So in your given pattern, you need to find first the derivatives and observe the patter that occurs in the given functions. So with this kind of pattern, every fourth one is the same; that makes the 114th derivative is the same as the second derivative. It is known since 114/4 has a remainder of two

8 0

3 years ago

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Apurse contains S 7.55 in quarters and dimes. There are

borishaifa [10]

Answer:

25 quarters
13 dimes

Step-by-step explanation:

If you subtract the extra 12 quarters from the total, you have $4.55 that can be made up of groups of 1 quarter and 1 dime. Since those groups are worth $0.35, there are $4.55/$0.35 = 13 of them.

There are 13 dimes and 13+12 = 25 quarters in the purse.

5 0

3 years ago

A kaleidoscope has been created by cutting a regular hexagonal hole with side length 2 cm through a cylinder. Find the volume of

posledela

Answer:

The volume of the kaleidoscope (hollow cylinder) is 613.33 in.³

Step-by-step explanation:

Here we have;

The equation for the volume of a cylinder given as follows;

Volume of cylinder = π × r² × h

Given that the height, h of the cylinder = 9 cm

The radius, r = 5 cm

Volume of the solid cylinder before cutting out the hexagon hole is thus found as follows;

Volume of cylinder = π × 5² × 9 = 706.86 cm³

Volume of hexagon hole = Area of base × height

Where:

Area, A of a regular hexagon of side a = $\frac{3\sqrt{3} }{2} \times a^2$

Therefore, volume of the regular hexagon = $\frac{3\sqrt{3} }{2} \times 2^2 \times 9 = 93.53 \ in.^3$

Therefore, the volume of the kaleidoscope (hollow cylinder) = 706.86 - 93.53 = 613.33 in.³.

3 0

3 years ago