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2 years ago

How do you do algebra

Mathematics

1 answer:

grin007 [14]2 years ago

4 0

Its not that hard... whats the question

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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

2 years ago

Find the mode of this set of data 18,27,28,44,44,50,67

8_murik_8 [283]

Answer:

Step-by-step explanation:

the mode of a set of data is the value that occurs most often, in this case it is 44

8 0

2 years ago

Read 2 more answers

What shape is produced when slicing a right rectangular pyramid perpendicular to the base?

matrenka [14]

C. triangle.
Pyramids are triangles to begin with you’re just making a smaller one

6 0

2 years ago

Given that X ~ N(120, 35). We survey samples of 25 and are interested in the distribution of X-bar. Find the z-score associated

lubasha [3.4K]

Answer:

Option c -2.8571

Step-by-step explanation:

z-score are calculated as

$z=\frac{xbar-mean}{\frac{S.D}{\sqrt{n} } }$ .

We are given that mean=120 and standard deviation=S.D=35 as X~N(120,35).

Sample size=n=25.

We have to find z-score for x-bar=100. So,

z-score=[100-120]/[35/√25]

z-score=[-20]/[35/5]

z-score=-20/7

z-score=-2.8571.

Thus, the z-score associated with x-bar = 100 is -2.8571.

8 0

2 years ago

A clothing store donated a percent of every sale to hospitals. The total sales were $7,750 so the

Flauer [41]

Answer:

Step-by-step explanation:

310 /7759 x 100% = 4%

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2 years ago