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3 years ago

What is the solution to 5a-15+9a=3a+29

Mathematics

2 answers:

mart [117]3 years ago

5 0

Combine like terms:

5a + 9a - 15 = 3a + 29

14a - 15 = 3a + 29

Subtract 3 from both sides and add 15 to both sides to get constants on one side of the equal side and variables on the other.

14a - 3a = 29 + 15

Combine like terms again:

11a = 44

Divide by 11 on both sides to isolate the variable:

a = 44/11

a = 4

pogonyaev3 years ago

3 0

5a-15+9a=3a+29

We simplify the equation to the form, which is simple to understand

5a-15+9a=3a+29

We move all terms containing a to the left and all other terms to the right.

+5a+9a-3a=+29+15

We simplify left and right side of the equation.

+11a=+44

We divide both sides of the equation by 11 to get a.

a=4

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Basile [38]

Answer:

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Step-by-step explanation:

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Total cost of metal is C= 2.00 $\pi r^2$ + $2.5 \pi r h$

Putting $h=\frac{25}{\pi r^2}$

$\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}$

$\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}$

Differentiating with respect to r

$C'=4\pi r- \frac{62.5}{ r^2}$

Again differentiating with respect to r

$C''=4\pi + \frac{125}{ r^3}$

To find the minimize cost, we set C'=0

$4\pi r- \frac{62.5}{ r^2}=0$

$\Rightarrow 4\pi r=\frac{62.5}{ r^2}$

$\Rightarrow r^3=\frac{62.5}{ 4\pi}$

⇒r=1.71

Now,

$\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0$

When r=1.71 cm, the metal cost will be minimum.

Therefore,

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⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

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