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3 years ago

Write an algebraic expression for 8 less than 4 times a number

Mathematics

1 answer:

Flura [38]3 years ago

4 0

Answer:

8<4*X

Step-by-step explanation:

8 less than is 8< the 4 times 4* a number so a variable, X

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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

The domain is the set of all values a function will accept as _____.

Marina86 [1]

Answer:

... inputs.

Step-by-step explanation:

A function is a map of inputs to outputs. The domain of a function is the set of <em>inputs</em> for which outputs are defined.

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3 years ago

The width of a rectangle is half as long as the

Dmitrij [34]

Length=20ft
width=10ft

4 0

3 years ago

Read 2 more answers

What are the solutions of the equation?

Maksim231197 [3]

Answer:

x₁ = √15

x₂ = - √15

Step-by-step explanation:

x² - 15 = 0

x² = 15

x = ±√15

x₁ = √15

x₂ = - √15

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4 years ago

24. A metal coin is located at (18, 10). How much closer or farther from Ann is the coin than the jewelry?

Vinvika [58]

Answer:

10.5

Step-by-step explanation:

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