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1 year ago

Select all numbers that are prime. 10 16 20 25 23

Mathematics

2 answers:

ira [324]1 year ago

7 0

Answer:

23 is the only prime number.

Step-by-step explanation: A prime number can only be divided by 1 and itself, while composite can be divided by more then 2 numbers.

creativ13 [48]1 year ago

3 0

Answer:

Only 23

Step-by-step explanation:

Prime numbers are numbers that cant be divided evenly

10 can be 5 and 2

16 can be 4 and 4

20 can be 4 and 5

25 can be 5 and 5

but there is even number for 23

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For what values of θ on the polar curve r=θ, with 0≤θ≤2π , are the tangent lines horizontal? Vertical?

Bond [772]

Given that $r=\theta$ , then $r'=1$

The slope of a tangent line in the polar coordinate is given by:

$m= \frac{r'\sin\theta+r\cos\theta}{r'\cos\theta-r\sin\theta}$

Thus, we have:

$m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}$

Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

$\sin\theta+\theta\cos\theta=0 \\ \\ \theta\cos\theta=-\sin\theta \\ \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta$

Therefore, the values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

θ = 0

θ = 2.02875783811043

θ = 4.91318043943488

Part B:

For vertical tangent lines, $\frac{1}{m} =0$

Thus, we have:

$\cos\theta-\theta\sin\theta=0 \\ \\ \Rightarrow\theta\sin\theta=\cos\theta \\ \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta$

Therefore, the values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:

θ = 4.91718592528713

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2 years ago

A quickie. If n identical dice are rolled, number of possible outcomes are?

nata0808 [166]

In rolling one die, there are 6 possible outcomes because each die has 4 faces. The number of outcomes when rolling n dice is equal to 6^n. By this, the number of outcomes when 2 dice are rolled is 36, 216 for 3 dice, and so on.

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2 years ago

How do you prove a rectangle in geometry?

dedylja [7]

- The opposite sides are parallel and congruent. - The diagonals bisect each other.

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2 years ago

What is the answer for this math problem 6x>12

k0ka [10]

Answer:

The correct answer is: " x > 2 " .

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Step-by-step explanation:

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Given the inequality:

" 6x > 12 " ;

Solve in terms of "x" :

______________________________________________________

Divide each side of the inequality by "6" ;

to isolate "x" on one side of the inequation; & to solve in terms of "x" ;

→ " 6x / 6 > 12 / 6 " ;

to get:

→ " x > 2 " .

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Hope this is helpful to you.

Best wishes to you in your academic pursuits

— and within the "Brainly" community!

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