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3 years ago

11

A candle is 6 in tall after burning for 1 hour. After 3 hours it is 5 1/2 in tall. Write a linear equation to model the height y

of the candle after burning x hours. When does the candle burn out?

1 answer:

wel3 years ago

4 0

6-x=y it will take 22 hours

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Paulina has read 58 pages of the 234-page book she is doing a book report on for Language Arts. She plans to finish her book by

goldfiish [28.3K]

The answer is d) 25d + 58= 234

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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

$Height = 12cm$

$Radius = 6cm$

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3 years ago

Solve the proportion X-16/x+6 = 3/5

BartSMP [9]

Answer:

x = 49

Step-by-step explanation:

Given

$\frac{x-16}{x+6}$ = $\frac{3}{5}$ ( cross- multiply )

5(x - 16) = 3(x + 6) ← distribute parenthesis on both sides

5x - 80 = 3x + 18 ( subtract 3x from both sides )

2x - 80 = 18 ( add 80 to both sides )

2x = 98 ( divide both sides by 2 )

x = 49

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2 years ago

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Hii! please help i’ll give brainliest

sergey [27]

The answer is the second one! He followed the customs himself :)

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