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3 years ago

I dont get it, I have notes but still get confused can someone help me with the worksheet.

Mathematics

1 answer:

Nimfa-mama [501]3 years ago

5 0

Please answer I. Need examples. So. I can finish the. Homework

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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

A family built a house in a beach resort area. In 1990, the house was 430 ft from the water. With erosion, the house was 400 ft

neonofarm [45]

We develop an equation for the given situation by first writing the general equation for lines,

y = mx + b

Substituting to this given the values given above,

(1990) 430 = b

(2000) 400 = m(10) + 430

The value of m from the equation in 2000 is -3. Thus, the equation of that relates the variables is,

y = -3x + 430

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2 years ago

Please help can you answer this please

lesya [120]

Answer:

its either a or b but like im pretty sure its A

Step-by-step explanation:

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2 years ago

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tiny-mole [99]

the answer is x=100°

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3 years ago

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ddd [48]

all "atomic" or constituent statements are true

at least one "atomic" or constituent statement is true

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2 years ago