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3 years ago

What numbers are perfect numbers

1 answer:

5 0

A perfect number is a number where the sum of its divisors is equal to the number.

For example 6: 1 + 2 + 3 = 6

Another example is 28: 1 + 2 + 4 + 7 + 14 = 28

Here is a short list of perfect numbers: 6, 28, 496, 8128, 33550336, and the numbers get way bigger as we go on.

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Let g be the function given by g(x)=limh→0sin(x h)−sinxh. What is the instantaneous rate of change of g with respect to x at x=π

lorasvet [3.4K]

The instantaneous rate of change of g with respect to x at x = π/3 is 1/2.

<h3>How to determine the instantaneous rate of change of a given function</h3>

The instantaneous rate of change at a given value of $x$ can be found by concept of derivative, which is described below:

$g(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Where $h$ is the difference rate.

In this question we must find an expression for the instantaneous rate of change of $g$ if $f(x) = \sin x$ and evaluate the resulting expression for $x = \frac{\pi}{3}$ . Then, we have the following procedure below:

$g(x) = \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}$

$g(x) = \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}$

$g(x) = \lim_{h \to 0} \frac{\sin h}{h}\cdot \lim_{h \to 0} \cos x$

$g(x) = \cos x$

Now we evaluate $g(x)$ for $x = \frac{\pi}{3}$ :

$g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}$

The instantaneous rate of change of g with respect to x at x = π/3 is 1/2. $\blacksquare$

To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037

4 0

1 year ago

Find the equation of the line that passes through (2,8) and (6,48)

kolezko [41]

Answer: m = 10

.........................

3 0

2 years ago

Plss finish fast the question is linked thank you for ur help

kobusy [5.1K]

Answer: B. 2 2/5

Step-by-step explanation: Hope this help :D

3 0

3 years ago

Read 2 more answers

Heelllppp please!!!!!!!

Brums [2.3K]

Answer:

7.9

Step-by-step explanation:

area of circle equals π× 5 = 15.7

area of half of the circle equals 15.7÷2

=7.85

now round it of and it's 7.9

8 0

2 years ago

How do i evaluate (7 to the power of 2)to the power of 3)=7 to the power of 5

kakasveta [241]

Step-by-step explanation:

$(7^2)^3=7^5\qquad\bold{FALSE}\\\\\text{because}\\\\7^2=7\cdot7\\\\(7^2)^3=(7\cdot7)^3=(7\cdot7)\cdot(7\cdot7)\cdot(7\cdot7)=\underbrace{7\cdot7\cdot7\cdot7\cdot7\cdot7}_6=7^6\\\\\text{or use}\ (a^n)^m=a^{nm}\\\\(7^2)^3=7^{2\cdot3}=7^6$

4 0

2 years ago

Read 2 more answers