Jordan buys a big drum. The diameter of a drum circle is 12 feet. What is the area of the drum?

How to differentiate y=x^n using the first principle. In this question, I cannot use the rule of differentiation. I have to do t

Zarrin [17]

By first principles, the derivative is

$\displaystyle\lim_{h\to0}\frac{(x+h)^n-x^n}h$

Use the binomial theorem to expand the numerator:

$(x+h)^n=\displaystyle\sum_{i=0}^n\binom nix^{n-i}h^i=\binom n0x^n+\binom n1x^{n-1}h+\cdots+\binom nnh^n$

$(x+h)^n=x^n+nx^{n-1}h+\dfrac{n(n-1)}2x^{n-2}h^2+\cdots+nxh^{n-1}+h^n$

where

$\dbinom nk=\dfrac{n!}{k!(n-k)!}$

The first term is eliminated, and the limit is

$\displaystyle\lim_{h\to0}\frac{nx^{n-1}h+\dfrac{n(n-1)}2x^{n-2}h^2+\cdots+nxh^{n-1}+h^n}h$

A power of $h$ in every term of the numerator cancels with $h$ in the denominator:

$\displaystyle\lim_{h\to0}\left(nx^{n-1}+\dfrac{n(n-1)}2x^{n-2}h+\cdots+nxh^{n-2}+h^{n-1}\right)$

Finally, each term containing $h$ approaches 0 as $h\to0$ , and the derivative is

$y=x^n\implies y'=nx^{n-1}$

4 0

3 years ago

Please help 6th grade math i will give brainliest to answer with worked shown

Wewaii [24]

Answer:

64

Step-by-step explanation:

She drinks 4 ounces every 30 minutes.

4*2= 8 She drinks 8 ounces in an hour.

8*8=64 She drinks 64 ounces in 8 hours

8 0

2 years ago

Express in terms of logarithm without exponents

sdas [7]

$\bf log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)
\\ \quad \\
% Logarithm of rationals
\\ \quad \\
% Logarithm of exponentials
log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\
-----------------------------\\\\
log_b(xy^2z^{-6}\implies log_b(x)+log_b(y^2)+log_b(z^{-6})
\\\\\\log_b(x)+2log_b(y)-6log_b(z)$

now, the one below that, which is equivalent to that? well, just look above it

6 0

3 years ago

A car travels 45km in an hour. In each of the next two hours, it travels 78km. What is the average speed of the car.

romanna [79]

Answer:

The average speed of car is 67 kilometers per hour.

Step-by-step explanation:

Given that:

Distance travelled in one hour = 45 km

Distance travelled in next 2 hours = 78*2 = 156 km

Total distance = 45+156 = 201

Total time = 1+2 = 3 hours

Average speed of the car = $\frac{Total\ distance}{Total\ time}$

Average speed of the car = $\frac{201}{3}$

Average speed of the car = 67 km/hr

Hence,

The average speed of car is 67 kilometers per hour.

7 0

3 years ago

Which relation represents a function? A. {(0, 3), (2, 4), (0, 6)} B. {(-7, 5), (-7, 1), (-10, 3), (-4, 3)} C. {(2, 0), (6, 2), (

xz_007 [3.2K]

If there are two of the same x values in a set, it is not a function. Therefore, the answer is D. Hope this helps, and please mark brainliest!

5 0

3 years ago