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3 years ago

1A. Jennifer bought some packs of pencils. Each pack has 9 pencils. Jennifer

Mathematics

1 answer:

iris [78.8K]3 years ago

6 0

The answer is A. The only multiple of 9 that is between 70 and 80 is 72. 72 divided by 9 equals 8.

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A box without a top is to be made from a rectangular piece of cardboard, with dimensions 9 in. by 10 in., by cutting out square

mariarad [96]

Answer:

The optimal volume is 63.1142 in3, with a cut of 1.5767 inches

Step-by-step explanation:

If we make a cut of x inches to create the box, the dimensions of the box will be:

Length = 10 - 2x

Width = 9 - 2x

Height = x

So the volume of the box would be:

Volume = (10 - 2x) * (9 - 2x) * x

Volume = 4x3 - 38x2 + 90x

To find the maximum volume, we need to take the derivative of the volume and find the values of x where it is equal to zero:

dV/dx = 12x2 - 76x + 90 = 0

6x2 - 38x + 45 = 0

Using Bhaskara's formula, we have:

Delta = 38^2 - 4*6*45 = 364

sqrt(Delta) = 19.08

x1 = (38 + 19.08) / 12 = 4.7567

x2 = (38 - 19.08) / 12 = 1.5767

Testing these values in the volume equation, we have:

Volume1 = 4*(4.7567)^3 - 38*(4.7567)^2 + 90*(4.7567) = -1.1883

(Negative value for the volume is not valid)

Volume1 = 4*(1.5767)^3 - 38*(1.5767)^2 + 90*(1.5767) = 63.1142

So the optimal volume is 63.1142 in3, with a cut of 1.5767 inches

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3 years ago

Larry has already read 60 pages out of a 400 page book. He wants to finish the book in the next 20 days. The equation 20x + 60 =

antiseptic1488 [7]

Answer:

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Step-by-step explanation:

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A cone with a volume of 640.23 has a radius of 7. What is the height of the cone?

USPshnik [31]

Answer:

Your answer is about 12.48

Step-by-step explanation:

h = 3(V/pi*r²)

h = 3(640.23/pi*7²)

h = 3(640.23/153.93804)

h = 3(4.157516881)

h = 12.47703

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2 years ago

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Answer:

x = 109°

Step-by-step explanation:

x° is 37° + 72°, due to exterior angle property.

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3 years ago

How to find the measure of an exterior angle on a triangle

nexus9112 [7]

Hi there!

There are many ways to find the measure of an exterior angle of a triangle. I'll explain the easiest method to you. As you can see in the image, a line is drawn extending a side of the triangle. In order to find the measure of the exterior angle, we can subtract the measure of the adjacent interior angle from 180 (a straight angle). Doing this subtraction will give us the measure of the exterior angle.

Hope this helps!! :)

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3 years ago

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