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2 years ago

10

A weather reporter in your area said that the speed of sound in air today is about 1100 ft./s what is the speed in scientific no

tation

1 answer:

ruslelena [56]2 years ago

5 0

Answer:

1.1x10^3

Step-by-step explanation:

You divide by 10 until you get one digit on the left of the decimal, and however many times you divided by ten is the exponent that goes with the 10 in scientific notation.

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Find the HCF of 96 and 108

White raven [17]

Step-by-step explanation:

it may help you to understand.

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2 years ago

Read 2 more answers

What is the value of 2m^2+12 when m = 3?<br> 24<br> 30<br> 37<br> 38

Crazy boy [7]

Answer:

30

Step-by-step explanation:

8 0

2 years ago

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

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

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

3 years ago

Please help question in the picture

anzhelika [568]

Answer:

50

Step-by-step explanation:

40 squared is 1600

30 squared is 900

1600+900=2500

$\sqrt{2500}$ =50

6 0

2 years ago

Solve for x <br> Need help asap

vlabodo [156]

Answer:

$x=55$

Step-by-step explanation:

Corresponding angles of two parallel lines are always equal. The angle on "top" of $2x+6$ corresponds with the angle marked as $x+9$ . Therefore, its measure must also be $x+9$ .

Since these two angles form one side of a line which has 180 degrees, we have the following equation:

$2x+6+x+9=180$

Combine like terms:

$3x+15=180$

Subtract 15 from both sides:

$3x=165$

Divide both sides by 3:

$x=\frac{165}{3}=\boxed{55}$

3 0

2 years ago