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2 years ago

The arithmetic mean of 10 consecutive even integers is 3. What is the least of these 10 even integers?

Mathematics

1 answer:

Lady bird [3.3K]2 years ago

6 0

Answer:

-6

Step-by-step explanation:

2n can be the smallest integer, and 2n + 18 will be the largest integer.

The sum of this, divided by two, will result in the average/mean.

(2n + 2n + 18)/2 = 3

Multiply each side by 2:

(2n + 2n + 18)/2 ⋅ 2 = 3 ⋅ 2

2n + 2n + 18 = 6

Combine the like terms:

4n + 18 = 6

Subtract 18 from both sides:

4n + 18 - 18 = 6 - 18

4n = -12

Divide each side by 4:

4n/4 = -12/4

n = -3

Since we decided to go by 2n:

2n = 2(-3) = <u>-6</u>

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Step-by-step explanation:

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Now, if we compute the n-th derivative at 0 we get

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and so the Maclaurin series for f(x)=ln(1+2x) is given by

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2 years ago

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Step-by-step explanation:

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2 years ago

A trough is 8 feet long and has perpendicular cross section in the shape of an isosceles triangle (point down) with base 1 foot

murzikaleks [220]

Answer:

Dh/dt = 0.082 ft/min

Step-by-step explanation:

As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of 1 feet and height h = 2 feet.

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Then differentiating on both sides of the equation we get:

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and we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment

By proportion we know

r/h ( at the top of the cone 0,5/ 2) is equal to r/0.5 when water is 1/2 foot deep

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