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3 years ago

Simplify. 57r−27r this problem

Mathematics

2 answers:

Rashid [163]3 years ago

7 0

Answer:

$\boxed{=30r}$

$\boxed{r=30}$

Step-by-step explanation:

Distributive property: ⇒ $a(b+c)=a(b)+a(c)$

First you had to add 57 from both sides of an equation form.

$57r+57-27+57$

$57+-27=30$

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

Leno4ka [110]3 years ago

5 0

The answer should be 30r

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Find an nth-degree polynomial function n= 3; - 2 and 6 + 2 i are zeros; f(-1)= 53

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Find an nth-degree polynomial function.

Step-by-step explanation:

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3 years ago

3.2 cm on the map correspond to 4 km in the actual distance?

geniusboy [140]

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Step-by-step explanation:

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4 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

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Step-by-step explanation:

Optimizing With Derivatives

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

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

Equating it to 4

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

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

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

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

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

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago

The graph of a line passes through the points (0, 5) and (-10, 0). What is the equation of the line?

natta225 [31]

First find the slope:
y-y/x-x
5-0/0-(-10
5/+10
slope: 1/2
then use:
y-5. 1
--- = ---
x-0. 2
cross multiply.
2 (y-5)=1 (x-0)
2y-10=x
move the ten to the other side, switch the sign
2y=x+10
divide by 2
y=1/2x+5
final answer is
y=1/2x+5

5 0

3 years ago

Read 2 more answers

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AfilCa [17]

Answer:

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