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2 years ago

What is the domain of F(x) = 1/x ?

Mathematics

1 answer:

Elenna [48]2 years ago

6 0

Step-by-step explanation:

The domain is the possible x values of a function.

Since our function is a reciprocal function, our denominator can't equal 0. Note x=0, is a vertical asymptote.

So our domain is

All Reals except 0,

or (-oo,0) U (0, oo).

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The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3

Alekssandra [29.7K]

Answer:

$9\pi \text{ cubic meters per hour}$

Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

If $A= 36\pi\text{ square meters}, h = 3\text{ meters}$

$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

$\implies r^2 + 3r - 18=0$

$r^2 + 6r - 3r - 18 = 0$ ( by middle term splitting )

$r(r+6)-3(r+6)=0$

$(r-3)(r+6)=0$

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

$9\pi = (12\pi + 6\pi )\frac{dr}{dt}$

$9\pi = 18\pi \frac{dr}{dt}$

$\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}$

Now,

Volume of a cylinder,

$V=\pi r^2 h$

Differentiating w. r. t. t,

$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

6 0

3 years ago

HELP QUICK! 15 POINTS

almond37 [142]

it will be 8.25 hope this helped

6 0

3 years ago

You are selling lemonade for $1.50 a bag of kettle corn for $3 and a hotdog for $2.50 at a fair write and simplify an expression

Free_Kalibri [48]

P(1.50+3+2.50)=the amount of money you receive.

5 0

3 years ago

Read 2 more answers

The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall sem

Naily [24]

Answer: 1406

Step-by-step explanation:

Given Table :

Admissions Probability

1,040 0.3

1,320 0.2

1,660 0.5

Now, the expected number of admissions for the fall semester is given by :-

$E(x)=p_1x_1+p_2x_2+p_3x_3\\\\\Rightarrow\ E(x)=0.3\times1040+0.2\times1320+0.5\times1660\\\\\Rightarrow\ E(x)=1406$

Hence, the expected number of admissions for the fall semester = 1406

3 0

3 years ago

Find the greatest common factor of 20c^2 and 12w

irga5000 [103]

Answer:

60c

Step-by-step explanation:

12x6

10x6

hope i helped bud! ;)

3 0

3 years ago