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3 years ago

5(2x − 12) + 21 = 2x + 41 I know the answer is 10 but can someone explain how to get that?

Mathematics

2 answers:

inessss [21]3 years ago

7 0

X= 10.
use LCM to subtract fractions.
start with add/minus
then divide/times
then bracket

dsp733 years ago

6 0

$5(2x-12)+21=2x+41\\\\5\cdot2x-5\cdot12+21=2x+41\\\\10x-60+21=2x+41\\\\10x-39=2x+41\qquad|+39\\\\10x-39+39=2x+41+39\\\\10x=2x+80\qquad|-2x\\\\10x-2x=2x+80-2x\\\\8x=80\qquad|:8\\\\\boxed{x=10}$

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3 years ago

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Hello , how to do 6(iii)?

Doss [256]

Answer:

$\displaystyle \frac{dS}{dt}=\frac{3}{50r}$

Step-by-step explanation:

Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.

So, dV/dt = 0.03.

We want to show that dS/dt is directly proportional to 1/r.

In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.

First, the volume of a sphere V is given by:

$\displaystyle V=\frac{4}{3}\pi r^3$

Therefore:

$\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

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$\displaystyle S=4\pi r^2$

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$\displaystyle \frac{dS}{dt}=8\pi r\frac{dr}{dt}$

We can divide both sides by 2:

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$\displaystyle \frac{dV}{dt}=r\Big(4\pi r\frac{dr}{dt}\Big)$

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$\displaystyle \frac{dS}{dt}=\frac{3}{50r}=\frac{3}{50}\Big(\frac{1}{r}\Big)$

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3 years ago

The cost, in dollars, of producing x yards of a certain fabric is C(x) = 1500 + 12x − 0.1x2 + 0.0005x3. (a) Find the marginal co

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Answer:

(a) The marginal cost function is 12 - 0.2x + 0.0015x^2

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C'(500) predicts the cost of producing the 500th yard of fabric.

The cost of manufacturing the 501st yard, C(501) = $287.6505.

C(501) is approximately the same as C'(500).

Step-by-step explanation:

(a) The marginal cost function is obtained by differentiating the cost function (C) with respect to the number of yards of fabric produced (x)

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C'(500) = $287 predicts that the cost of producing the 500th yard of fabric is $287.

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Answer:

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