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Musya8 [376]
3 years ago
11

How can you use a number line to compare and order numbers

Mathematics
1 answer:
Nookie1986 [14]3 years ago
8 0

by arranging the line to the correct order in order to do whatever it is you need the number line for

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A box is being created out of a 15 inch by 10 inch sheet of metal. Equal-sized squares are cutout of the corners, then the sides
ivolga24 [154]

Answer:

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

Step-by-step explanation:

Given that,

A box is being created out of a 15 inches by 10 inches sheet of metal.

The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.

The length of the metal box be = (15-2x) inches.

The width of the metal box be =(10-2x) inches

The height of the metal box be =x inches

Then, the volume of the metal box= length×width×height

                                                         =(15-2x)(10-2x)x cubic inches

                                                         =(150x-50x²+4x³) cubic inches

∴ V= 4x³-50x²+15x

Differentiating with respect to x

V'=12x²-100x+15

Again differentiating with respect to x

V''=24x-100

For maximum or minimum value, V'=0

12x²-100x+15=0

Apply quadratic formula x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}, here a=12, b= -100 and c=15

x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}

\Rightarrow x=\frac{100\pm\sqrt{9280}}{2.12}

\Rightarrow x=0.1528,8.18

For x= 8.18, The value of (15-2x) and (10-2x) will negative.

∴x=0.1528 .

Now, V''|_{x=0.1528}=24(0.1528)-100

∴At x=0.1528 inch, the volume of the metal box will be maximum.

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

4 0
3 years ago
3. The measures of the angles of a triangle are in the extended ratio 2:3. 10. What is the measure of the
Kay [80]

Answer:

120

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
You and your friend are painting the walls in your apartment. You estimate that there is 1000 square feet of space to be painted
leva [86]
After 45 minutes you will have painted 4*45=180 square feet.

so the total number of painted area, y, is:

y=180+x*(3+4) after the 45 minutes

where x is the number of minutes AFTER THE 45 minutes:

if y is 1000 then

1000=180+x*7
820=x*7
x=117.14

so 117 minutes, or one hour and 57 minutes.
5 0
2 years ago
The product of eight minus a number and seven equals forty when decreased by five. Which equation represents the sentence?
weeeeeb [17]
The "product" of two numbers means you multiply them.

So, you are multiplying (8-n), where n = "a number," by 7.

Then, when you decrease (subtract) this product by 5, you get 40.

So the whole thing looks like

7(8-n) - 5 = 40.
8 0
3 years ago
-x-1=5 can somebody answer this fo me THX :)
Nitella [24]

Answer: -6

Step-by-step explanation:

-x-1=5

-x=5+1

-x=6

divide both sides by -1

x=-6

8 0
2 years ago
Read 2 more answers
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