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2 years ago

Determine the sum of the first 27 even Natural Numbers. 378 2,700 270 756

Mathematics

1 answer:

kicyunya [14]2 years ago

3 0

Answer:

this is called AP arithmetic progression

2, 4, 6.........

sn=n/2(2a+(n-1)d)

S27=

$\frac{27}{2 } (2 \times 2 + (27 - 1)2)$

$\frac{72}{2} (4 + (26 \times 2)$

$\frac{27}{2} (4 + 52)$

$\frac{27}{2} \times 56$

$27 \times 28$

=756

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3 years ago

How to find the length of the midsegment

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3 years ago

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A model for the basal metabolism rate, in kcal/h, of a young man is R(t) = 95 − 0.18 cos(πt/12), where t is the time in hours me

11111nata11111 [884]

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3 years ago

Do any of you know how to easily and properly convert a mixed fraction to a decimal?

arlik [135]

Answer:

Here's a 2 step conversion.

Step-by-step explanation:

1. Convert the fraction to a decimal: Divide the numerator by the denominator

2. Add this decimal number to the whole number part of the mixed number

A mixed number is a whole number plus a fraction. To find the decimal form of a fraction just divide the numerator by the denominator using a calculator or long division. Then add the decimal number to the whole number.

Example: Convert the mixed number 7 1/4 to a decimal

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3 years ago

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(a) The function k is defined by k(x)=f(x)g(x). Find k′(0).

Brut [27]

Answer:

(a) k'(0) = f'(0)g(0) + f(0)g'(0)

(b) m'(5) = $\frac{f'(5)g(5) - f(5)g'(5)}{2g^{2}(5) }$

Step-by-step explanation:

(a) Since k(x) is a function of two functions f(x) and g(x) [ k(x)=f(x)g(x) ], so for differentiating k(x) we need to use product rule,i.e., $\frac{\mathrm{d} [f(x)\times g(x)]}{\mathrm{d} x}=\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}$

this will give k'(x)=f'(x)g(x) + f(x)g'(x)

on substituting the value x=0, we will get the value of k'(0)

{for expressing the value in terms of numbers first we need to know the value of f(0), g(0), f'(0) and g'(0) in terms of numbers}{If f(0)=0 and g(0)=0, and f'(0) and g'(0) exists then k'(0)=0}

(b) m(x) is a function of two functions f(x) and g(x) [ $m(x)=\frac{1}{2}\times\frac{f(x)}{g(x)}$ ]. Since m(x) has a function g(x) in the denominator so we need to use division rule to differentiate m(x). Division rule is as follows : $\frac{\mathrm{d} \frac{f(x)}{g(x)}}{\mathrm{d} x}=\frac{\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}}{g^{2}(x)}$

this will give $m'(x) = \frac{1}{2}\times\frac{f'(x)g(x) - f(x)g'(x)}{g^{2}(x) }$

on substituting the value x=5, we will get the value of m'(5).

{for expressing the value in terms of numbers first we need to know the value of f(5), g(5), f'(5) and g'(5) in terms of numbers}

{NOTE : in m(x), g(x) ≠ 0 for all x in domain to make m(x) defined and even m'(x) }

{ NOTE : $\frac{\mathrm{d} f(x)}{\mathrm{d} x}=f'(x)$ }

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3 years ago