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3 years ago

It's been a while since I've taken a math class and I'm stressed please help me out. The question is circled.

Mathematics

2 answers:

brilliants [131]3 years ago

8 0

-3/2x

The rational expression would not be defined only when the denominator is divided by 0

That is:

2x =0

x = 0/2

x =0

Hence it would not be defined when x = 0.

Hope this helps.

emmainna [20.7K]3 years ago

3 0

Where it is not defined is where the denomenator is equal to 0 because division by 0 is not allowed

2x=denomenator
find the value of x wher
2x=0
x=0

the restricted value is 0

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You have been asked to design a can shaped like right circular cylinder that can hold a volume of 432π-cm3. What dimensions of t

rosijanka [135]

Answer:

$Height = 12cm$

$Radius = 6cm$

Step-by-step explanation:

Given

Represent volume with v, height with h and radius with r

$V = 432\pi$

Required

Determine the values of h and r that uses the least amount of material

Volume is calculated as:

$V = \pi r^2h\\$

Substitute 432π for V

$432\pi = \pi r^2h$

Divide through by π

$432 = r^2h$

Make h the subject:

$h = \frac{432}{r^2}$

Surface Area (A) of a cylinder is calculated as thus:

$A=2\pi rh+2\pi r^2$

Substitute $\frac{432}{r^2}$ for h in $A=2\pi rh+2\pi r^2$

$A=2\pi r(\frac{432}{r^2})+2\pi r^2$

$A=2\pi (\frac{432}{r})+2\pi r^2$

Factorize:

$A=2\pi (\frac{432}{r} + r^2)$

To minimize, we have to differentiate both sides and set $A' = 0$

$A'=2\pi (-\frac{432}{r^2} + 2r)$

Set $A' = 0$

$0=2\pi (-\frac{432}{r^2} + 2r)$

Divide through by $2\pi$

$0= -\frac{432}{r^2} + 2r$

$\frac{432}{r^2} = 2r$

Cross Multiply

$2r * r^2 = 432$

$2r^3 = 432$

Divide through by 2

$r^3 = 216$

Take cube roots of both sides

$r = \sqrt[3]{216}$

$r = 6$

Recall that:

$h = \frac{432}{r^2}$

$h = \frac{432}{6^2}$

$h = \frac{432}{36}$

$h = 12$

Hence, the dimension that requires the least amount of material is when

$Height = 12cm$

$Radius = 6cm$

3 0

3 years ago

45.3297 rounded to the nearest tenth would be?

Alex

45.3297 rounded to the nearest tenth is 45.3
3 is in the tenths place, so you look at the number to the right of it. If that number is 5 or more, you round up. If the number is 4 or less, you round down. So you round 45.3297 down to 45.3

5 0

3 years ago

If f(x) = 10 + 50x, solve for x when f(x) = 310.

weqwewe [10]

x = 6

given f(x) = 310, we obtain the equation

10 + 50x = 310 ( subtract 10 from both sides )

50x = 300 ( divide both sides by 50 )

x = $\frac{300}{50}$ = 6