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r-ruslan [8.4K]
3 years ago
12

Write an algebraic expression which represents the volume of a cylinder whose radius is 3k and height is 2k + 1.

Mathematics
2 answers:
AlekseyPX3 years ago
8 0
V= Pi r^2 h
V = Pi (3k)^2 (2K+1) = Pi (9k^2)(2K+1)
V = (18K^3 + 9K^2 )Pi
pickupchik [31]3 years ago
5 0
V=hπr^2

V=(2k+1)π(3k)^2

V=π(2k+1)(9k^2)

V=π(18k^3+9k^2)

V=18πk^3+9πk^2
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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 <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>.

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

The <em>instantaneous</em> 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 <em>difference</em> rate.

In this question we must find an expression for the <em>instantaneous</em> 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 <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>. \blacksquare

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

4 0
2 years ago
Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
mestny [16]

For a binomial experiment in which success is defined to be a particular quality or attribute that interests us, with n=36 and p as 0.23,  we can approximate p hat by a normal distribution.

Since n=36 , p=0.23 , thus q= 1-p = 1-0.23=0.77

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The question is incomplete, a possible complete question is:

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

Suppose n = 36 and p = 0.23. Can we approximate p hat by a normal distribution? Why? (Use 2 decimal places.)

n*p = ?

n*q = ?

Learn to know more about binomial experiments at

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Select the reason why these triangles are
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Answer:

c.sss because they have the same angles and triangles

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