All categories

3 years ago

Does any two square prime number have to be even

Mathematics

1 answer:

NeTakaya3 years ago

6 0

There are no numbers that are both prime and square.
In addition, only one prime number is even, which is 2.

You might be interested in

A cylindrical can without a top is made to contain 25 3 cm of liquid. What are the dimensions of the can that will minimize the

Basile [38]

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= $\pi r^2h$

According to the problem,

$\pi r^2 h=25$

$\Rightarrow h=\frac{25}{\pi r^2}$

The surface area of the base of the can is = $\pi r^2$

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× $\pi r^2$ )

The lateral surface area of the can is = $2\pi rh$

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× $2\pi rh$ )

$=\$2.5 \pi r h$

Total cost of metal is C= 2.00 $\pi r^2$ + $2.5 \pi r h$

Putting $h=\frac{25}{\pi r^2}$

$\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}$

$\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}$

Differentiating with respect to r

$C'=4\pi r- \frac{62.5}{ r^2}$

Again differentiating with respect to r

$C''=4\pi + \frac{125}{ r^3}$

To find the minimize cost, we set C'=0

$4\pi r- \frac{62.5}{ r^2}=0$

$\Rightarrow 4\pi r=\frac{62.5}{ r^2}$

$\Rightarrow r^3=\frac{62.5}{ 4\pi}$

⇒r=1.71

Now,

$\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0$

When r=1.71 cm, the metal cost will be minimum.

Therefore,

$h=\frac{25}{\pi\times 1.71^2}$

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

6 0

3 years ago

20 POINTS HELP PLEASE: A diver descends to a location of -50 1/4 meters relative to the surface of the water. He then descends a

vlada-n [284]

Answer:

[14 1/2]

Step-by-step explanation:

4 0

4 years ago

PLEASE HELP ME I’m Stuck on this

raketka [301]

Answer:

Correct answer is option A.

Step-by-step explanation:

Please refer the attachment above

Hope it helps you.

6 0

3 years ago

Michael took in 91 mile bike trip. he left home at 7 AM. If he stopped for a total of two hours for rest and food and averaged 1

Korvikt [17]

Distance = rate * time
t = d / r

t = 91 / 14 = 6.5 hrs

plus 2 hour rest stop

8.5 hrs

start at 7 AM
end at 3:30 PM

5 0

3 years ago

Don opened a checking account. Let F represent the

Law Incorporation [45]

Answer:

B and E

Step-by-step explanation:

In the function f(m)= -50m+300

-50 is the gradient meaning it is the rate of change per month. This means that the rate of change is -50 since this is the coefficient of m.

Also, -50m must be negative since m represents a month and you cant have negative months, so you know that the amount of money is decreasing

6 0

3 years ago