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2 years ago

List all prime numbers. between 10 and 20

Mathematics

2 answers:

Wewaii [24]2 years ago

6 0

Answer:

11, 13, 17, 19

Step-by-step explanation:

A) Find the prime #'s less than 30.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

2) See which #'s add and is less than 30 but, equal to 8.

17.

B) Find prime #'s between 30 & 60

31, 37, 41, 43, 47, 53, 59

2) See which #'s add and is add to 10.

37.

Leviafan [203]2 years ago

3 0

B it is between 30 and 60

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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

2 years ago

Can anyone help please

Akimi4 [234]

Answer: X = 27

Step-by-step explanation: If we observe very closely, we have two similar triangles in the diagram. The first one is ABC and the other triangle is EDC. Also take note that angle ACB in the first triangle is equal in measurement to angle ECD (45 degrees) in the other triangle, (Opposite angles).

Hence in triangle ECD, we have identified two angles so far which are angle 2x + 10 and angle 45. Same applies to triangle ABC, we already have two angles which are, 3x - 10 and 45.

However angle D in the second triangle is equal in measurement to angle B in the first triangle

(Alternate angles).

Hence we have a third angle in triangle ABC which is

Angle B = 2x + 10.

Therefore 3x - 10 + (2x + 10) + 45 = 180

(Sum of angles in a triangle)

3x - 10 + 2x + 10 + 45 = 180

By collecting like terms we now have

3x + 2x = 180 + 10 - 10 - 45

5x = 135

Divide both sides by 5,

x = 27

8 0

2 years ago

irakobra [83]

X = 42 - 19, so A - x = 23

7 0

3 years ago

Read 2 more answers

What expression is equivalent to the expression 2(6y-4)

Kobotan [32]

Answer:

12y-8

Step-by-step explanation:

If you distribute the 2 you will 12y-8

4 0

3 years ago

What is the solution to the linear equation?

patriot [66]

Equation: 2/5 + p = 4/5 + 3/5p

Simplify Both Sides:
p + 2/5 = 3/5p + 4/5

Subtract 3/5p from both sides:
p + 2/5 - 3/5p = 3/5p + 4/5 - 3/5p

2/5p + 2/5 = 4/5

Subtract 2/5 from both sides:
2/5p + 2/5 - 2/5 = 4/5 - 2/5

2/5p = 2/5

Multiply both sides by 5/2

(5/2) * (2/5p) = (5/2) * (2/5)

p = 1

Answer: p = 1

Hope that helps!!! (Answer: Letter Choice (A), p = 1

8 0

2 years ago