of L2=-1/(-1/2)=2
Since it passes throug P(2,0), we can use the point-slope formula:
(y-0)=2(x-2)  =>
L2: 2x-y-4=0.............(2)

Solve for x & y using (1) and (2) to get intersection point required:
(1)-(2)
2x-2x + 4y-(-y) -3 -(-4) =0
5y=-1, y=-1/5
Substitute y=1/5 in equation (1)
2x+4(-1/5)-3=0 =>
2x-19/5=0
x=19/10

=> the point on L1 closest to (2,0) is (19/10, -1/5)

7 0
3 years ago
The length of a field in feet is a function f(n) of the length nin yards. Write a function rule for this situation.
qwelly [4]

Given:

The length of field is n yards.

The length of a field in feet is a function f(n).

To find:

The function rule for this situation.

Solution:

We know that,

1 yard = 3 feet

Using this conversion, we get

n yard = 3n feet

The length of field is n yards. So, the length of the field is 3n feets.

The length of a field in feet is a function f(n). So,

f(n)=3n

Therefore, the required function rule for this situation is f(n)=3n.

5 0
2 years ago
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