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3 years ago

Find the 90 th derivative of the function ƒ(x)=cos(x)

1 answer:

5 0

F(x) = cos x
f'(x) = -sin x
f''(x) = -cos x
f'''(x) = sin x
f''''(x) = cos x

90/4 = 22 Remainder 2
Therefore, 90th derivative of f(x) = cos x is -cos x.

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Suppose the radius of the sphere is increasing at a constant rate of 0.3 centimeters per second. At the moment when the radius i

elixir [45]

<h2>At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.</h2>

Step-by-step explanation:

We have equation for volume of a sphere

$V=\frac{4}{3}\pi r^3$

where r is the radius

Differentiating with respect to time,

$\frac{dV}{dt}=\frac{d}{dt}\left (\frac{4}{3}\pi r^3 \right )\\\\\frac{dV}{dt}=\frac{4}{3}\pi \times 3r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}$

Given that

Radius, r = 24 cm

$\frac{dr}{dt}=0.3cm/s$

Substituting

$\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi \times 24^2\times 0.3\\\\\frac{dV}{dt}=2171.47cm^3/min$

At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.

4 0

3 years ago

3(1-5x)=2(3x+1) find the solution set

tiny-mole [99]

Answer:

1/21

Step-by-Step Explanation:

Let's solve your equation step-by-step.

3(1−5x)=2(3x+1)

Step 1: Simplify both sides of the equation.

3(1−5x)=2(3x+1)

(3)(1)+(3)(−5x)=(2)(3x)+(2)(1)(Distribute)

3+−15x=6x+2

−15x+3=6x+2

Step 2: Subtract 6x from both sides.

−15x+3−6x=6x+2−6x

−21x+3=2

Step 3: Subtract 3 from both sides.

−21x+3−3=2−3

−21x=−1

Step 4: Divide both sides by -21.

-21x/-21=-1/-21

x=1/21

7 0

2 years ago

Read 2 more answers

Graph the line with slope -2 passing through the point (3,4)

Maurinko [17]

Answer: The line that contains the points A and B

Step-by-step explanation: In this problem, we're asked to graph the line that contains the point (3,4) and has a slope of -2.

We would start things off by plotting our point, (3,4).

If you need a review on plotting points, take a look below.

The first number in our point represents the x coordinate or how far we move to the left or right from the origin.

The second number in our point represents the y coordinate or how far we move up or down from the origin.

So we go over 3 units and up 4 units and call that point A.

In order to graph a line however, we need two points

and that's where our slope comes in.

Remember that slope means rise over run. So from our original point that we have already plotted, we rise -2 units and run 1 unit.

When you have a slope that's an integer like -2, just put it over 1.

After rising 2 units and running 1 unit, plot your second point

which I have plotted as point B.

You could if you wanted to continue to plot more and more points but we just need at least two points to graph a line.

So our answer is then the line that contains the points A and B.

8 0

3 years ago

Can every number be represented as a decimal? explain

Sav [38]

Yes if its 10%,20%,30%,40%,50%,60%,70%,80%,90%,100%,but if its like 21%,29%,68%,74%,probably if your doing math

7 0

3 years ago

The lunch special at Sams restaurant is a sandwhich, a drink and a dessert. There are 2 sanwhiches, 3 drinks, and 2 desserts to

expeople1 [14]

i think 3 and a half im not sure

7 0

3 years ago