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Mars2501 [29]
3 years ago
13

I am thinking of a 3-digit number.

Mathematics
1 answer:
koban [17]3 years ago
7 0

Answer:

The answer is 939

Step-by-step explanation:

If you divide 939 by 9 it equals 104 R3.

If you divided 939 by 2 it equals 469 R1

And if you divide 939 by 5 it equals 187 R4

  Hope this helps!

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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

\displaystyle A=11.07\ ft^2

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

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
(3*10)*8=240*(10*8) what is the property
strojnjashka [21]

Answer:

2 + (3 + 4) = (2 + 3) + 4 ⇒2+7 = 5+4.

Step-by-step explanation:

5 0
3 years ago
Which part of the circle is labelled ? Thank you
Vilka [71]

Answer:

None of the following

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
5 × 4) × (16 ÷ 8) × (24 − 22) =
saw5 [17]

Answer:

80

Step-by-step explanation:

(5 * 4) = 20

(16 / 8) = 2

(24 - 22) = 2

20 * 2 * 2 = 80

7 0
3 years ago
Read 2 more answers
The area of a triangle is 18 square feet. If the base is 3 feet, what is the height of the triangle? no pic
Leya [2.2K]

Answer:

Im pretty sure the height of triangle would be 6

Step-by-step explanation:

5 0
3 years ago
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