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3 years ago

6

2x + 3 + 4x + 8 = 3x - 10

1 answer:

vodomira [7]3 years ago

8 0

$\text {Hello! Let's solve this Equation!}$

$\text {Your First Step is to Simplify the Equation:}$

$\text {(2x+4x)+(8+3)}$

$\text {6x+11=3x-10}$

$\text {The Next Step is to Subtract 3x:}$

$\text {6x+11-3x=3x-10-3x}\\\text {3x+11=-10}$

$\text {Next Step is to Subtract 11:}$

$\text {Q: Why Subtract 11?}$

$\text {A: So they cancel out. We cross them out once we subtract.}$

$\text {3x+11-11=-10-11}\\\text {3x=-21}$

$\text {The Final Step is to Divide 3:}$

$\text {3x/3=-21/3}$

$\text {Your Answer will be}$

$\fbox {x=-7}$

$\text {Best of Luck!}$

$\text {-LimitedX}$

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Xelga [282]

Answer:

30(x+1)/(x+7)

Step-by-step explanation:

This is not a rational expression because denominator has a domain of which it can be undefined.

To rationalize multiply by the reciprocal of the denominator (1/6+1/x+1)

___<u>5___ </u>*(6)(x+1) --> _____<u>30(x+1)_____</u> --><u> 30x+1</u>_ --> <u>30x+1</u>

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3 years ago

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