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2 years ago

How would you "remove the discontinuity" of f ? In other words, how would you define

1 answer:

5 0

There is a hole at x=4 because the top factors to (x-4)(x+3)
in the end we get

f(x)=(x-4)(x+3)/(x-4)
the (x-4) cancels out and we get
f(x)=x+3
so baiscally f(x) is y=x+3 but with a hole at (4,7)

one way is to make a piecewise function defined as(x^2-x-12)/(x-4) for all x≠4 and defined as 7 for x=4

or, to just do f(x)=x+3

You might be interested in

If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate (in cm/min) at which the diameter d

zhuklara [117]

Answer:

The diameter decreases at a rate of 0.143cm/min when it is of 10 cm.

Step-by-step explanation:

Surface area of an snowball:

An snowball has spherical format. The surface area of an sphere is given by:

$S = d^2\pi$

In which d is the diameter of the sphere.

In this question:

We need to differentiate S implicitly in function of time. So

$\frac{dS}{dt} = 2d\pi\frac{dd}{dt}$

Surface area decreases at a rate of 9 cm2/min

This means that $\frac{dS}{dt} = -9$

At which the diameter decreases when the diameter is 10 cm?

This is $\frac{dd}{dt}$ when $d = 10$ . So

$\frac{dS}{dt} = 2d\pi\frac{dd}{dt}$

$-9 = 2(10)\pi\frac{dd}{dt}$

$\frac{dd}{dt} = -\frac{9}{20\pi}$

$\frac{dd}{dt} = -0.143$

Area in cm², so diameter in cm.

The diameter decreases at a rate of 0.143cm/min when it is of 10 cm.

8 0

2 years ago

martha goes to the store to buy a shirt. the final price of her order is 22. if the store charged 8% tax, what was fhe original

prisoha [69]

20.24 that was his price before

5 0

2 years ago

Read 2 more answers

Please help me with this! Anything will be appreciated!! :)

kumpel [21]

The formula for volume is Length x Width x Height.

So when you apply this formula to these questions the answers should be:

#7. 3x4x2 = 24

#8. 2x4x1 = 8

#9. 3x4x2 = 24

#10. 4x3x1 = 12

I hope this helps!

5 0

3 years ago

F(x) = -x^2+10x-6<br> Find f(-5)

lianna [129]

9514 1404 393

Answer:

f(-5) = -81

Step-by-step explanation:

Put -5 where x is and do the arithmetic.

f(-5) = -(-5)^2 +10(-5) -6

f(-5) = -25 -50 -6

f(-5) = -81

8 0

2 years ago

Problem 5 <br><br><br> Please help

Anon25 [30]

90 degrees that’s the answer for this question

4 0

3 years ago