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3 years ago

Write the next three integers in the pattern -4, -2, 0, 2

Mathematics

1 answer:

Oduvanchick [21]3 years ago

5 0

First one would be 4, then 6, then 8

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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

Joel is considering putting a $

olganol [36]

Answer: $53.84

Step-by-step explanation: 3500 divided buy 65

6 0

3 years ago

What is the factored form of the expression. (2n^2 + 5n + 3) (4n - 5)

7nadin3 [17]

So firstly, <u>the factor (4n - 5) cannot be further factored, so we will be focusing on 2n² + 5n + 3.</u>

So for this, we will be factoring by grouping. Firstly, what two terms have a product of 6n² and a sum of 5n? That would be 2n and 3n. Replace 5n with 2n + 3n:

$(2n^2 + 2n + 3n + 3)(4n - 5)$

Next, factor 2n² + 2n and 3n + 3 separately. Make sure that they have the same quantity on the inside of the parentheses:

$(2n(n+1)+3(n+1))(4n-5)$

Now we can rewrite this expression as<u> $(2n+3)(n+1)(4n-5)$ , which is your final answer.</u>

7 0

3 years ago

the larger room is twice as long as the smaller room. how long is the larger room. small room is 20 4/5 feet

masya89 [10]

Answer:

41 3/5 is the answer

8 0

2 years ago

Help me please with math

koban [17]

Answer:

2) y = x - 4

y = -x + 2

=> x - 4 = -x + 2

=> 2x = -6

=> x = -3

=> y = -3 - 4 = -7

3) y = 3x + 1

y = 5x - 3

=> 3x + 1 = 5x - 3

=> 2x = 4

=> x = 2

=> y = 3(2) + 1 = 7

4) 2x + y = 8 => y = -2x + 8

y = x - 7

=> -2x + 8 = x - 7

=> 3x = 15

=> x = 5

=> y = 5 - 7 = -2

7 0

2 years ago

Read 2 more answers