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3 years ago

How many solutions does the equation have? 4(2x+3) =2(3x-4 open study?

Mathematics

1 answer:

scZoUnD [109]3 years ago

7 0

4(2x + 3) = 2(3x - 4)

8x + 24 = 6x - 8

2x + 24 = -8

2x = -32

x = -16

Answer: ONE solution <em>x = -16</em>

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The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6

Arlecino [84]

Answer:

$\approx \bold{6544\ in^3/sec}$

Step-by-step explanation:

Given:

Rate of change of radius of cylinder:

$\dfrac{dr}{dt} = +7\ in/sec$

(This is increasing rate so positive)

Rate of change of height of cylinder:

$\dfrac{dh}{dt} = -6\ in/sec$

(This is decreasing rate so negative)

To find:

Rate of change of volume when r = 20 inches and h = 16 inches.

Solution:

First of all, let us have a look at the formula for Volume:

$V = \pi r^2h$

Differentiating it w.r.to 't':

$\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)$

Let us have a look at the formula:

$1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))$

$3.\ \dfrac{dx^n}{dx} = nx^{n-1}$

Applying the two formula for the above differentiation:

$\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}$

Now, putting the values:

$\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}$

So, the answer is: $\approx \bold{6544\ in^3/sec}$

3 0

3 years ago

Peace out guys. im done for the night. take some free points

iren2701 [21]

Answer:

YAAAAAY TY!!!!!!!!!

Step-by-step explanation:

6 0

3 years ago

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When a warehouse opened, it had an inventory of 6,000 items. Every month, the inventory increases by 3,000 items.

ehidna [41]

Answer:

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3 years ago

Explain how to write and solve an equation to find an unknown side length of a rectangle when given the perimeter

ratelena [41]

P=2(L+W)
if given one side and the perimiter
(P/2)-L=W
(P/2)-W=L

4 0

3 years ago

The table shows the distance Randy drove on one day of her vacation

horsena [70]

Given the table showing the distance Randy drove on one day of her vacation as follows:

$\begin{tabular}
{|c|c|c|c|c|c|}
Time (h)&1&2&3&4&5\\[1ex]
Distance (mi)&55&110&165&220&275
\end{tabular}$

The rate at which she travels is given by

$rate= \frac{distance}{time} \\ \\ = \frac{55}{1} =55mi/h$

If Randy has driven for one more hour at the same rate, the number of hours she must have droven is 6 hrs and the total distance is given by

distance = 55 x 6 = 330 miles.

4 0

3 years ago