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3 years ago

Find the sum of the squares of the first five natural numbers.

Mathematics

1 answer:

creativ13 [48]3 years ago

7 0

Answer:

Step-by-step explanation:

The sum of the squares of the first five natural numbers.

Natural numbers are the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.

Therefore:

(1^2) + (2^2) + (3^2) + (4^2) + (5^2)

1 + 4 + 9 + 16 + 25

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Convert this number given in standard form into scientific notation. 0. 0000069 What is the value in scientific notation? 0. 69

Len [333]

Scientific notation is used so that the order of the number is known in first glance. The value of the given number in scientific notation is given by: Option B: $6.9 \times 10^{-6}$

<h3>How does scientific notations work?</h3>

The number is written in the form $a \times 10^b$ where we have $1 \leq a < 10$

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

Scientific notations have some of the profits as:

Better readability due to compact representation
Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

For the given case, the number in consideration is 0.0000069

Rewriting it in fraction form, we get:

$0.0000069 = \dfrac{69}{10000000} = \dfrac{69}{10^7} = 69 \times 10^{-7} = 6.9 \times 10 \times 10^{-7}\\\\0.0000069 = 6.9 \time 10 ^{-7 +1} \\0.0000069 = 6.9\times 10^{-6}$

(we used two facts: first that : $\dfrac{a}{b} = a \times \dfrac{1}{b}$

and second that: $a^{-b}= \dfrac{1}{a^b}$

Thus, the value of the given number in scientific notation is given by: Option B: $6.9 \times 10^{-6}$

Learn more about scientific notations here:

brainly.com/question/3112062

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3 years ago

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harkovskaia [24]

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Step-by-step explanation:

$\frac{dy}{dx}+3y=18\\\\\mathrm{Substitute\quad }\frac{dy}{dx}\mathrm{\:with\:}y'\:\\\\y'\:+3y=18\\\\Rewrite\\\\\frac{1}{6-y}y'\:=3\\\\Solve \::\frac{1}{6-y}y'\:=3\\\\-In(6-y)=3x+c_1\\\\Isolate\:y\\\\\\y=-e^{-3x-c_1}+6$

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Sunny_sXe [5.5K]

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